text:
using Rubin
using Tests
using Elliptic
using HypergeometricFunctions
using Polylogarithms
using SpecialFunctions

@test integrate(sec(c+d*x)^3*(A+C*sec(c+d*x)^2)*(a+a*sec(c+d*x)), x) == :(1//5*a*d^-1*(4C+5A)*tan(c+d*x)+1//8*a*d^-1*(3C+4A)*arctanh(sin(c+d*x))+1//15*a*d^-1*tan(c+d*x)^3*(4C+5A)+1//4*C*a*d^-1*sec(c+d*x)^3*tan(c+d*x)+1//5*C*a*d^-1*sec(c+d*x)^4*tan(c+d*x)+1//8*a*d^-1*(3C+4A)*sec(c+d*x)*tan(c+d*x))
@test integrate(sec(c+d*x)^2*(A+C*sec(c+d*x)^2)*(a+a*sec(c+d*x)), x) == :(1//3*a*d^-1*(2C+3A)*tan(c+d*x)+1//8*a*d^-1*(3C+4A)*arctanh(sin(c+d*x))+1//3*C*a*d^-1*sec(c+d*x)^2*tan(c+d*x)+1//4*C*a*d^-1*sec(c+d*x)^3*tan(c+d*x)+1//8*a*d^-1*(3C+4A)*sec(c+d*x)*tan(c+d*x))
@test integrate((A+C*sec(c+d*x)^2)*(a+a*sec(c+d*x))*sec(c+d*x), x) == :((1/2)*a*d^-1*(C+2A)*arctanh(sin(c+d*x))+1//3*a*d^-1*(2C+3A)*tan(c+d*x)+(1/2)*C*a*d^-1*sec(c+d*x)*tan(c+d*x)+1//3*C*a*d^-1*sec(c+d*x)^2*tan(c+d*x))
@test integrate((A+C*sec(c+d*x)^2)*(a+a*sec(c+d*x)), x) == :(A*a*x+C*a*d^-1*tan(c+d*x)+(1/2)*a*d^-1*(C+2A)*arctanh(sin(c+d*x))+(1/2)*C*a*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((A+C*sec(c+d*x)^2)*(a+a*sec(c+d*x))*cos(c+d*x), x) == :(A*a*x+A*a*d^-1*sin(c+d*x)+C*a*d^-1*arctanh(sin(c+d*x))+C*a*d^-1*tan(c+d*x))
@test integrate(cos(c+d*x)^2*(A+C*sec(c+d*x)^2)*(a+a*sec(c+d*x)), x) == :((1/2)*a*x*(A+2C)+A*a*d^-1*sin(c+d*x)+C*a*d^-1*arctanh(sin(c+d*x))+(1/2)*A*a*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^3*(A+C*sec(c+d*x)^2)*(a+a*sec(c+d*x)), x) == :((1/2)*a*x*(A+2C)+1//3*a*d^-1*(2A+3C)*sin(c+d*x)+(1/2)*A*a*d^-1*cos(c+d*x)*sin(c+d*x)+1//3*A*a*d^-1*cos(c+d*x)^2*sin(c+d*x))
@test integrate(cos(c+d*x)^4*(A+C*sec(c+d*x)^2)*(a+a*sec(c+d*x)), x) == :(1//8*a*x*(3A+4C)+a*d^-1*(A+C)*sin(c+d*x)+-1//3*A*a*d^-1*sin(c+d*x)^3+1//4*A*a*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//8*a*d^-1*(3A+4C)*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^5*(A+C*sec(c+d*x)^2)*(a+a*sec(c+d*x)), x) == :(1//8*a*x*(3A+4C)+-1//15*a*d^-1*sin(c+d*x)^3*(4A+5C)+1//5*a*d^-1*(4A+5C)*sin(c+d*x)+1//4*A*a*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//5*A*a*d^-1*cos(c+d*x)^4*sin(c+d*x)+1//8*a*d^-1*(3A+4C)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(1//3*a^2*d^-1*(3C+4A)*tan(c+d*x)+1//4*a^2*d^-1*(3C+4A)*arctanh(sin(c+d*x))+1//30*d^-1*(a+a*sec(c+d*x))^2*(3C+10A)*tan(c+d*x)+1//5*C*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^2*tan(c+d*x)+1//10*C*a^-1*d^-1*(a+a*sec(c+d*x))^3*tan(c+d*x)+1//12*a^2*d^-1*(3C+4A)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*(A+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(-1//12*C*d^-1*(a+a*sec(c+d*x))^2*tan(c+d*x)+1//6*a^2*d^-1*(7C+12A)*tan(c+d*x)+1//8*a^2*d^-1*(7C+12A)*arctanh(sin(c+d*x))+1//4*C*a^-1*d^-1*(a+a*sec(c+d*x))^3*tan(c+d*x)+1//24*a^2*d^-1*(7C+12A)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*(A+C*sec(c+d*x)^2), x) == :(A*x*a^2+a^2*d^-1*(A+C)*tan(c+d*x)+a^2*d^-1*(C+2A)*arctanh(sin(c+d*x))+1//3*C*d^-1*(a+a*sec(c+d*x))^2*tan(c+d*x)+1//3*C*d^-1*(a^2+a^2*sec(c+d*x))*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*(A+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(2*A*x*a^2+A*d^-1*(a+a*sec(c+d*x))^2*sin(c+d*x)+(1/2)*a^2*d^-1*(2A+3C)*arctanh(sin(c+d*x))+-1//2*a^2*d^-1*(-3C+2A)*tan(c+d*x)+-1//2*d^-1*(a^2+a^2*sec(c+d*x))*(-1C+2A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :((1/2)*x*a^2*(2C+3A)+(1/2)*a^2*d^-1*(-2C+3A)*sin(c+d*x)+2*C*a^2*d^-1*arctanh(sin(c+d*x))+-1//2*d^-1*(A+-2C)*(a^2+a^2*sec(c+d*x))*sin(c+d*x)+(1/2)*A*d^-1*(a+a*sec(c+d*x))^2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(x*a^2*(A+2C)+C*a^2*d^-1*arctanh(sin(c+d*x))+a^2*d^-1*(A+C)*sin(c+d*x)+1//3*A*d^-1*(a+a*sec(c+d*x))^2*cos(c+d*x)^2*sin(c+d*x)+1//3*A*d^-1*(a^2+a^2*sec(c+d*x))*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^4*(A+C*sec(c+d*x)^2), x) == :(1//8*x*a^2*(7A+12C)+1//6*a^2*d^-1*(7A+12C)*sin(c+d*x)+1//4*A*d^-1*(a+a*sec(c+d*x))^2*cos(c+d*x)^3*sin(c+d*x)+1//6*A*d^-1*(a+a*sec(c+d*x))^2*cos(c+d*x)^2*sin(c+d*x)+1//24*a^2*d^-1*(7A+12C)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^5*(A+C*sec(c+d*x)^2), x) == :(1//4*x*a^2*(3A+4C)+1//15*a^2*d^-1*(18A+25C)*sin(c+d*x)+1//4*a^2*d^-1*(3A+4C)*cos(c+d*x)*sin(c+d*x)+1//5*A*d^-1*(a+a*sec(c+d*x))^2*cos(c+d*x)^4*sin(c+d*x)+1//10*A*d^-1*cos(c+d*x)^3*(a^2+a^2*sec(c+d*x))*sin(c+d*x)+1//30*a^2*d^-1*cos(c+d*x)^2*(9A+10C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^6*(A+C*sec(c+d*x)^2), x) == :(1//16*x*a^2*(11A+14C)+-2//15*a^2*d^-1*sin(c+d*x)^3*(4A+5C)+2//5*a^2*d^-1*(4A+5C)*sin(c+d*x)+1//6*A*d^-1*(a+a*sec(c+d*x))^2*cos(c+d*x)^5*sin(c+d*x)+1//15*A*d^-1*cos(c+d*x)^4*(a^2+a^2*sec(c+d*x))*sin(c+d*x)+1//16*a^2*d^-1*(11A+14C)*cos(c+d*x)*sin(c+d*x)+1//40*a^2*d^-1*cos(c+d*x)^3*(9A+10C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(1//10*a^3*d^-1*(23C+30A)*tan(c+d*x)+1//16*a^3*d^-1*(23C+30A)*arctanh(sin(c+d*x))+1//120*a^3*d^-1*tan(c+d*x)^3*(23C+30A)+1//120*d^-1*(a+a*sec(c+d*x))^3*(7C+30A)*tan(c+d*x)+1//6*C*d^-1*(a+a*sec(c+d*x))^3*sec(c+d*x)^2*tan(c+d*x)+1//10*C*a^-1*d^-1*(a+a*sec(c+d*x))^4*tan(c+d*x)+3//80*a^3*d^-1*(23C+30A)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*(A+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(-1//20*C*d^-1*(a+a*sec(c+d*x))^3*tan(c+d*x)+1//5*a^3*d^-1*(13C+20A)*tan(c+d*x)+1//8*a^3*d^-1*(13C+20A)*arctanh(sin(c+d*x))+1//60*a^3*d^-1*tan(c+d*x)^3*(13C+20A)+1//5*C*a^-1*d^-1*(a+a*sec(c+d*x))^4*tan(c+d*x)+3//40*a^3*d^-1*(13C+20A)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*(A+C*sec(c+d*x)^2), x) == :(A*x*a^3+1//4*C*d^-1*(a+a*sec(c+d*x))^3*tan(c+d*x)+1//8*a^3*d^-1*(15C+28A)*arctanh(sin(c+d*x))+1//8*d^-1*(a^3+a^3*sec(c+d*x))*(4A+5C)*tan(c+d*x)+5//8*a^3*d^-1*(3C+4A)*tan(c+d*x)+1//4*C*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*(A+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(3*A*x*a^3+A*d^-1*(a+a*sec(c+d*x))^3*sin(c+d*x)+(1/2)*a^3*d^-1*(5C+6A)*arctanh(sin(c+d*x))+-1//6*d^-1*(a^3+a^3*sec(c+d*x))*(-5C+6A)*tan(c+d*x)+5//2*C*a^3*d^-1*tan(c+d*x)+-1//3*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*(-1C+3A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :((1/2)*x*a^3*(2C+7A)+(1/2)*a^3*d^-1*(2A+7C)*arctanh(sin(c+d*x))+-1//2*d^-1*(A+-4C)*(a^3+a^3*sec(c+d*x))*sin(c+d*x)+5//2*a^3*d^-1*(A+-1C)*sin(c+d*x)+(1/2)*A*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)*sin(c+d*x)+-1//2*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*(A+-1C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :((1/2)*x*a^3*(5A+6C)+3*C*a^3*d^-1*arctanh(sin(c+d*x))+-1//6*d^-1*(a^3+a^3*sec(c+d*x))*(-6C+5A)*sin(c+d*x)+5//2*A*a^3*d^-1*sin(c+d*x)+1//3*A*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)^2*sin(c+d*x)+(1/2)*A*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^4*(A+C*sec(c+d*x)^2), x) == :(1//8*x*a^3*(15A+28C)+C*a^3*d^-1*arctanh(sin(c+d*x))+5//8*a^3*d^-1*(3A+4C)*sin(c+d*x)+1//4*A*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)^3*sin(c+d*x)+1//8*d^-1*(a^3+a^3*sec(c+d*x))*(4C+5A)*cos(c+d*x)*sin(c+d*x)+1//4*A*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^5*(A+C*sec(c+d*x)^2), x) == :(1//8*x*a^3*(13A+20C)+-1//60*a^3*d^-1*sin(c+d*x)^3*(13A+20C)+1//5*a^3*d^-1*(13A+20C)*sin(c+d*x)+1//5*A*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)^4*sin(c+d*x)+3//20*A*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)^3*sin(c+d*x)+3//40*a^3*d^-1*(13A+20C)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^6*(A+C*sec(c+d*x)^2), x) == :(1//16*x*a^3*(23A+30C)+1//15*a^3*d^-1*(34A+45C)*sin(c+d*x)+1//6*A*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)^5*sin(c+d*x)+1//16*a^3*d^-1*(23A+30C)*cos(c+d*x)*sin(c+d*x)+1//120*a^3*d^-1*cos(c+d*x)^2*(73A+90C)*sin(c+d*x)+1//120*d^-1*cos(c+d*x)^3*(a^3+a^3*sec(c+d*x))*(30C+31A)*sin(c+d*x)+1//10*A*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*cos(c+d*x)^4*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(1//4*a^4*d^-1*(11C+14A)*arctanh(sin(c+d*x))+1//105*d^-1*(a+a*sec(c+d*x))^4*(4C+21A)*tan(c+d*x)+8//105*a^4*d^-1*tan(c+d*x)^3*(11C+14A)+16//35*a^4*d^-1*(11C+14A)*tan(c+d*x)+1//7*C*d^-1*(a+a*sec(c+d*x))^4*sec(c+d*x)^2*tan(c+d*x)+1//70*a^4*d^-1*sec(c+d*x)^3*(11C+14A)*tan(c+d*x)+2//21*C*a^-1*d^-1*(a+a*sec(c+d*x))^5*tan(c+d*x)+27//140*a^4*d^-1*(11C+14A)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*(A+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(-1//30*C*d^-1*(a+a*sec(c+d*x))^4*tan(c+d*x)+2//15*a^4*d^-1*tan(c+d*x)^3*(7C+10A)+4//5*a^4*d^-1*(7C+10A)*tan(c+d*x)+7//16*a^4*d^-1*(7C+10A)*arctanh(sin(c+d*x))+1//6*C*a^-1*d^-1*(a+a*sec(c+d*x))^5*tan(c+d*x)+1//40*a^4*d^-1*sec(c+d*x)^3*(7C+10A)*tan(c+d*x)+27//80*a^4*d^-1*(7C+10A)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*(A+C*sec(c+d*x)^2), x) == :(A*x*a^4+(1/2)*a^4*d^-1*(7C+10A)*tan(c+d*x)+(1/2)*a^4*d^-1*(7C+12A)*arctanh(sin(c+d*x))+1//5*C*d^-1*(a+a*sec(c+d*x))^4*tan(c+d*x)+1//6*d^-1*(a^4+a^4*sec(c+d*x))*(7C+8A)*tan(c+d*x)+1//15*d^-1*(a^2+a^2*sec(c+d*x))^2*(5A+7C)*tan(c+d*x)+1//5*C*a*d^-1*(a+a*sec(c+d*x))^3*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*(A+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(4*A*x*a^4+A*d^-1*(a+a*sec(c+d*x))^4*sin(c+d*x)+-1//12*d^-1*(a^2+a^2*sec(c+d*x))^2*(-7C+12A)*tan(c+d*x)+-1//24*d^-1*(a^4+a^4*sec(c+d*x))*(-35C+12A)*tan(c+d*x)+1//8*a^4*d^-1*(35C+52A)*arctanh(sin(c+d*x))+5//8*a^4*d^-1*(4A+7C)*tan(c+d*x)+-1//4*a*d^-1*(a+a*sec(c+d*x))^3*(-1C+4A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :((1/2)*x*a^4*(2C+13A)+2*a^4*d^-1*(2A+3C)*arctanh(sin(c+d*x))+-1//2*d^-1*(a^2+a^2*sec(c+d*x))^2*(A+-2C)*sin(c+d*x)+1//6*d^-1*(a^4+a^4*sec(c+d*x))*(3A+22C)*sin(c+d*x)+5//2*a^4*d^-1*(A+-2C)*sin(c+d*x)+(1/2)*A*d^-1*(a+a*sec(c+d*x))^4*cos(c+d*x)*sin(c+d*x)+-1//6*a*d^-1*(a+a*sec(c+d*x))^3*(-2C+3A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(2*x*a^4*(2C+3A)+(1/2)*a^4*d^-1*(2A+13C)*arctanh(sin(c+d*x))+-1//2*d^-1*(a^2+a^2*sec(c+d*x))^2*(-1C+2A)*sin(c+d*x)+-1//3*d^-1*(a^4+a^4*sec(c+d*x))*(-9C+4A)*sin(c+d*x)+5//2*a^4*d^-1*(-1C+2A)*sin(c+d*x)+1//3*A*d^-1*(a+a*sec(c+d*x))^4*cos(c+d*x)^2*sin(c+d*x)+2//3*A*a*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^4*(A+C*sec(c+d*x)^2), x) == :(1//8*x*a^4*(35A+52C)+4*C*a^4*d^-1*arctanh(sin(c+d*x))+-1//24*d^-1*(a^4+a^4*sec(c+d*x))*(-12C+35A)*sin(c+d*x)+5//8*a^4*d^-1*(4C+7A)*sin(c+d*x)+1//4*A*d^-1*(a+a*sec(c+d*x))^4*cos(c+d*x)^3*sin(c+d*x)+1//8*d^-1*(a^2+a^2*sec(c+d*x))^2*(4C+7A)*cos(c+d*x)*sin(c+d*x)+1//3*A*a*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^5*(A+C*sec(c+d*x)^2), x) == :((1/2)*x*a^4*(7A+12C)+C*a^4*d^-1*arctanh(sin(c+d*x))+(1/2)*a^4*d^-1*(7A+10C)*sin(c+d*x)+1//5*A*d^-1*(a+a*sec(c+d*x))^4*cos(c+d*x)^4*sin(c+d*x)+1//6*d^-1*(a^4+a^4*sec(c+d*x))*(7A+8C)*cos(c+d*x)*sin(c+d*x)+1//15*d^-1*(a^2+a^2*sec(c+d*x))^2*cos(c+d*x)^2*(5C+7A)*sin(c+d*x)+1//5*A*a*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^6*(A+C*sec(c+d*x)^2), x) == :(7//16*x*a^4*(7A+10C)+-2//15*a^4*d^-1*sin(c+d*x)^3*(7A+10C)+4//5*a^4*d^-1*(7A+10C)*sin(c+d*x)+1//6*A*d^-1*(a+a*sec(c+d*x))^4*cos(c+d*x)^5*sin(c+d*x)+1//40*a^4*d^-1*cos(c+d*x)^3*(7A+10C)*sin(c+d*x)+2//15*A*d^-1*(a+a*sec(c+d*x))^4*cos(c+d*x)^4*sin(c+d*x)+27//80*a^4*d^-1*(7A+10C)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^7*(A+C*sec(c+d*x)^2), x) == :(1//4*x*a^4*(11A+14C)+1//105*a^4*d^-1*(454A+581C)*sin(c+d*x)+1//4*a^4*d^-1*(11A+14C)*cos(c+d*x)*sin(c+d*x)+1//7*A*d^-1*(a+a*sec(c+d*x))^4*cos(c+d*x)^6*sin(c+d*x)+1//35*d^-1*(a^2+a^2*sec(c+d*x))^2*cos(c+d*x)^4*(7C+8A)*sin(c+d*x)+1//210*a^4*d^-1*cos(c+d*x)^2*(247A+308C)*sin(c+d*x)+1//210*d^-1*cos(c+d*x)^3*(a^4+a^4*sec(c+d*x))*(109A+126C)*sin(c+d*x)+2//21*A*a*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)^5*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^4*(A+C*sec(c+d*x)^2), x) == :(-1*a^-1*d^-1*(3A+4C)*tan(c+d*x)+-1//3*a^-1*d^-1*tan(c+d*x)^3*(3A+4C)+1//8*a^-1*d^-1*(12A+15C)*arctanh(sin(c+d*x))+-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^4*(A+C)*tan(c+d*x)+1//4*a^-1*d^-1*sec(c+d*x)^3*(4A+5C)*tan(c+d*x)+1//8*a^-1*d^-1*(12A+15C)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(a^-1*d^-1*(3A+4C)*tan(c+d*x)+-1//2*a^-1*d^-1*(2A+3C)*arctanh(sin(c+d*x))+1//3*a^-1*d^-1*tan(c+d*x)^3*(3A+4C)+-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^3*(A+C)*tan(c+d*x)+-1//2*a^-1*d^-1*(2A+3C)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :((1/2)*a^-1*d^-1*(2A+3C)*arctanh(sin(c+d*x))+-1*a^-1*d^-1*(A+2C)*tan(c+d*x)+(1/2)*a^-1*d^-1*(2A+3C)*sec(c+d*x)*tan(c+d*x)+-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^2*(A+C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*(A+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(C*a^-1*d^-1*tan(c+d*x)+-1*C*a^-1*d^-1*arctanh(sin(c+d*x))+a^-1*d^-1*(1+sec(c+d*x))^-1*(A+C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*(A+C*sec(c+d*x)^2), x) == :(A*x*a^-1+C*a^-1*d^-1*arctanh(sin(c+d*x))+-1*a^-1*d^-1*(1+sec(c+d*x))^-1*(A+C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*(A+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(-1*A*x*a^-1+a^-1*d^-1*(C+2A)*sin(c+d*x)+-1*d^-1*(a+a*sec(c+d*x))^-1*(A+C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :((1/2)*x*a^-1*(2C+3A)+-1*a^-1*d^-1*(C+2A)*sin(c+d*x)+(1/2)*a^-1*d^-1*(2C+3A)*cos(c+d*x)*sin(c+d*x)+-1*d^-1*(a+a*sec(c+d*x))^-1*(A+C)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(-1//2*x*a^-1*(2C+3A)+a^-1*d^-1*(3C+4A)*sin(c+d*x)+-1//3*a^-1*d^-1*sin(c+d*x)^3*(3C+4A)+-1*d^-1*(a+a*sec(c+d*x))^-1*cos(c+d*x)^2*(A+C)*sin(c+d*x)+-1//2*a^-1*d^-1*(2C+3A)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^4*(A+C*sec(c+d*x)^2), x) == :(1//8*x*a^-1*(12C+15A)+-1*a^-1*d^-1*(3C+4A)*sin(c+d*x)+1//3*a^-1*d^-1*sin(c+d*x)^3*(3C+4A)+-1*d^-1*(a+a*sec(c+d*x))^-1*cos(c+d*x)^3*(A+C)*sin(c+d*x)+1//4*a^-1*d^-1*cos(c+d*x)^3*(4C+5A)*sin(c+d*x)+1//8*a^-1*d^-1*(12C+15A)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^4*(A+C*sec(c+d*x)^2), x) == :(a^-2*d^-1*(5A+12C)*tan(c+d*x)+-1*a^-2*d^-1*(2A+5C)*arctanh(sin(c+d*x))+1//3*a^-2*d^-1*tan(c+d*x)^3*(5A+12C)+-1*a^-2*d^-1*(2A+5C)*sec(c+d*x)*tan(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^4*(A+C)*tan(c+d*x)+-1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^3*(4A+10C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :((1/2)*a^-2*d^-1*(2A+7C)*arctanh(sin(c+d*x))+-1//3*a^-2*d^-1*(4A+16C)*tan(c+d*x)+(1/2)*a^-2*d^-1*(2A+7C)*sec(c+d*x)*tan(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^3*(A+C)*tan(c+d*x)+-1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^2*(2A+8C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(-2*C*a^-2*d^-1*arctanh(sin(c+d*x))+1//3*a^-2*d^-1*(A+4C)*tan(c+d*x)+2*C*a^-2*d^-1*(1+sec(c+d*x))^-1*tan(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^2*(A+C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*(A+C*sec(c+d*x)^2), x) == :(A*x*a^-2+-1//3*d^-1*(a+a*sec(c+d*x))^-2*(A+C)*tan(c+d*x)+-1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*(-2C+4A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*(A+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(-2*A*x*a^-2+-1//3*d^-1*(a+a*sec(c+d*x))^-2*(A+C)*sin(c+d*x)+1//3*a^-2*d^-1*(C+10A)*sin(c+d*x)+-2*A*a^-2*d^-1*(1+sec(c+d*x))^-1*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :((1/2)*x*a^-2*(2C+7A)+-1//3*a^-2*d^-1*(4C+16A)*sin(c+d*x)+(1/2)*a^-2*d^-1*(2C+7A)*cos(c+d*x)*sin(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*(A+C)*cos(c+d*x)*sin(c+d*x)+-1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*(2C+8A)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(-1*x*a^-2*(2C+5A)+a^-2*d^-1*(5C+12A)*sin(c+d*x)+-1//3*a^-2*d^-1*sin(c+d*x)^3*(5C+12A)+-1*a^-2*d^-1*(2C+5A)*cos(c+d*x)*sin(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)^2*(A+C)*sin(c+d*x)+-1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*cos(c+d*x)^2*(4C+10A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^4*(A+C*sec(c+d*x)^2), x) == :((1/2)*a^-3*d^-1*(2A+13C)*arctanh(sin(c+d*x))+-1//15*a^-3*d^-1*(22A+152C)*tan(c+d*x)+(1/2)*a^-3*d^-1*(2A+13C)*sec(c+d*x)*tan(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^4*(A+C)*tan(c+d*x)+-1//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^2*(11A+76C)*tan(c+d*x)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^3*(A+11C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(-3*C*a^-3*d^-1*arctanh(sin(c+d*x))+3*C*d^-1*(a^3+a^3*sec(c+d*x))^-1*tan(c+d*x)+1//15*a^-3*d^-1*(2A+27C)*tan(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^3*(A+C)*tan(c+d*x)+1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^2*(A+-9C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(C*a^-3*d^-1*arctanh(sin(c+d*x))+1//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*(-29C+6A)*tan(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^2*(A+C)*tan(c+d*x)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*(-7C+3A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*(A+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*(2A+7C)*tan(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*(A+C)*sec(c+d*x)*tan(c+d*x)+1//3*a^-1*d^-1*(a+a*sec(c+d*x))^-2*(A+-1C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*(A+C*sec(c+d*x)^2), x) == :(A*x*a^-3+-1//5*d^-1*(a+a*sec(c+d*x))^-3*(A+C)*tan(c+d*x)+-1//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*(-3C+22A)*tan(c+d*x)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*(-3C+7A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*(A+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(-3*A*x*a^-3+-3*A*d^-1*(a^3+a^3*sec(c+d*x))^-1*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*(A+C)*sin(c+d*x)+1//15*a^-3*d^-1*(2C+72A)*sin(c+d*x)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*(-1C+9A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :((1/2)*x*a^-3*(2C+13A)+-1//15*a^-3*d^-1*(22C+152A)*sin(c+d*x)+(1/2)*a^-3*d^-1*(2C+13A)*cos(c+d*x)*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*(A+C)*cos(c+d*x)*sin(c+d*x)+-1//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*(11C+76A)*cos(c+d*x)*sin(c+d*x)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*(C+11A)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(-1//2*x*a^-3*(6C+23A)+-1//15*a^-3*d^-1*sin(c+d*x)^3*(36C+136A)+1//5*a^-3*d^-1*(36C+136A)*sin(c+d*x)+-1//2*a^-3*d^-1*(6C+23A)*cos(c+d*x)*sin(c+d*x)+-1//3*d^-1*(a^3+a^3*sec(c+d*x))^-1*cos(c+d*x)^2*(6C+23A)*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*cos(c+d*x)^2*(A+C)*sin(c+d*x)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)^2*(3C+13A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*sec(c+d*x)^5*(A+C*sec(c+d*x)^2), x) == :((1/2)*a^-4*d^-1*(2A+21C)*arctanh(sin(c+d*x))+-1//105*a^-4*d^-1*(160A+1728C)*tan(c+d*x)+(1/2)*a^-4*d^-1*(2A+21C)*sec(c+d*x)*tan(c+d*x)+-1//7*d^-1*(a+a*sec(c+d*x))^-4*sec(c+d*x)^5*(A+C)*tan(c+d*x)+-2//5*C*a^-1*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^4*tan(c+d*x)+-1//105*a^-4*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^2*(80A+864C)*tan(c+d*x)+-1//105*a^-4*d^-1*(1+sec(c+d*x))^-2*sec(c+d*x)^3*(10A+129C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*sec(c+d*x)^4*(A+C*sec(c+d*x)^2), x) == :(-4*C*a^-4*d^-1*arctanh(sin(c+d*x))+1//105*a^-4*d^-1*(6A+244C)*tan(c+d*x)+4*C*a^-4*d^-1*(1+sec(c+d*x))^-1*tan(c+d*x)+-1//7*d^-1*(a+a*sec(c+d*x))^-4*sec(c+d*x)^4*(A+C)*tan(c+d*x)+1//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^3*(-12C+2A)*tan(c+d*x)+1//105*a^-4*d^-1*(1+sec(c+d*x))^-2*sec(c+d*x)^2*(-88C+3A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*sec(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(C*a^-4*d^-1*arctanh(sin(c+d*x))+-1//7*d^-1*(a+a*sec(c+d*x))^-4*sec(c+d*x)^3*(A+C)*tan(c+d*x)+-1//105*a^-4*d^-1*(1+sec(c+d*x))^-2*(-55C+8A)*tan(c+d*x)+1//105*a^-4*d^-1*(1+sec(c+d*x))^-1*(-215C+16A)*tan(c+d*x)+1//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^2*(-10C+4A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(-1//7*d^-1*(a+a*sec(c+d*x))^-4*sec(c+d*x)^2*(A+C)*tan(c+d*x)+-1//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*(-8C+6A)*tan(c+d*x)+1//105*a^-4*d^-1*(1+sec(c+d*x))^-1*(8A+36C)*tan(c+d*x)+1//105*a^-4*d^-1*(1+sec(c+d*x))^-2*(-54C+23A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*(A+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//105*d^-1*(a^2+a^2*sec(c+d*x))^-2*(6A+13C)*tan(c+d*x)+1//105*d^-1*(a^4+a^4*sec(c+d*x))^-1*(6A+13C)*tan(c+d*x)+-1//7*d^-1*(a+a*sec(c+d*x))^-4*(A+C)*sec(c+d*x)*tan(c+d*x)+1//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*(-6C+8A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*(A+C*sec(c+d*x)^2), x) == :(A*x*a^-4+-1//7*d^-1*(a+a*sec(c+d*x))^-4*(A+C)*tan(c+d*x)+-1//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*(-4C+10A)*tan(c+d*x)+-1//105*a^-4*d^-1*(1+sec(c+d*x))^-1*(-8C+160A)*tan(c+d*x)+-1//105*a^-4*d^-1*(1+sec(c+d*x))^-2*(-8C+55A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*(A+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(-4*A*x*a^-4+-1//7*d^-1*(a+a*sec(c+d*x))^-4*(A+C)*sin(c+d*x)+1//105*a^-4*d^-1*(6C+664A)*sin(c+d*x)+-4*A*a^-4*d^-1*(1+sec(c+d*x))^-1*sin(c+d*x)+-1//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*(-2C+12A)*sin(c+d*x)+-1//105*a^-4*d^-1*(1+sec(c+d*x))^-2*(-3C+88A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*cos(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :((1/2)*x*a^-4*(2C+21A)+-1//105*a^-4*d^-1*(160C+1728A)*sin(c+d*x)+(1/2)*a^-4*d^-1*(2C+21A)*cos(c+d*x)*sin(c+d*x)+-1//7*d^-1*(a+a*sec(c+d*x))^-4*(A+C)*cos(c+d*x)*sin(c+d*x)+-2//5*A*a^-1*d^-1*(a+a*sec(c+d*x))^-3*cos(c+d*x)*sin(c+d*x)+-1//105*a^-4*d^-1*(1+sec(c+d*x))^-1*(80C+864A)*cos(c+d*x)*sin(c+d*x)+-1//105*a^-4*d^-1*(1+sec(c+d*x))^-2*(10C+129A)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*cos(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(-1*x*a^-4*(4C+22A)+-1//105*a^-4*d^-1*sin(c+d*x)^3*(332C+1816A)+1//35*a^-4*d^-1*(332C+1816A)*sin(c+d*x)+-1*a^-4*d^-1*(4C+22A)*cos(c+d*x)*sin(c+d*x)+-1//7*d^-1*(a+a*sec(c+d*x))^-4*cos(c+d*x)^2*(A+C)*sin(c+d*x)+-1//3*a^-4*d^-1*(1+sec(c+d*x))^-1*cos(c+d*x)^2*(8C+44A)*sin(c+d*x)+-1//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*cos(c+d*x)^2*(2C+16A)*sin(c+d*x)+-1//105*a^-4*d^-1*(1+sec(c+d*x))^-2*cos(c+d*x)^2*(31C+178A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^4*(A+C*sec(c+d*x)^2), x) == :(-1//3465*d^-1*(a+a*sec(c+d*x))^(1/2)*(640C+792A)*tan(c+d*x)+1//1155*a^-1*d^-1*(a+a*sec(c+d*x))^3//2*(320C+396A)*tan(c+d*x)+2//11*C*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^4*tan(c+d*x)+4//495*a*d^-1*(a+a*sec(c+d*x))^-1//2*(80C+99A)*tan(c+d*x)+2//99*C*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^4*tan(c+d*x)+2//693*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*(80C+99A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(-1//315*d^-1*(a+a*sec(c+d*x))^(1/2)*(64C+84A)*tan(c+d*x)+1//105*a^-1*d^-1*(a+a*sec(c+d*x))^3//2*(32C+42A)*tan(c+d*x)+2//9*C*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3*tan(c+d*x)+2//45*a*d^-1*(a+a*sec(c+d*x))^-1//2*(16C+21A)*tan(c+d*x)+2//63*C*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(1//105*d^-1*(a+a*sec(c+d*x))^(1/2)*(36C+70A)*tan(c+d*x)+2//7*C*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^2*tan(c+d*x)+2//35*C*a^-1*d^-1*(a+a*sec(c+d*x))^3//2*tan(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^-1//2*(27C+35A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*(A+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(-4//15*C*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x)+2//5*C*a^-1*d^-1*(a+a*sec(c+d*x))^3//2*tan(c+d*x)+2//15*a*d^-1*(a+a*sec(c+d*x))^-1//2*(7C+15A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*(A+C*sec(c+d*x)^2), x) == :(2*A*a^(1/2)*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//3*C*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x)+2//3*C*a*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*(A+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(A*a^(1/2)*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+A*d^-1*(a+a*sec(c+d*x))^(1/2)*sin(c+d*x)+-1*a*d^-1*(a+a*sec(c+d*x))^-1//2*(A+-2C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(1//4*a^(1/2)*d^-1*(3A+8C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*A*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)*sin(c+d*x)+1//4*A*a*d^-1*(a+a*sec(c+d*x))^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(1//8*a^(1/2)*d^-1*(5A+8C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//3*A*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^2*sin(c+d*x)+1//8*a*d^-1*(a+a*sec(c+d*x))^-1//2*(5A+8C)*sin(c+d*x)+1//12*A*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^4*(A+C*sec(c+d*x)^2), x) == :(1//64*a^(1/2)*d^-1*(35A+48C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//4*A*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^3*sin(c+d*x)+1//64*a*d^-1*(a+a*sec(c+d*x))^-1//2*(35A+48C)*sin(c+d*x)+1//24*A*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*sin(c+d*x)+1//96*a*d^-1*(a+a*sec(c+d*x))^-1//2*(35A+48C)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(1//385*d^-1*(a+a*sec(c+d*x))^3//2*(224C+286A)*tan(c+d*x)+-4//1155*a*d^-1*(a+a*sec(c+d*x))^(1/2)*(112C+143A)*tan(c+d*x)+2//11*C*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^3*tan(c+d*x)+2//165*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(112C+143A)*tan(c+d*x)+2//33*C*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3*tan(c+d*x)+2//231*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*(28C+33A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(1//315*d^-1*(a+a*sec(c+d*x))^3//2*(44C+126A)*tan(c+d*x)+2//9*C*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^2*tan(c+d*x)+2//21*C*a^-1*d^-1*(a+a*sec(c+d*x))^5//2*tan(c+d*x)+2//315*a*d^-1*(a+a*sec(c+d*x))^(1/2)*(47C+63A)*tan(c+d*x)+8//315*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(47C+63A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*(A+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(-4//35*C*d^-1*(a+a*sec(c+d*x))^3//2*tan(c+d*x)+2//7*C*a^-1*d^-1*(a+a*sec(c+d*x))^5//2*tan(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^(1/2)*(19C+35A)*tan(c+d*x)+8//105*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(19C+35A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*(A+C*sec(c+d*x)^2), x) == :(2*A*a^3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//5*C*d^-1*(a+a*sec(c+d*x))^3//2*tan(c+d*x)+2//5*C*a*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x)+2//5*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(4C+5A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*(A+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(A*d^-1*(a+a*sec(c+d*x))^3//2*sin(c+d*x)+3*A*a^3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//3*a*d^-1*(a+a*sec(c+d*x))^(1/2)*(-2C+3A)*tan(c+d*x)+-1//3*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(-8C+3A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(1//4*a^3//2*d^-1*(7A+8C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*A*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)*sin(c+d*x)+-1//2*a*d^-1*(a+a*sec(c+d*x))^(1/2)*(A+-4C)*sin(c+d*x)+1//4*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(-8C+5A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(1//8*a^3//2*d^-1*(11A+24C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//3*A*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^2*sin(c+d*x)+1//24*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(19A+24C)*sin(c+d*x)+1//4*A*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^4*(A+C*sec(c+d*x)^2), x) == :(1//64*a^3//2*d^-1*(75A+112C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//4*A*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^3*sin(c+d*x)+1//64*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(75A+112C)*sin(c+d*x)+1//8*A*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^2*sin(c+d*x)+1//32*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(13A+16C)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^5*(A+C*sec(c+d*x)^2), x) == :(1//128*a^3//2*d^-1*(133A+176C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//5*A*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^4*sin(c+d*x)+1//128*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(133A+176C)*sin(c+d*x)+1//192*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(133A+176C)*cos(c+d*x)*sin(c+d*x)+1//240*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*(67A+80C)*sin(c+d*x)+3//40*A*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(-4//45045*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(8368C+10439A)*tan(c+d*x)+2//13*C*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^3*tan(c+d*x)+2//6435*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(8368C+10439A)*tan(c+d*x)+2//15015*a*d^-1*(a+a*sec(c+d*x))^3//2*(8368C+10439A)*tan(c+d*x)+2//1287*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3*(136C+143A)*tan(c+d*x)+2//9009*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*(2224C+2717A)*tan(c+d*x)+10//143*C*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(1//693*d^-1*(a+a*sec(c+d*x))^5//2*(52C+198A)*tan(c+d*x)+2//11*C*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^2*tan(c+d*x)+2//231*a*d^-1*(a+a*sec(c+d*x))^3//2*(25C+33A)*tan(c+d*x)+10//99*C*a^-1*d^-1*(a+a*sec(c+d*x))^7//2*tan(c+d*x)+16//693*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(25C+33A)*tan(c+d*x)+64//693*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(25C+33A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*(A+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(-4//63*C*d^-1*(a+a*sec(c+d*x))^5//2*tan(c+d*x)+2//9*C*a^-1*d^-1*(a+a*sec(c+d*x))^7//2*tan(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^3//2*(13C+21A)*tan(c+d*x)+16//315*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(13C+21A)*tan(c+d*x)+64//315*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(13C+21A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*(A+C*sec(c+d*x)^2), x) == :(2*A*a^5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//7*C*d^-1*(a+a*sec(c+d*x))^5//2*tan(c+d*x)+2//7*C*a*d^-1*(a+a*sec(c+d*x))^3//2*tan(c+d*x)+2//21*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(7A+8C)*tan(c+d*x)+2//21*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(32C+49A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*(A+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(A*d^-1*(a+a*sec(c+d*x))^5//2*sin(c+d*x)+5*A*a^5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//5*a*d^-1*(a+a*sec(c+d*x))^3//2*(-2C+5A)*tan(c+d*x)+-1//15*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(-16C+15A)*tan(c+d*x)+1//15*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(15A+64C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(1//4*a^5//2*d^-1*(8C+19A)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*A*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)*sin(c+d*x)+-1//2*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(A+-8C)*sin(c+d*x)+-1//6*a*d^-1*(a+a*sec(c+d*x))^3//2*(-4C+3A)*sin(c+d*x)+1//12*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(-56C+27A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(5//8*a^5//2*d^-1*(5A+8C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(-8C+3A)*sin(c+d*x)+1//3*A*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^2*sin(c+d*x)+1//24*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(-24C+49A)*sin(c+d*x)+5//12*A*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^4*(A+C*sec(c+d*x)^2), x) == :(1//64*a^5//2*d^-1*(163A+304C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//4*A*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^3*sin(c+d*x)+1//192*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(299A+432C)*sin(c+d*x)+1//32*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(16C+17A)*cos(c+d*x)*sin(c+d*x)+5//24*A*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^5*(A+C*sec(c+d*x)^2), x) == :(1//128*a^5//2*d^-1*(283A+400C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//5*A*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^4*sin(c+d*x)+1//128*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(283A+400C)*sin(c+d*x)+1//8*A*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^3*sin(c+d*x)+1//240*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^2*(79A+80C)*sin(c+d*x)+1//960*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(787A+1040C)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^6*(A+C*sec(c+d*x)^2), x) == :(1//512*a^5//2*d^-1*(1015A+1304C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//6*A*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^5*sin(c+d*x)+1//512*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(1015A+1304C)*sin(c+d*x)+1//12*A*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^4*sin(c+d*x)+1//96*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^3*(23A+24C)*sin(c+d*x)+1//192*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*(109A+136C)*sin(c+d*x)+1//768*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(1015A+1304C)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^4*(A+C*sec(c+d*x)^2), x) == :(1//315*d^-1*(a+a*sec(c+d*x))^-1//2*(572C+588A)*tan(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*(A+C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-2//63*C*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*tan(c+d*x)+-1//315*a^-1*d^-1*(a+a*sec(c+d*x))^(1/2)*(42A+58C)*tan(c+d*x)+1//105*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*(38C+42A)*tan(c+d*x)+2//9*C*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^4*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(-1//105*d^-1*(a+a*sec(c+d*x))^-1//2*(140A+148C)*tan(c+d*x)+2^(1/2)*a^-1//2*d^-1*(A+C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-2//35*C*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*tan(c+d*x)+1//105*a^-1*d^-1*(a+a*sec(c+d*x))^(1/2)*(62C+70A)*tan(c+d*x)+2//7*C*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(1//15*d^-1*(a+a*sec(c+d*x))^-1//2*(28C+30A)*tan(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*(A+C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-2//15*C*a^-1*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x)+2//5*C*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*(A+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(-4//3*C*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+2^(1/2)*a^-1//2*d^-1*(A+C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//3*C*a^-1*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*(A+C*sec(c+d*x)^2), x) == :(2*A*a^-1//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2*C*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*(A+C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*(A+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(A*d^-1*(a+a*sec(c+d*x))^-1//2*sin(c+d*x)+-1*A*a^-1//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2^(1/2)*a^-1//2*d^-1*(A+C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(-1//4*A*d^-1*(a+a*sec(c+d*x))^-1//2*sin(c+d*x)+1//4*a^-1//2*d^-1*(7A+8C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*A*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)*sin(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*(A+C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(-1//8*a^-1//2*d^-1*(8C+9A)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//8*d^-1*(a+a*sec(c+d*x))^-1//2*(7A+8C)*sin(c+d*x)+2^(1/2)*a^-1//2*d^-1*(A+C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//12*A*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)*sin(c+d*x)+1//3*A*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^4*(A+C*sec(c+d*x)^2), x) == :(-1//64*d^-1*(a+a*sec(c+d*x))^-1//2*(16C+21A)*sin(c+d*x)+1//64*a^-1//2*d^-1*(107A+112C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1*2^(1/2)*a^-1//2*d^-1*(A+C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//24*A*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*sin(c+d*x)+1//4*A*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3*sin(c+d*x)+1//96*d^-1*(a+a*sec(c+d*x))^-1//2*(43A+48C)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^4*(A+C*sec(c+d*x)^2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^4*(A+C)*tan(c+d*x)+-1//105*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(455A+799C)*tan(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(11A+19C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//210*a^-2*d^-1*(a+a*sec(c+d*x))^(1/2)*(245A+397C)*tan(c+d*x)+-1//70*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*(35A+67C)*tan(c+d*x)+1//14*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*(7A+11C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3*(A+C)*tan(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*(7A+15C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//10*a^-2*d^-1*(a+a*sec(c+d*x))^(1/2)*(5A+13C)*tan(c+d*x)+1//5*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(15A+31C)*tan(c+d*x)+1//10*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*(5A+9C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^2*(A+C)*tan(c+d*x)+-1//3*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(3A+13C)*tan(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(3A+11C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//6*a^-2*d^-1*(a+a*sec(c+d*x))^(1/2)*(3A+7C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*(A+C*sec(c+d*x)^2)*sec(c+d*x), x) == :((1/2)*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(A+5C)*tan(c+d*x)+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*(A+C)*sec(c+d*x)*tan(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(A+-7C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*(A+C*sec(c+d*x)^2), x) == :(2*A*a^-3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*(A+C)*tan(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*(-3C+5A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*(A+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(-3*A*a^-3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*(A+C)*sin(c+d*x)+(1/2)*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(C+3A)*sin(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(C+9A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(1//4*a^-3//2*d^-1*(8C+19A)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*(A+C)*cos(c+d*x)*sin(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*(5C+13A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(2C+7A)*sin(c+d*x)+(1/2)*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(C+2A)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(-1//8*a^-3//2*d^-1*(24C+47A)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^2*(A+C)*sin(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(9C+17A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//8*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(12C+21A)*sin(c+d*x)+-1//12*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(6C+13A)*cos(c+d*x)*sin(c+d*x)+1//6*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*(3C+5A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^4*(A+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^4*(A+C)*tan(c+d*x)+-1//32*2^(1/2)*a^-5//2*d^-1*(75A+283C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//240*a^-3*d^-1*(a+a*sec(c+d*x))^(1/2)*(195A+787C)*tan(c+d*x)+1//120*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*(465A+1729C)*tan(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3*(5A+21C)*tan(c+d*x)+1//80*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*(45A+157C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^3*(A+C)*tan(c+d*x)+-1//24*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*(21A+197C)*tan(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(19A+163C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//48*a^-3*d^-1*(a+a*sec(c+d*x))^(1/2)*(15A+95C)*tan(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^2*(A+17C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^2*(A+C)*tan(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*(-13C+3A)*tan(c+d*x)+1//4*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*(A+9C)*tan(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(-75C+5A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*(A+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*(A+C)*sec(c+d*x)*tan(c+d*x)+1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*(-9C+7A)*tan(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(3A+19C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*(A+C*sec(c+d*x)^2), x) == :(2*A*a^-5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*(A+C)*tan(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*(-5C+11A)*tan(c+d*x)+-1//32*2^(1/2)*a^-5//2*d^-1*(-5C+43A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*(A+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(-5*A*a^-5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*(A+C)*sin(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*(-1C+15A)*sin(c+d*x)+1//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*(3C+35A)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(3C+115A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(1//4*a^-5//2*d^-1*(8C+39A)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*(A+C)*cos(c+d*x)*sin(c+d*x)+-1//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*(11C+63A)*sin(c+d*x)+-1//32*2^(1/2)*a^-5//2*d^-1*(43C+219A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*(3C+19A)*cos(c+d*x)*sin(c+d*x)+1//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*(7C+31A)*cos(c+d*x)*sin(c+d*x))
@test integrate(sec(c+d*x)^3//2*(A+C*sec(c+d*x)^2)*(a+a*sec(c+d*x)), x) == :(2//5*C*a*d^-1*sec(c+d*x)^5//2*sin(c+d*x)+2//5*a*d^-1*sec(c+d*x)^(1/2)*(3C+5A)*sin(c+d*x)+2//7*C*a*d^-1*sec(c+d*x)^7//2*sin(c+d*x)+2//21*a*d^-1*sec(c+d*x)^3//2*(5C+7A)*sin(c+d*x)+-2//5*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3C+5A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//21*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5C+7A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^(1/2)*(A+C*sec(c+d*x)^2)*(a+a*sec(c+d*x)), x) == :(2//3*C*a*d^-1*sec(c+d*x)^3//2*sin(c+d*x)+2//5*C*a*d^-1*sec(c+d*x)^5//2*sin(c+d*x)+2//5*a*d^-1*sec(c+d*x)^(1/2)*(3C+5A)*sin(c+d*x)+-2//5*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3C+5A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(C+3A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^-1//2*(A+C*sec(c+d*x)^2)*(a+a*sec(c+d*x)), x) == :(2*C*a*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+2//3*C*a*d^-1*sec(c+d*x)^3//2*sin(c+d*x)+2*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(C+3A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^-3//2*(A+C*sec(c+d*x)^2)*(a+a*sec(c+d*x)), x) == :(2*C*a*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+2//3*A*a*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+2*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+3C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^-5//2*(A+C*sec(c+d*x)^2)*(a+a*sec(c+d*x)), x) == :(2//3*A*a*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+2//5*A*a*d^-1*sec(c+d*x)^-3//2*sin(c+d*x)+2//3*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+3C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3A+5C)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^-7//2*(A+C*sec(c+d*x)^2)*(a+a*sec(c+d*x)), x) == :(2//5*A*a*d^-1*sec(c+d*x)^-3//2*sin(c+d*x)+2//7*A*a*d^-1*sec(c+d*x)^-5//2*sin(c+d*x)+2//21*a*d^-1*sec(c+d*x)^-1//2*(5A+7C)*sin(c+d*x)+2//5*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3A+5C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//21*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5A+7C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^-9//2*(A+C*sec(c+d*x)^2)*(a+a*sec(c+d*x)), x) == :(2//7*A*a*d^-1*sec(c+d*x)^-5//2*sin(c+d*x)+2//9*A*a*d^-1*sec(c+d*x)^-7//2*sin(c+d*x)+2//21*a*d^-1*sec(c+d*x)^-1//2*(5A+7C)*sin(c+d*x)+2//45*a*d^-1*sec(c+d*x)^-3//2*(7A+9C)*sin(c+d*x)+2//15*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(7A+9C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//21*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5A+7C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^3//2*(A+C*sec(c+d*x)^2), x) == :(2//9*C*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^5//2*sin(c+d*x)+2//105*a^2*d^-1*sec(c+d*x)^5//2*(19C+21A)*sin(c+d*x)+4//21*a^2*d^-1*sec(c+d*x)^3//2*(5C+7A)*sin(c+d*x)+8//63*C*d^-1*sec(c+d*x)^5//2*(a^2+a^2*sec(c+d*x))*sin(c+d*x)+16//15*a^2*d^-1*sec(c+d*x)^(1/2)*(2C+3A)*sin(c+d*x)+-16//15*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2C+3A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5C+7A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^(1/2)*(A+C*sec(c+d*x)^2), x) == :(2//7*C*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^3//2*sin(c+d*x)+2//105*a^2*d^-1*sec(c+d*x)^3//2*(33C+35A)*sin(c+d*x)+4//5*a^2*d^-1*sec(c+d*x)^(1/2)*(3C+5A)*sin(c+d*x)+8//35*C*d^-1*sec(c+d*x)^3//2*(a^2+a^2*sec(c+d*x))*sin(c+d*x)+-4//5*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3C+5A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+8//21*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3C+7A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^-1//2*(A+C*sec(c+d*x)^2), x) == :(2//5*C*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^(1/2)*sin(c+d*x)+2//15*a^2*d^-1*sec(c+d*x)^(1/2)*(15A+17C)*sin(c+d*x)+8//15*C*d^-1*sec(c+d*x)^(1/2)*(a^2+a^2*sec(c+d*x))*sin(c+d*x)+-16//5*C*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//3*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(C+3A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^-3//2*(A+C*sec(c+d*x)^2), x) == :(-2//3*a^2*d^-1*sec(c+d*x)^(1/2)*(A+-5C)*sin(c+d*x)+-1//3*d^-1*sec(c+d*x)^(1/2)*(a^2+a^2*sec(c+d*x))*(-2C+2A)*sin(c+d*x)+2//3*A*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^-1//2*sin(c+d*x)+4*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+8//3*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^-5//2*(A+C*sec(c+d*x)^2), x) == :(-2//15*a^2*d^-1*sec(c+d*x)^(1/2)*(-15C+7A)*sin(c+d*x)+2//5*A*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^-3//2*sin(c+d*x)+8//15*A*d^-1*sec(c+d*x)^-1//2*(a^2+a^2*sec(c+d*x))*sin(c+d*x)+4//3*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+3C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+16//5*A*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^-7//2*(A+C*sec(c+d*x)^2), x) == :(2//7*A*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^-5//2*sin(c+d*x)+2//105*a^2*d^-1*sec(c+d*x)^-1//2*(33A+35C)*sin(c+d*x)+8//35*A*d^-1*sec(c+d*x)^-3//2*(a^2+a^2*sec(c+d*x))*sin(c+d*x)+4//5*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3A+5C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+8//21*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3A+7C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^-9//2*(A+C*sec(c+d*x)^2), x) == :(2//9*A*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^-7//2*sin(c+d*x)+2//105*a^2*d^-1*sec(c+d*x)^-3//2*(19A+21C)*sin(c+d*x)+4//21*a^2*d^-1*sec(c+d*x)^-1//2*(5A+7C)*sin(c+d*x)+8//63*A*d^-1*sec(c+d*x)^-5//2*(a^2+a^2*sec(c+d*x))*sin(c+d*x)+4//21*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5A+7C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+16//15*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2A+3C)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^-11//2*(A+C*sec(c+d*x)^2), x) == :(2//11*A*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^-9//2*sin(c+d*x)+2//693*a^2*d^-1*sec(c+d*x)^-5//2*(89A+99C)*sin(c+d*x)+4//45*a^2*d^-1*sec(c+d*x)^-3//2*(7A+9C)*sin(c+d*x)+8//99*A*d^-1*sec(c+d*x)^-7//2*(a^2+a^2*sec(c+d*x))*sin(c+d*x)+8//231*a^2*d^-1*sec(c+d*x)^-1//2*(25A+33C)*sin(c+d*x)+4//15*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(7A+9C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+8//231*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(25A+33C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^3//2*(A+C*sec(c+d*x)^2), x) == :(1//231*d^-1*sec(c+d*x)^5//2*(a^3+a^3*sec(c+d*x))*(66A+70C)*sin(c+d*x)+2//11*C*d^-1*(a+a*sec(c+d*x))^3*sec(c+d*x)^5//2*sin(c+d*x)+4//5*a^3*d^-1*sec(c+d*x)^(1/2)*(5C+7A)*sin(c+d*x)+4//231*a^3*d^-1*sec(c+d*x)^3//2*(105C+143A)*sin(c+d*x)+8//385*a^3*d^-1*sec(c+d*x)^5//2*(35C+44A)*sin(c+d*x)+-4//5*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5C+7A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//33*C*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*sec(c+d*x)^5//2*sin(c+d*x)+4//231*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(105C+143A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^(1/2)*(A+C*sec(c+d*x)^2), x) == :(1//315*d^-1*sec(c+d*x)^3//2*(a^3+a^3*sec(c+d*x))*(126A+146C)*sin(c+d*x)+2//9*C*d^-1*(a+a*sec(c+d*x))^3*sec(c+d*x)^3//2*sin(c+d*x)+4//15*a^3*d^-1*sec(c+d*x)^(1/2)*(17C+27A)*sin(c+d*x)+8//105*a^3*d^-1*sec(c+d*x)^3//2*(16C+21A)*sin(c+d*x)+-4//15*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(17C+27A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*C*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*sec(c+d*x)^3//2*sin(c+d*x)+4//21*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(11C+21A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^-1//2*(A+C*sec(c+d*x)^2), x) == :(1//15*d^-1*sec(c+d*x)^(1/2)*(a^3+a^3*sec(c+d*x))*(10A+14C)*sin(c+d*x)+2//7*C*d^-1*(a+a*sec(c+d*x))^3*sec(c+d*x)^(1/2)*sin(c+d*x)+8//105*a^3*d^-1*sec(c+d*x)^(1/2)*(53C+70A)*sin(c+d*x)+-4//5*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5A+7C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(13C+35A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+12//35*C*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^-3//2*(A+C*sec(c+d*x)^2), x) == :(-1//15*d^-1*sec(c+d*x)^(1/2)*(a^3+a^3*sec(c+d*x))*(-18C+10A)*sin(c+d*x)+2//3*A*d^-1*(a+a*sec(c+d*x))^3*sec(c+d*x)^-1//2*sin(c+d*x)+4//15*a^3*d^-1*sec(c+d*x)^(1/2)*(5A+21C)*sin(c+d*x)+-1//15*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*sec(c+d*x)^(1/2)*(-6C+10A)*sin(c+d*x)+4//3*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3C+5A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+4//5*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-9C+5A)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^-5//2*(A+C*sec(c+d*x)^2), x) == :(-8//15*a^3*d^-1*sec(c+d*x)^(1/2)*(-10C+3A)*sin(c+d*x)+-1//15*d^-1*sec(c+d*x)^(1/2)*(a^3+a^3*sec(c+d*x))*(-10C+18A)*sin(c+d*x)+2//5*A*d^-1*(a+a*sec(c+d*x))^3*sec(c+d*x)^-3//2*sin(c+d*x)+4//3*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3A+5C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+4//5*A*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*sec(c+d*x)^-1//2*sin(c+d*x)+4//5*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-5C+9A)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^-7//2*(A+C*sec(c+d*x)^2), x) == :(-4//105*a^3*d^-1*sec(c+d*x)^(1/2)*(-35C+41A)*sin(c+d*x)+1//15*d^-1*sec(c+d*x)^-1//2*(a^3+a^3*sec(c+d*x))*(10C+14A)*sin(c+d*x)+2//7*A*d^-1*(a+a*sec(c+d*x))^3*sec(c+d*x)^-5//2*sin(c+d*x)+4//5*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5C+7A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(13A+35C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+12//35*A*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*sec(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^-9//2*(A+C*sec(c+d*x)^2), x) == :(1//315*d^-1*sec(c+d*x)^-3//2*(a^3+a^3*sec(c+d*x))*(126C+146A)*sin(c+d*x)+2//9*A*d^-1*(a+a*sec(c+d*x))^3*sec(c+d*x)^-7//2*sin(c+d*x)+8//105*a^3*d^-1*sec(c+d*x)^-1//2*(16A+21C)*sin(c+d*x)+4//15*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(17A+27C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*A*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*sec(c+d*x)^-5//2*sin(c+d*x)+4//21*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(11A+21C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^-11//2*(A+C*sec(c+d*x)^2), x) == :(1//231*d^-1*sec(c+d*x)^-5//2*(a^3+a^3*sec(c+d*x))*(66C+70A)*sin(c+d*x)+2//11*A*d^-1*(a+a*sec(c+d*x))^3*sec(c+d*x)^-9//2*sin(c+d*x)+4//231*a^3*d^-1*sec(c+d*x)^-1//2*(105A+143C)*sin(c+d*x)+8//385*a^3*d^-1*sec(c+d*x)^-3//2*(35A+44C)*sin(c+d*x)+4//5*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5A+7C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//33*A*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*sec(c+d*x)^-7//2*sin(c+d*x)+4//231*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(105A+143C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^-13//2*(A+C*sec(c+d*x)^2), x) == :(1//1287*d^-1*sec(c+d*x)^-7//2*(a^3+a^3*sec(c+d*x))*(286C+290A)*sin(c+d*x)+2//13*A*d^-1*(a+a*sec(c+d*x))^3*sec(c+d*x)^-11//2*sin(c+d*x)+4//231*a^3*d^-1*sec(c+d*x)^-1//2*(95A+121C)*sin(c+d*x)+4//585*a^3*d^-1*sec(c+d*x)^-3//2*(175A+221C)*sin(c+d*x)+40//9009*a^3*d^-1*sec(c+d*x)^-5//2*(118A+143C)*sin(c+d*x)+4//195*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(175A+221C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//231*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(95A+121C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+12//143*A*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*sec(c+d*x)^-9//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^5//2*(A+C*sec(c+d*x)^2), x) == :(-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^7//2*(A+C)*sin(c+d*x)+-1//3*a^-1*d^-1*sec(c+d*x)^3//2*(3A+5C)*sin(c+d*x)+1//5*a^-1*d^-1*sec(c+d*x)^(1/2)*(15A+21C)*sin(c+d*x)+1//5*a^-1*d^-1*sec(c+d*x)^5//2*(5A+7C)*sin(c+d*x)+-1//3*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3A+5C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-21C+-15A)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^3//2*(A+C*sec(c+d*x)^2), x) == :(-1*a^-1*d^-1*sec(c+d*x)^(1/2)*(A+3C)*sin(c+d*x)+-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^5//2*(A+C)*sin(c+d*x)+1//3*a^-1*d^-1*sec(c+d*x)^3//2*(3A+5C)*sin(c+d*x)+a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+3C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3A+5C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^(1/2)*(A+C*sec(c+d*x)^2), x) == :(a^-1*d^-1*sec(c+d*x)^(1/2)*(A+3C)*sin(c+d*x)+-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^3//2*(A+C)*sin(c+d*x)+a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+3C)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^-1//2*(A+C*sec(c+d*x)^2), x) == :(-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^(1/2)*(A+C)*sin(c+d*x)+a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(C+3A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^-3//2*(A+C*sec(c+d*x)^2), x) == :(-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^-1//2*(A+C)*sin(c+d*x)+1//3*a^-1*d^-1*sec(c+d*x)^-1//2*(3C+5A)*sin(c+d*x)+-1*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(C+3A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3C+5A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^-5//2*(A+C*sec(c+d*x)^2), x) == :(-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^-3//2*(A+C)*sin(c+d*x)+-1//3*a^-1*d^-1*sec(c+d*x)^-1//2*(3C+5A)*sin(c+d*x)+1//5*a^-1*d^-1*sec(c+d*x)^-3//2*(5C+7A)*sin(c+d*x)+-1//3*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3C+5A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(15C+21A)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^5//2*(A+C*sec(c+d*x)^2), x) == :(-1*a^-2*d^-1*sec(c+d*x)^(1/2)*(A+7C)*sin(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^7//2*(A+C)*sin(c+d*x)+1//3*a^-2*d^-1*sec(c+d*x)^3//2*(2A+10C)*sin(c+d*x)+a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+7C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^5//2*(A+7C)*sin(c+d*x)+1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2A+10C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^3//2*(A+C*sec(c+d*x)^2), x) == :(4*C*a^-2*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^5//2*(A+C)*sin(c+d*x)+-4*C*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^3//2*(A+-5C)*sin(c+d*x)+1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-5C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^(1/2)*(A+C*sec(c+d*x)^2), x) == :(-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^3//2*(A+C)*sin(c+d*x)+a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^(1/2)*(A+-1C)*sin(c+d*x)+-1*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2A+2C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^-1//2*(A+C*sec(c+d*x)^2), x) == :(-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^(1/2)*(A+C)*sin(c+d*x)+4*A*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^(1/2)*(-1C+5A)*sin(c+d*x)+-1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-1C+5A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^-3//2*(A+C*sec(c+d*x)^2), x) == :(-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^-1//2*(A+C)*sin(c+d*x)+1//3*a^-2*d^-1*sec(c+d*x)^-1//2*(2C+10A)*sin(c+d*x)+-1*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(C+7A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^-1//2*(C+7A)*sin(c+d*x)+1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2C+10A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^-5//2*(A+C*sec(c+d*x)^2), x) == :(-1//3*a^-2*d^-1*sec(c+d*x)^-1//2*(5C+15A)*sin(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^-3//2*(A+C)*sin(c+d*x)+1//15*a^-2*d^-1*sec(c+d*x)^-3//2*(20C+56A)*sin(c+d*x)+-1*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^-3//2*(C+3A)*sin(c+d*x)+-1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5C+15A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(20C+56A)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^7//2*(A+C*sec(c+d*x)^2), x) == :((1/2)*a^-3*d^-1*sec(c+d*x)^3//2*(A+11C)*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^9//2*(A+C)*sin(c+d*x)+-1//10*a^-3*d^-1*sec(c+d*x)^(1/2)*(9A+119C)*sin(c+d*x)+-1//30*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^5//2*(9A+119C)*sin(c+d*x)+(1/2)*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+11C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-2//3*C*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^7//2*sin(c+d*x)+1//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(9A+119C)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^5//2*(A+C*sec(c+d*x)^2), x) == :(-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^7//2*(A+C)*sin(c+d*x)+-1//10*a^-3*d^-1*sec(c+d*x)^(1/2)*(A+-49C)*sin(c+d*x)+1//6*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^3//2*(A+-13C)*sin(c+d*x)+1//6*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-13C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-49C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^5//2*(-8C+2A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^3//2*(A+C*sec(c+d*x)^2), x) == :(-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^5//2*(A+C)*sin(c+d*x)+1//10*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^(1/2)*(A+-9C)*sin(c+d*x)+-1//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-9C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//6*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+3C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^3//2*(-6C+4A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^(1/2)*(A+C*sec(c+d*x)^2), x) == :(-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^3//2*(A+C)*sin(c+d*x)+1//6*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^(1/2)*(C+3A)*sin(c+d*x)+-1//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-1C+9A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//6*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(C+3A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^(1/2)*(-4C+6A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^-1//2*(A+C*sec(c+d*x)^2), x) == :(-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^(1/2)*(A+C)*sin(c+d*x)+-1//6*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^(1/2)*(-1C+13A)*sin(c+d*x)+-1//6*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-1C+13A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^(1/2)*(-2C+8A)*sin(c+d*x)+1//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-1C+49A)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^-3//2*(A+C*sec(c+d*x)^2), x) == :((1/2)*a^-3*d^-1*sec(c+d*x)^-1//2*(C+11A)*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^-1//2*(A+C)*sin(c+d*x)+-1//30*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^-1//2*(9C+119A)*sin(c+d*x)+(1/2)*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(C+11A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-2//3*A*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^-1//2*sin(c+d*x)+-1//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(9C+119A)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^-5//2*(A+C*sec(c+d*x)^2), x) == :(-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^-3//2*(A+C)*sin(c+d*x)+-1//6*a^-3*d^-1*sec(c+d*x)^-1//2*(13C+63A)*sin(c+d*x)+-1//10*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^-3//2*(13C+63A)*sin(c+d*x)+1//30*a^-3*d^-1*sec(c+d*x)^-3//2*(49C+231A)*sin(c+d*x)+-1//6*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(13C+63A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^-3//2*(2C+12A)*sin(c+d*x)+1//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(49C+231A)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^5//2*(A+C*sec(c+d*x)^2), x) == :(1//64*a^(1/2)*d^-1*(35C+48A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//4*C*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^7//2*sin(c+d*x)+1//24*C*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^7//2*sin(c+d*x)+1//64*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(35C+48A)*sin(c+d*x)+1//96*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*(35C+48A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3//2*(A+C*sec(c+d*x)^2), x) == :(1//8*a^(1/2)*d^-1*(5C+8A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//3*C*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^5//2*sin(c+d*x)+1//8*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(5C+8A)*sin(c+d*x)+1//12*C*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*(A+C*sec(c+d*x)^2), x) == :(1//4*a^(1/2)*d^-1*(3C+8A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*C*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3//2*sin(c+d*x)+1//4*C*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(A+C*sec(c+d*x)^2), x) == :(C*a^(1/2)*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+C*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*sin(c+d*x)+a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-1C+2A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*(A+C*sec(c+d*x)^2), x) == :(2*C*a^(1/2)*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//3*A*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*sin(c+d*x)+2//3*A*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*(A+C*sec(c+d*x)^2), x) == :(2//5*A*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*sin(c+d*x)+2//15*A*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*sin(c+d*x)+2//15*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(7A+15C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-7//2*(A+C*sec(c+d*x)^2), x) == :(2//7*A*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*sin(c+d*x)+2//35*A*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*sin(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(24A+35C)*sin(c+d*x)+4//105*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(24A+35C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-9//2*(A+C*sec(c+d*x)^2), x) == :(2//9*A*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-7//2*sin(c+d*x)+2//63*A*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-5//2*sin(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(16A+21C)*sin(c+d*x)+8//315*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(16A+21C)*sin(c+d*x)+16//315*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(16A+21C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^5//2*(A+C*sec(c+d*x)^2), x) == :(1//128*a^3//2*d^-1*(133C+176A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//5*C*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^7//2*sin(c+d*x)+1//128*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(133C+176A)*sin(c+d*x)+1//192*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*(133C+176A)*sin(c+d*x)+1//240*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^7//2*(67C+80A)*sin(c+d*x)+3//40*C*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^7//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^3//2*(A+C*sec(c+d*x)^2), x) == :(1//64*a^3//2*d^-1*(75C+112A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//4*C*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^5//2*sin(c+d*x)+1//8*C*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^5//2*sin(c+d*x)+1//32*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*(13C+16A)*sin(c+d*x)+1//64*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(75C+112A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^(1/2)*(A+C*sec(c+d*x)^2), x) == :(1//8*a^3//2*d^-1*(11C+24A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//3*C*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^3//2*sin(c+d*x)+1//4*C*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3//2*sin(c+d*x)+1//24*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(19C+24A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^-1//2*(A+C*sec(c+d*x)^2), x) == :(1//4*a^3//2*d^-1*(7C+8A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*C*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^(1/2)*sin(c+d*x)+1//4*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-5C+8A)*sin(c+d*x)+3//4*C*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^-3//2*(A+C*sec(c+d*x)^2), x) == :(3*C*a^3//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//3*A*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-1//2*sin(c+d*x)+-1//3*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*(-3C+2A)*sin(c+d*x)+1//3*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-3C+8A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^-5//2*(A+C*sec(c+d*x)^2), x) == :(2*C*a^3//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//5*A*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-3//2*sin(c+d*x)+2//5*A*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*sin(c+d*x)+2//5*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(4A+5C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^-7//2*(A+C*sec(c+d*x)^2), x) == :(2//7*A*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-5//2*sin(c+d*x)+6//35*A*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-3//2*sin(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(19A+35C)*sin(c+d*x)+8//105*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(19A+35C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^-9//2*(A+C*sec(c+d*x)^2), x) == :(2//9*A*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-7//2*sin(c+d*x)+2//21*A*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*sin(c+d*x)+2//315*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(52A+63C)*sin(c+d*x)+2//315*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(136A+189C)*sin(c+d*x)+4//315*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(136A+189C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^-11//2*(A+C*sec(c+d*x)^2), x) == :(2//11*A*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-9//2*sin(c+d*x)+2//33*A*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-7//2*sin(c+d*x)+2//231*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-5//2*(28A+33C)*sin(c+d*x)+2//385*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(112A+143C)*sin(c+d*x)+8//1155*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(112A+143C)*sin(c+d*x)+16//1155*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(112A+143C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^5//2*(A+C*sec(c+d*x)^2), x) == :(1//512*a^5//2*d^-1*(1015C+1304A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//6*C*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^7//2*sin(c+d*x)+1//12*C*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^7//2*sin(c+d*x)+1//96*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^7//2*(23C+24A)*sin(c+d*x)+1//192*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^7//2*(109C+136A)*sin(c+d*x)+1//512*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(1015C+1304A)*sin(c+d*x)+1//768*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*(1015C+1304A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^3//2*(A+C*sec(c+d*x)^2), x) == :(1//128*a^5//2*d^-1*(283C+400A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//5*C*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^5//2*sin(c+d*x)+1//8*C*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^5//2*sin(c+d*x)+1//128*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(283C+400A)*sin(c+d*x)+1//240*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^5//2*(79C+80A)*sin(c+d*x)+1//960*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*(787C+1040A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^(1/2)*(A+C*sec(c+d*x)^2), x) == :(1//64*a^5//2*d^-1*(163C+304A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//4*C*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^3//2*sin(c+d*x)+1//32*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3//2*(16A+17C)*sin(c+d*x)+1//192*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(299C+432A)*sin(c+d*x)+5//24*C*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-1//2*(A+C*sec(c+d*x)^2), x) == :(5//8*a^5//2*d^-1*(5C+8A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//3*C*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^(1/2)*sin(c+d*x)+1//24*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*(24A+31C)*sin(c+d*x)+1//24*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-49C+24A)*sin(c+d*x)+5//12*C*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-3//2*(A+C*sec(c+d*x)^2), x) == :(1//4*a^5//2*d^-1*(8A+19C)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//3*A*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^-1//2*sin(c+d*x)+-1//6*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^(1/2)*(-3C+4A)*sin(c+d*x)+-1//12*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*(-21C+8A)*sin(c+d*x)+1//12*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-27C+56A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-5//2*(A+C*sec(c+d*x)^2), x) == :(5*C*a^5//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//5*A*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^-3//2*sin(c+d*x)+-1//15*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*(-15C+16A)*sin(c+d*x)+1//15*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(15C+64A)*sin(c+d*x)+2//3*A*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-7//2*(A+C*sec(c+d*x)^2), x) == :(2*C*a^5//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//7*A*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^-5//2*sin(c+d*x)+2//7*A*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-3//2*sin(c+d*x)+2//21*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(7C+8A)*sin(c+d*x)+2//21*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(32A+49C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-9//2*(A+C*sec(c+d*x)^2), x) == :(2//9*A*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^-7//2*sin(c+d*x)+10//63*A*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^-5//2*sin(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-3//2*(13A+21C)*sin(c+d*x)+16//315*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(13A+21C)*sin(c+d*x)+64//315*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(13A+21C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-11//2*(A+C*sec(c+d*x)^2), x) == :(2//11*A*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^-9//2*sin(c+d*x)+2//231*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*(32A+33C)*sin(c+d*x)+2//693*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(232A+297C)*sin(c+d*x)+2//693*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(568A+759C)*sin(c+d*x)+4//693*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(568A+759C)*sin(c+d*x)+10//99*A*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-7//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-13//2*(A+C*sec(c+d*x)^2), x) == :(2//13*A*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^-11//2*sin(c+d*x)+2//1287*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-7//2*(136A+143C)*sin(c+d*x)+2//9009*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-5//2*(2224A+2717C)*sin(c+d*x)+2//15015*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(8368A+10439C)*sin(c+d*x)+8//45045*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(8368A+10439C)*sin(c+d*x)+10//143*A*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-9//2*sin(c+d*x)+16//45045*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(8368A+10439C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*(A+C*sec(c+d*x)^2), x) == :(-1//8*a^-1//2*d^-1*(8A+9C)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2^(1/2)*a^-1//2*d^-1*(A+C)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//12*C*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*sin(c+d*x)+1//3*C*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^7//2*sin(c+d*x)+1//8*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(7C+8A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(A+C*sec(c+d*x)^2), x) == :(1//4*a^-1//2*d^-1*(7C+8A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*C*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*sin(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*(A+C)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//4*C*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(A+C*sec(c+d*x)^2), x) == :(-1*C*a^-1//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+C*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x)+2^(1/2)*a^-1//2*d^-1*(A+C)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(A+C*sec(c+d*x)^2), x) == :(2*C*a^-1//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1*2^(1/2)*a^-1//2*d^-1*(A+C)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+2*A*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(A+C*sec(c+d*x)^2), x) == :(2^(1/2)*a^-1//2*d^-1*(A+C)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-2//3*A*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)+2//3*A*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-5//2*(A+C*sec(c+d*x)^2), x) == :(-1*2^(1/2)*a^-1//2*d^-1*(A+C)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-2//15*A*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x)+1//15*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(26A+30C)*sin(c+d*x)+2//5*A*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-7//2*(A+C*sec(c+d*x)^2), x) == :(2^(1/2)*a^-1//2*d^-1*(A+C)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-2//35*A*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*sin(c+d*x)+-1//105*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(70C+86A)*sin(c+d*x)+1//105*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(62A+70C)*sin(c+d*x)+2//7*A*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-5//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3//2*(A+C*sec(c+d*x)^2), x) == :(-3*C*a^-3//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^5//2*(A+C)*sin(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(A+9C)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+(1/2)*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(A+3C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^(1/2)*(A+C*sec(c+d*x)^2), x) == :(2*C*a^-3//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3//2*(A+C)*sin(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(-5C+3A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-1//2*(A+C*sec(c+d*x)^2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^(1/2)*(A+C)*sin(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*(-1C+7A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+(1/2)*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(C+5A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-3//2*(A+C*sec(c+d*x)^2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-1//2*(A+C)*sin(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(3C+11A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//6*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(3C+19A)*sin(c+d*x)+1//6*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(3C+7A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-5//2*(A+C*sec(c+d*x)^2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-3//2*(A+C)*sin(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*(7C+15A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//10*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(5C+13A)*sin(c+d*x)+1//10*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(25C+49A)*sin(c+d*x)+1//10*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(5C+9A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^5//2*(A+C*sec(c+d*x)^2), x) == :(-5*C*a^-5//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^7//2*(A+C)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(3A+115C)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^5//2*(A+-15C)*sin(c+d*x)+1//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(3A+35C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^3//2*(A+C*sec(c+d*x)^2), x) == :(2*C*a^-5//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^5//2*(A+C)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(-43C+5A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3//2*(-11C+5A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^(1/2)*(A+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^3//2*(A+C)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(3C+19A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3//2*(-7C+9A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^-1//2*(A+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^(1/2)*(A+C)*sin(c+d*x)+-1//32*2^(1/2)*a^-5//2*d^-1*(-5C+75A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^(1/2)*(-3C+13A)*sin(c+d*x)+1//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(C+49A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^-3//2*(A+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^-1//2*(A+C)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(19C+163A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-1//2*(C+17A)*sin(c+d*x)+-1//48*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(27C+299A)*sin(c+d*x)+1//48*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(15C+95A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^-5//2*(A+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^-3//2*(A+C)*sin(c+d*x)+-1//32*2^(1/2)*a^-5//2*d^-1*(75C+283A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-3//2*(5C+21A)*sin(c+d*x)+-1//240*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(195C+787A)*sin(c+d*x)+1//80*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(45C+157A)*sin(c+d*x)+1//240*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(735C+2671A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^n*sec(c+d*x)^(-1+-1n)*(A+C*sec(c+d*x)^2)+a^-1*(1+n)^-1*(a+a*sec(c+d*x))^n*sec(c+d*x)^(-1n)*(-1*A*a*n+-1*C*a*(1+n)*sec(c+d*x)), x) == :(A*d^-1*(1+n)^-1*(a+a*sec(c+d*x))^n*sec(c+d*x)^(-1n)*sin(c+d*x))
@test integrate(sec(c+d*x)^2*(a+a*sec(c+d*x))*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a*d^-1*(B+C)*tan(c+d*x)+1//3*a*d^-1*tan(c+d*x)^3*(B+C)+1//8*a*d^-1*(3C+4B)*arctanh(sin(c+d*x))+1//4*C*a*d^-1*sec(c+d*x)^3*tan(c+d*x)+1//8*a*d^-1*(3C+4B)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))*(B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :((1/2)*a*d^-1*(B+C)*arctanh(sin(c+d*x))+1//3*a*d^-1*(2C+3B)*tan(c+d*x)+(1/2)*a*d^-1*(B+C)*sec(c+d*x)*tan(c+d*x)+1//3*C*a*d^-1*sec(c+d*x)^2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a*d^-1*(B+C)*tan(c+d*x)+(1/2)*a*d^-1*(C+2B)*arctanh(sin(c+d*x))+(1/2)*C*a*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))*(B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(B*a*x+C*a*d^-1*tan(c+d*x)+a*d^-1*(B+C)*arctanh(sin(c+d*x)))
@test integrate(cos(c+d*x)^2*(a+a*sec(c+d*x))*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a*x*(B+C)+B*a*d^-1*sin(c+d*x)+C*a*d^-1*arctanh(sin(c+d*x)))
@test integrate(cos(c+d*x)^3*(a+a*sec(c+d*x))*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*a*x*(B+2C)+a*d^-1*(B+C)*sin(c+d*x)+(1/2)*B*a*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^4*(a+a*sec(c+d*x))*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*a*x*(B+C)+1//3*a*d^-1*(2B+3C)*sin(c+d*x)+(1/2)*a*d^-1*(B+C)*cos(c+d*x)*sin(c+d*x)+1//3*B*a*d^-1*cos(c+d*x)^2*sin(c+d*x))
@test integrate(cos(c+d*x)^5*(a+a*sec(c+d*x))*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//8*a*x*(3B+4C)+a*d^-1*(B+C)*sin(c+d*x)+-1//3*a*d^-1*sin(c+d*x)^3*(B+C)+1//4*B*a*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//8*a*d^-1*(3B+4C)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//5*a^2*d^-1*(9C+10B)*tan(c+d*x)+1//8*a^2*d^-1*(6C+7B)*arctanh(sin(c+d*x))+1//15*a^2*d^-1*tan(c+d*x)^3*(9C+10B)+1//5*C*d^-1*sec(c+d*x)^3*(a^2+a^2*sec(c+d*x))*tan(c+d*x)+1//8*a^2*d^-1*(6C+7B)*sec(c+d*x)*tan(c+d*x)+1//20*a^2*d^-1*sec(c+d*x)^3*(5B+6C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*(B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//6*a^2*d^-1*(7C+8B)*tan(c+d*x)+1//8*a^2*d^-1*(7C+8B)*arctanh(sin(c+d*x))+1//12*d^-1*(a+a*sec(c+d*x))^2*(-1C+4B)*tan(c+d*x)+1//4*C*a^-1*d^-1*(a+a*sec(c+d*x))^3*tan(c+d*x)+1//24*a^2*d^-1*(7C+8B)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*a^2*d^-1*(2C+3B)*arctanh(sin(c+d*x))+1//3*C*d^-1*(a+a*sec(c+d*x))^2*tan(c+d*x)+2//3*a^2*d^-1*(2C+3B)*tan(c+d*x)+1//6*a^2*d^-1*(2C+3B)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*(B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(B*x*a^2+(1/2)*C*d^-1*(a^2+a^2*sec(c+d*x))*tan(c+d*x)+(1/2)*a^2*d^-1*(2B+3C)*tan(c+d*x)+(1/2)*a^2*d^-1*(3C+4B)*arctanh(sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*a^2*(C+2B)+C*d^-1*(a^2+a^2*sec(c+d*x))*sin(c+d*x)+a^2*d^-1*(B+-1C)*sin(c+d*x)+a^2*d^-1*(B+2C)*arctanh(sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*x*a^2*(3B+4C)+C*a^2*d^-1*arctanh(sin(c+d*x))+(1/2)*a^2*d^-1*(2C+3B)*sin(c+d*x)+(1/2)*B*d^-1*(a^2+a^2*sec(c+d*x))*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^4*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*x*a^2*(2B+3C)+2//3*a^2*d^-1*(2B+3C)*sin(c+d*x)+1//3*B*d^-1*(a+a*sec(c+d*x))^2*cos(c+d*x)^2*sin(c+d*x)+1//6*a^2*d^-1*(2B+3C)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^5*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//8*x*a^2*(7B+8C)+1//3*a^2*d^-1*(4B+5C)*sin(c+d*x)+1//4*B*d^-1*cos(c+d*x)^3*(a^2+a^2*sec(c+d*x))*sin(c+d*x)+1//8*a^2*d^-1*(7B+8C)*cos(c+d*x)*sin(c+d*x)+1//12*a^2*d^-1*cos(c+d*x)^2*(4C+5B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^6*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//8*x*a^2*(6B+7C)+-1//15*a^2*d^-1*sin(c+d*x)^3*(9B+10C)+1//5*a^2*d^-1*(9B+10C)*sin(c+d*x)+1//5*B*d^-1*cos(c+d*x)^4*(a^2+a^2*sec(c+d*x))*sin(c+d*x)+1//8*a^2*d^-1*(6B+7C)*cos(c+d*x)*sin(c+d*x)+1//20*a^2*d^-1*cos(c+d*x)^3*(5C+6B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*(B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//5*a^3*d^-1*(13C+15B)*tan(c+d*x)+1//8*a^3*d^-1*(13C+15B)*arctanh(sin(c+d*x))+1//20*d^-1*(a+a*sec(c+d*x))^3*(-1C+5B)*tan(c+d*x)+1//60*a^3*d^-1*tan(c+d*x)^3*(13C+15B)+1//5*C*a^-1*d^-1*(a+a*sec(c+d*x))^4*tan(c+d*x)+3//40*a^3*d^-1*(13C+15B)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^3*d^-1*(3C+4B)*tan(c+d*x)+1//4*C*d^-1*(a+a*sec(c+d*x))^3*tan(c+d*x)+1//12*a^3*d^-1*tan(c+d*x)^3*(3C+4B)+5//8*a^3*d^-1*(3C+4B)*arctanh(sin(c+d*x))+3//8*a^3*d^-1*(3C+4B)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*(B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(B*x*a^3+(1/2)*a^3*d^-1*(5C+7B)*arctanh(sin(c+d*x))+1//6*d^-1*(a^3+a^3*sec(c+d*x))*(3B+5C)*tan(c+d*x)+5//2*a^3*d^-1*(B+C)*tan(c+d*x)+1//3*C*a*d^-1*(a+a*sec(c+d*x))^2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*a^3*(C+3B)+d^-1*(B+2C)*(a^3+a^3*sec(c+d*x))*sin(c+d*x)+(1/2)*a^3*d^-1*(6B+7C)*arctanh(sin(c+d*x))+-5//2*C*a^3*d^-1*sin(c+d*x)+(1/2)*C*a*d^-1*(a+a*sec(c+d*x))^2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*x*a^3*(6C+7B)+a^3*d^-1*(B+3C)*arctanh(sin(c+d*x))+-1//2*d^-1*(B+-2C)*(a^3+a^3*sec(c+d*x))*sin(c+d*x)+5//2*B*a^3*d^-1*sin(c+d*x)+(1/2)*B*a*d^-1*(a+a*sec(c+d*x))^2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^4*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*x*a^3*(5B+7C)+C*a^3*d^-1*arctanh(sin(c+d*x))+5//2*a^3*d^-1*(B+C)*sin(c+d*x)+1//6*d^-1*(a^3+a^3*sec(c+d*x))*(3C+5B)*cos(c+d*x)*sin(c+d*x)+1//3*B*a*d^-1*(a+a*sec(c+d*x))^2*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^5*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(5//8*x*a^3*(3B+4C)+a^3*d^-1*(3B+4C)*sin(c+d*x)+-1//12*a^3*d^-1*sin(c+d*x)^3*(3B+4C)+1//4*B*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)^3*sin(c+d*x)+3//8*a^3*d^-1*(3B+4C)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^6*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//8*x*a^3*(13B+15C)+1//15*a^3*d^-1*(38B+45C)*sin(c+d*x)+1//8*a^3*d^-1*(13B+15C)*cos(c+d*x)*sin(c+d*x)+1//20*d^-1*cos(c+d*x)^3*(a^3+a^3*sec(c+d*x))*(5C+7B)*sin(c+d*x)+1//60*a^3*d^-1*cos(c+d*x)^2*(43B+45C)*sin(c+d*x)+1//5*B*a*d^-1*(a+a*sec(c+d*x))^2*cos(c+d*x)^4*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^7*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//16*x*a^3*(23B+26C)+-1//15*a^3*d^-1*sin(c+d*x)^3*(17B+19C)+1//5*a^3*d^-1*(17B+19C)*sin(c+d*x)+1//15*d^-1*cos(c+d*x)^4*(a^3+a^3*sec(c+d*x))*(3C+4B)*sin(c+d*x)+1//16*a^3*d^-1*(23B+26C)*cos(c+d*x)*sin(c+d*x)+1//40*a^3*d^-1*cos(c+d*x)^3*(21B+22C)*sin(c+d*x)+1//6*B*a*d^-1*(a+a*sec(c+d*x))^2*cos(c+d*x)^5*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*a^-1*d^-1*(-3C+3B)*arctanh(sin(c+d*x))+-1*a^-1*d^-1*(-4C+3B)*tan(c+d*x)+-1//3*a^-1*d^-1*tan(c+d*x)^3*(-4C+3B)+d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^3*(B+-1C)*tan(c+d*x)+(1/2)*a^-1*d^-1*(-3C+3B)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^-1*d^-1*(-2C+2B)*tan(c+d*x)+-1//2*a^-1*d^-1*(-3C+2B)*arctanh(sin(c+d*x))+d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^2*(B+-1C)*tan(c+d*x)+-1//2*a^-1*d^-1*(-3C+2B)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*(B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(C*a^-1*d^-1*tan(c+d*x)+a^-1*d^-1*(B+-1C)*arctanh(sin(c+d*x))+-1*d^-1*(a+a*sec(c+d*x))^-1*(B+-1C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(C*a^-1*d^-1*arctanh(sin(c+d*x))+a^-1*d^-1*(1+sec(c+d*x))^-1*(B+-1C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*(B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(B*x*a^-1+-1*d^-1*(a+a*sec(c+d*x))^-1*(B+-1C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1*x*a^-1*(B+-1C)+a^-1*d^-1*(-1C+2B)*sin(c+d*x)+-1*d^-1*(a+a*sec(c+d*x))^-1*(B+-1C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*x*a^-1*(-2C+3B)+-1*a^-1*d^-1*(-2C+2B)*sin(c+d*x)+(1/2)*a^-1*d^-1*(-2C+3B)*cos(c+d*x)*sin(c+d*x)+-1*d^-1*(a+a*sec(c+d*x))^-1*(B+-1C)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^4*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//2*x*a^-1*(-3C+3B)+a^-1*d^-1*(-3C+4B)*sin(c+d*x)+-1//3*a^-1*d^-1*sin(c+d*x)^3*(-3C+4B)+-1*d^-1*(a+a*sec(c+d*x))^-1*cos(c+d*x)^2*(B+-1C)*sin(c+d*x)+-1//2*a^-1*d^-1*(-3C+3B)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//2*a^-2*d^-1*(-7C+4B)*arctanh(sin(c+d*x))+1//3*a^-2*d^-1*(-16C+10B)*tan(c+d*x)+-1//2*a^-2*d^-1*(-7C+4B)*sec(c+d*x)*tan(c+d*x)+1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^3*(B+-1C)*tan(c+d*x)+1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^2*(-8C+5B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^-2*d^-1*(B+-2C)*arctanh(sin(c+d*x))+-1//3*a^-2*d^-1*(B+-4C)*tan(c+d*x)+-1*a^-2*d^-1*(1+sec(c+d*x))^-1*(B+-2C)*tan(c+d*x)+1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^2*(B+-1C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*(B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(C*a^-2*d^-1*arctanh(sin(c+d*x))+-1//3*d^-1*(a+a*sec(c+d*x))^-2*(B+-1C)*tan(c+d*x)+1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*(-5C+2B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//3*d^-1*(a+a*sec(c+d*x))^-2*(B+-1C)*tan(c+d*x)+1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*(B+2C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*(B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(B*x*a^-2+-1//3*d^-1*(a+a*sec(c+d*x))^-2*(B+-1C)*tan(c+d*x)+-1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*(-1C+4B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1*x*a^-2*(-1C+2B)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*(B+-1C)*sin(c+d*x)+1//3*a^-2*d^-1*(-4C+10B)*sin(c+d*x)+-1*a^-2*d^-1*(1+sec(c+d*x))^-1*(-1C+2B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*x*a^-2*(-4C+7B)+-1//3*a^-2*d^-1*(-10C+16B)*sin(c+d*x)+(1/2)*a^-2*d^-1*(-4C+7B)*cos(c+d*x)*sin(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*(B+-1C)*cos(c+d*x)*sin(c+d*x)+-1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*(-5C+8B)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^4*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//2*x*a^-2*(-7C+10B)+a^-2*d^-1*(-8C+12B)*sin(c+d*x)+-1//3*a^-2*d^-1*sin(c+d*x)^3*(-8C+12B)+-1//2*a^-2*d^-1*(-7C+10B)*cos(c+d*x)*sin(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)^2*(B+-1C)*sin(c+d*x)+-1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*cos(c+d*x)^2*(-7C+10B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^4*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//2*a^-3*d^-1*(-13C+6B)*arctanh(sin(c+d*x))+1//15*a^-3*d^-1*(-152C+72B)*tan(c+d*x)+-1//2*a^-3*d^-1*(-13C+6B)*sec(c+d*x)*tan(c+d*x)+1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^4*(B+-1C)*tan(c+d*x)+1//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^2*(-76C+36B)*tan(c+d*x)+1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^3*(-11C+6B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^-3*d^-1*(B+-3C)*arctanh(sin(c+d*x))+-1*d^-1*(a^3+a^3*sec(c+d*x))^-1*(B+-3C)*tan(c+d*x)+-1//15*a^-3*d^-1*(-27C+7B)*tan(c+d*x)+1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^3*(B+-1C)*tan(c+d*x)+1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^2*(-9C+4B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(C*a^-3*d^-1*arctanh(sin(c+d*x))+1//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*(-29C+4B)*tan(c+d*x)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*(-7C+2B)*tan(c+d*x)+1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^2*(B+-1C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*(B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(-1//5*d^-1*(a+a*sec(c+d*x))^-3*(B+-1C)*tan(c+d*x)+1//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*(3B+7C)*tan(c+d*x)+1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*(-8C+3B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//5*d^-1*(a+a*sec(c+d*x))^-3*(B+-1C)*tan(c+d*x)+1//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*(2B+3C)*tan(c+d*x)+1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*(2B+3C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*(B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(B*x*a^-3+-1//5*d^-1*(a+a*sec(c+d*x))^-3*(B+-1C)*tan(c+d*x)+-1//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*(-2C+22B)*tan(c+d*x)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*(-2C+7B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1*x*a^-3*(-1C+3B)+-1*d^-1*(a^3+a^3*sec(c+d*x))^-1*(-1C+3B)*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*(B+-1C)*sin(c+d*x)+1//15*a^-3*d^-1*(-22C+72B)*sin(c+d*x)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*(-4C+9B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*x*a^-3*(-6C+13B)+-1//15*a^-3*d^-1*(-72C+152B)*sin(c+d*x)+(1/2)*a^-3*d^-1*(-6C+13B)*cos(c+d*x)*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*(B+-1C)*cos(c+d*x)*sin(c+d*x)+-1//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*(-36C+76B)*cos(c+d*x)*sin(c+d*x)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*(-6C+11B)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^4*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//3465*d^-1*(a+a*sec(c+d*x))^(1/2)*(640C+704B)*tan(c+d*x)+1//1155*a^-1*d^-1*(a+a*sec(c+d*x))^3//2*(320C+352B)*tan(c+d*x)+32//495*a*d^-1*(a+a*sec(c+d*x))^-1//2*(10C+11B)*tan(c+d*x)+2//11*C*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5*tan(c+d*x)+2//99*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^4*(10C+11B)*tan(c+d*x)+16//693*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*(10C+11B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//315*d^-1*(a+a*sec(c+d*x))^(1/2)*(64C+72B)*tan(c+d*x)+1//105*a^-1*d^-1*(a+a*sec(c+d*x))^3//2*(32C+36B)*tan(c+d*x)+4//45*a*d^-1*(a+a*sec(c+d*x))^-1//2*(8C+9B)*tan(c+d*x)+2//9*C*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^4*tan(c+d*x)+2//63*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*(8C+9B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//105*d^-1*(a+a*sec(c+d*x))^(1/2)*(24C+28B)*tan(c+d*x)+1//35*a^-1*d^-1*(a+a*sec(c+d*x))^3//2*(12C+14B)*tan(c+d*x)+2//15*a*d^-1*(a+a*sec(c+d*x))^-1//2*(6C+7B)*tan(c+d*x)+2//7*C*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*(B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//15*d^-1*(a+a*sec(c+d*x))^(1/2)*(-4C+10B)*tan(c+d*x)+2//5*C*a^-1*d^-1*(a+a*sec(c+d*x))^3//2*tan(c+d*x)+2//15*a*d^-1*(a+a*sec(c+d*x))^-1//2*(5B+7C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//3*C*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x)+2//3*a*d^-1*(a+a*sec(c+d*x))^-1//2*(C+3B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*(B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(2*B*a^(1/2)*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2*C*a*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^(1/2)*d^-1*(B+2C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+B*a*d^-1*(a+a*sec(c+d*x))^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//4*a^(1/2)*d^-1*(3B+4C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//4*a*d^-1*(a+a*sec(c+d*x))^-1//2*(3B+4C)*sin(c+d*x)+(1/2)*B*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^4*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//8*a^(1/2)*d^-1*(5B+6C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//8*a*d^-1*(a+a*sec(c+d*x))^-1//2*(5B+6C)*sin(c+d*x)+1//3*B*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*sin(c+d*x)+1//12*a*d^-1*(a+a*sec(c+d*x))^-1//2*(5B+6C)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//1155*d^-1*(a+a*sec(c+d*x))^3//2*(672C+748B)*tan(c+d*x)+-8//3465*a*d^-1*(a+a*sec(c+d*x))^(1/2)*(168C+187B)*tan(c+d*x)+4//495*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(168C+187B)*tan(c+d*x)+2//11*C*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^4*tan(c+d*x)+2//99*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^4*(11B+12C)*tan(c+d*x)+2//693*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*(168C+187B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//105*d^-1*(a+a*sec(c+d*x))^3//2*(68C+78B)*tan(c+d*x)+-4//315*a*d^-1*(a+a*sec(c+d*x))^(1/2)*(34C+39B)*tan(c+d*x)+2//45*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(34C+39B)*tan(c+d*x)+2//9*C*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3*tan(c+d*x)+2//63*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*(9B+10C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*(B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//35*d^-1*(a+a*sec(c+d*x))^3//2*(-4C+14B)*tan(c+d*x)+2//7*C*a^-1*d^-1*(a+a*sec(c+d*x))^5//2*tan(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^(1/2)*(19C+21B)*tan(c+d*x)+8//105*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(19C+21B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//5*C*d^-1*(a+a*sec(c+d*x))^3//2*tan(c+d*x)+2//15*a*d^-1*(a+a*sec(c+d*x))^(1/2)*(3C+5B)*tan(c+d*x)+8//15*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(3C+5B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*(B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(2*B*a^3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//3*C*a*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x)+2//3*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(3B+4C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^3//2*d^-1*(2C+3B)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(B+-2C)*sin(c+d*x)+2*C*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//4*a^3//2*d^-1*(7B+12C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//4*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(4C+5B)*sin(c+d*x)+(1/2)*B*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^4*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//8*a^3//2*d^-1*(11B+14C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//8*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(11B+14C)*sin(c+d*x)+1//3*B*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^2*sin(c+d*x)+1//12*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(6C+7B)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^5*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//64*a^3//2*d^-1*(75B+88C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//64*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(75B+88C)*sin(c+d*x)+1//4*B*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^3*sin(c+d*x)+1//24*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*(8C+9B)*sin(c+d*x)+1//96*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(75B+88C)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-8//45045*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(4184C+4615B)*tan(c+d*x)+4//6435*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(4184C+4615B)*tan(c+d*x)+4//15015*a*d^-1*(a+a*sec(c+d*x))^3//2*(4184C+4615B)*tan(c+d*x)+2//13*C*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^4*tan(c+d*x)+2//143*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^4*(13B+16C)*tan(c+d*x)+2//1287*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^4*(280C+299B)*tan(c+d*x)+2//9009*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*(4184C+4615B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-4//3465*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(710C+803B)*tan(c+d*x)+2//495*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(710C+803B)*tan(c+d*x)+2//1155*a*d^-1*(a+a*sec(c+d*x))^3//2*(710C+803B)*tan(c+d*x)+2//11*C*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^3*tan(c+d*x)+2//99*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3*(11B+14C)*tan(c+d*x)+2//693*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*(194C+209B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*(B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//63*d^-1*(a+a*sec(c+d*x))^5//2*(-4C+18B)*tan(c+d*x)+2//9*C*a^-1*d^-1*(a+a*sec(c+d*x))^7//2*tan(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^3//2*(13C+15B)*tan(c+d*x)+16//315*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(13C+15B)*tan(c+d*x)+64//315*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(13C+15B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//7*C*d^-1*(a+a*sec(c+d*x))^5//2*tan(c+d*x)+2//35*a*d^-1*(a+a*sec(c+d*x))^3//2*(5C+7B)*tan(c+d*x)+16//105*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(5C+7B)*tan(c+d*x)+64//105*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(5C+7B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*(B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(2*B*a^5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//5*C*a*d^-1*(a+a*sec(c+d*x))^3//2*tan(c+d*x)+2//15*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(5B+8C)*tan(c+d*x)+2//15*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(32C+35B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^5//2*d^-1*(2C+5B)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(B+2C)*sin(c+d*x)+-1//3*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(3B+14C)*sin(c+d*x)+2//3*C*a*d^-1*(a+a*sec(c+d*x))^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//4*a^5//2*d^-1*(19B+20C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(B+-4C)*sin(c+d*x)+1//4*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(-4C+9B)*sin(c+d*x)+(1/2)*B*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^4*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//8*a^5//2*d^-1*(25B+38C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//24*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(49B+54C)*sin(c+d*x)+1//3*B*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^2*sin(c+d*x)+1//4*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(2C+3B)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^5*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//64*a^5//2*d^-1*(163B+200C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//64*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(163B+200C)*sin(c+d*x)+1//4*B*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^3*sin(c+d*x)+1//24*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^2*(8C+11B)*sin(c+d*x)+1//96*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(95B+104C)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^6*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//128*a^5//2*d^-1*(283B+326C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//128*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(283B+326C)*sin(c+d*x)+1//5*B*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^4*sin(c+d*x)+1//40*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^3*(10C+13B)*sin(c+d*x)+1//192*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(283B+326C)*cos(c+d*x)*sin(c+d*x)+1//240*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*(157B+170C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^4*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//315*d^-1*(a+a*sec(c+d*x))^-1//2*(-572C+444B)*tan(c+d*x)+2^(1/2)*a^-1//2*d^-1*(B+-1C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//105*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*(-38C+6B)*tan(c+d*x)+1//63*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*(-2C+18B)*tan(c+d*x)+1//315*a^-1*d^-1*(a+a*sec(c+d*x))^(1/2)*(-58C+186B)*tan(c+d*x)+2//9*C*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^4*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//105*d^-1*(a+a*sec(c+d*x))^-1//2*(-148C+196B)*tan(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*(B+-1C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//105*a^-1*d^-1*(a+a*sec(c+d*x))^(1/2)*(-62C+14B)*tan(c+d*x)+1//35*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*(-2C+14B)*tan(c+d*x)+2//7*C*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//15*d^-1*(a+a*sec(c+d*x))^-1//2*(-28C+20B)*tan(c+d*x)+2^(1/2)*a^-1//2*d^-1*(B+-1C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//15*a^-1*d^-1*(a+a*sec(c+d*x))^(1/2)*(-2C+10B)*tan(c+d*x)+2//5*C*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*(B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//3*d^-1*(a+a*sec(c+d*x))^-1//2*(-4C+6B)*tan(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*(B+-1C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//3*C*a^-1*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2*C*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+2^(1/2)*a^-1//2*d^-1*(B+-1C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*(B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(2*B*a^-1//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1*2^(1/2)*a^-1//2*d^-1*(B+-1C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(B*d^-1*(a+a*sec(c+d*x))^-1//2*sin(c+d*x)+-1*a^-1//2*d^-1*(B+-2C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2^(1/2)*a^-1//2*d^-1*(B+-1C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-1//2*(B+-4C)*sin(c+d*x)+1//4*a^-1//2*d^-1*(-4C+7B)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*B*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)*sin(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*(B+-1C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^4*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//8*a^-1//2*d^-1*(-14C+9B)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//8*d^-1*(a+a*sec(c+d*x))^-1//2*(-2C+7B)*sin(c+d*x)+2^(1/2)*a^-1//2*d^-1*(B+-1C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//12*d^-1*(a+a*sec(c+d*x))^-1//2*(B+-6C)*cos(c+d*x)*sin(c+d*x)+1//3*B*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^4*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^4*(B+-1C)*tan(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*(-19C+15B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//210*a^-2*d^-1*(a+a*sec(c+d*x))^(1/2)*(-397C+273B)*tan(c+d*x)+1//105*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(-799C+651B)*tan(c+d*x)+-1//14*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*(-11C+7B)*tan(c+d*x)+1//70*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*(-67C+63B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3*(B+-1C)*tan(c+d*x)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(-93C+65B)*tan(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(-15C+11B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//30*a^-2*d^-1*(a+a*sec(c+d*x))^(1/2)*(-39C+35B)*tan(c+d*x)+-1//10*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*(-9C+5B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^2*(B+-1C)*tan(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*(-11C+7B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//6*a^-2*d^-1*(a+a*sec(c+d*x))^(1/2)*(-7C+3B)*tan(c+d*x)+1//3*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(-13C+9B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*(B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*(B+-1C)*tan(c+d*x)+2*C*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(-7C+3B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*d^-1*(a+a*sec(c+d*x))^-3//2*(B+-1C)*tan(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(B+3C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*(B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(2*B*a^-3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*(B+-1C)*tan(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*(-1C+5B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1*a^-3//2*d^-1*(-2C+3B)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*(B+-1C)*sin(c+d*x)+(1/2)*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(-1C+3B)*sin(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(-5C+9B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//4*a^-3//2*d^-1*(-12C+19B)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*(B+-1C)*cos(c+d*x)*sin(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*(-9C+13B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(-6C+7B)*sin(c+d*x)+(1/2)*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(-1C+2B)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^4*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//120*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*(-1729C+985B)*tan(c+d*x)+1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^4*(B+-1C)*tan(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(-283C+163B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//240*a^-3*d^-1*(a+a*sec(c+d*x))^(1/2)*(-787C+475B)*tan(c+d*x)+-1//80*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*(-157C+85B)*tan(c+d*x)+1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3*(-21C+13B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//32*2^(1/2)*a^-5//2*d^-1*(-163C+75B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//48*a^-3*d^-1*(a+a*sec(c+d*x))^(1/2)*(-95C+39B)*tan(c+d*x)+1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^3*(B+-1C)*tan(c+d*x)+1//24*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*(-197C+93B)*tan(c+d*x)+1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^2*(-17C+9B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//4*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*(B+-9C)*tan(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*(-13C+5B)*tan(c+d*x)+1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^2*(B+-1C)*tan(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(-75C+19B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*(B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*(B+-1C)*tan(c+d*x)+1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*(-13C+5B)*tan(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(5B+19C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//4*d^-1*(a+a*sec(c+d*x))^-5//2*(B+-1C)*tan(c+d*x)+1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*(3B+5C)*tan(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(3B+5C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*(B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(2*B*a^-5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*(B+-1C)*tan(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*(-3C+11B)*tan(c+d*x)+-1//32*2^(1/2)*a^-5//2*d^-1*(-3C+43B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1*a^-5//2*d^-1*(-2C+5B)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*(B+-1C)*sin(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*(-7C+15B)*sin(c+d*x)+1//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*(-11C+35B)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(-43C+115B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate(sec(c+d*x)^3*(a+a*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//5*a*d^-1*(4C+5A+5B)*tan(c+d*x)+1//8*a*d^-1*(3B+3C+4A)*arctanh(sin(c+d*x))+1//15*a*d^-1*tan(c+d*x)^3*(4C+5A+5B)+1//4*a*d^-1*sec(c+d*x)^3*(B+C)*tan(c+d*x)+1//5*C*a*d^-1*sec(c+d*x)^4*tan(c+d*x)+1//8*a*d^-1*(3B+3C+4A)*sec(c+d*x)*tan(c+d*x))
@test integrate(sec(c+d*x)^2*(a+a*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//3*a*d^-1*(2B+2C+3A)*tan(c+d*x)+1//8*a*d^-1*(3C+4A+4B)*arctanh(sin(c+d*x))+1//3*a*d^-1*sec(c+d*x)^2*(B+C)*tan(c+d*x)+1//4*C*a*d^-1*sec(c+d*x)^3*tan(c+d*x)+1//8*a*d^-1*(3C+4A+4B)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :((1/2)*a*d^-1*(B+C+2A)*arctanh(sin(c+d*x))+1//3*a*d^-1*(2C+3A+3B)*tan(c+d*x)+(1/2)*a*d^-1*(B+C)*sec(c+d*x)*tan(c+d*x)+1//3*C*a*d^-1*sec(c+d*x)^2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(A*a*x+a*d^-1*(B+C)*tan(c+d*x)+(1/2)*a*d^-1*(C+2A+2B)*arctanh(sin(c+d*x))+(1/2)*C*a*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(a*x*(A+B)+A*a*d^-1*sin(c+d*x)+C*a*d^-1*tan(c+d*x)+a*d^-1*(B+C)*arctanh(sin(c+d*x)))
@test integrate(cos(c+d*x)^2*(a+a*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*a*x*(A+2B+2C)+C*a*d^-1*arctanh(sin(c+d*x))+a*d^-1*(A+B)*sin(c+d*x)+(1/2)*A*a*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^3*(a+a*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*a*x*(A+B+2C)+1//3*a*d^-1*(2A+3B+3C)*sin(c+d*x)+(1/2)*a*d^-1*(A+B)*cos(c+d*x)*sin(c+d*x)+1//3*A*a*d^-1*cos(c+d*x)^2*sin(c+d*x))
@test integrate(cos(c+d*x)^4*(a+a*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//8*a*x*(3A+4B+4C)+a*d^-1*(A+B+C)*sin(c+d*x)+-1//3*a*d^-1*sin(c+d*x)^3*(A+B)+1//4*A*a*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//8*a*d^-1*(3A+4B+4C)*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^5*(a+a*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//8*a*x*(3A+3B+4C)+-1//15*a*d^-1*sin(c+d*x)^3*(4A+5B+5C)+1//5*a*d^-1*(4A+5B+5C)*sin(c+d*x)+1//4*a*d^-1*cos(c+d*x)^3*(A+B)*sin(c+d*x)+1//5*A*a*d^-1*cos(c+d*x)^4*sin(c+d*x)+1//8*a*d^-1*(3A+3B+4C)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//5*a^2*d^-1*(8C+9B+10A)*tan(c+d*x)+1//15*a^2*d^-1*tan(c+d*x)^3*(8C+9B+10A)+1//16*a^2*d^-1*(11C+12B+14A)*arctanh(sin(c+d*x))+1//6*C*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^3*tan(c+d*x)+1//15*d^-1*sec(c+d*x)^3*(C+3B)*(a^2+a^2*sec(c+d*x))*tan(c+d*x)+1//16*a^2*d^-1*(11C+12B+14A)*sec(c+d*x)*tan(c+d*x)+1//40*a^2*d^-1*sec(c+d*x)^3*(9C+10A+12B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//6*a^2*d^-1*(6C+7B+8A)*tan(c+d*x)+1//8*a^2*d^-1*(6C+7B+8A)*arctanh(sin(c+d*x))+1//60*d^-1*(a+a*sec(c+d*x))^2*(-5B+6C+20A)*tan(c+d*x)+1//5*C*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^2*tan(c+d*x)+1//20*a^-1*d^-1*(a+a*sec(c+d*x))^3*(2C+5B)*tan(c+d*x)+1//24*a^2*d^-1*(6C+7B+8A)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//6*a^2*d^-1*(7C+8B+12A)*tan(c+d*x)+1//8*a^2*d^-1*(7C+8B+12A)*arctanh(sin(c+d*x))+1//12*d^-1*(a+a*sec(c+d*x))^2*(-1C+4B)*tan(c+d*x)+1//4*C*a^-1*d^-1*(a+a*sec(c+d*x))^3*tan(c+d*x)+1//24*a^2*d^-1*(7C+8B+12A)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(A*x*a^2+(1/2)*a^2*d^-1*(2A+2C+3B)*tan(c+d*x)+(1/2)*a^2*d^-1*(2C+3B+4A)*arctanh(sin(c+d*x))+1//3*C*d^-1*(a+a*sec(c+d*x))^2*tan(c+d*x)+1//6*d^-1*(a^2+a^2*sec(c+d*x))*(2C+3B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(x*a^2*(B+2A)+A*d^-1*(a+a*sec(c+d*x))^2*sin(c+d*x)+(1/2)*a^2*d^-1*(2A+3C+4B)*arctanh(sin(c+d*x))+-1//2*a^2*d^-1*(-3C+-2B+2A)*tan(c+d*x)+-1//2*d^-1*(a^2+a^2*sec(c+d*x))*(-1C+2A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*x*a^2*(2C+3A+4B)+a^2*d^-1*(B+2C)*arctanh(sin(c+d*x))+(1/2)*a^2*d^-1*(-2C+2B+3A)*sin(c+d*x)+-1//2*d^-1*(A+-2C)*(a^2+a^2*sec(c+d*x))*sin(c+d*x)+(1/2)*A*d^-1*(a+a*sec(c+d*x))^2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*x*a^2*(2A+3B+4C)+C*a^2*d^-1*arctanh(sin(c+d*x))+(1/2)*a^2*d^-1*(2A+2C+3B)*sin(c+d*x)+1//3*A*d^-1*(a+a*sec(c+d*x))^2*cos(c+d*x)^2*sin(c+d*x)+1//6*d^-1*(a^2+a^2*sec(c+d*x))*(2A+3B)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//8*x*a^2*(7A+8B+12C)+1//6*a^2*d^-1*(7A+8B+12C)*sin(c+d*x)+1//4*A*d^-1*(a+a*sec(c+d*x))^2*cos(c+d*x)^3*sin(c+d*x)+1//6*d^-1*(a+a*sec(c+d*x))^2*cos(c+d*x)^2*(A+2B)*sin(c+d*x)+1//24*a^2*d^-1*(7A+8B+12C)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^5*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//8*x*a^2*(6A+7B+8C)+1//15*a^2*d^-1*(18A+20B+25C)*sin(c+d*x)+1//5*A*d^-1*(a+a*sec(c+d*x))^2*cos(c+d*x)^4*sin(c+d*x)+1//8*a^2*d^-1*(6A+7B+8C)*cos(c+d*x)*sin(c+d*x)+1//20*d^-1*cos(c+d*x)^3*(a^2+a^2*sec(c+d*x))*(2A+5B)*sin(c+d*x)+1//60*a^2*d^-1*cos(c+d*x)^2*(18A+20C+25B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^6*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//16*x*a^2*(11A+12B+14C)+-1//15*a^2*d^-1*sin(c+d*x)^3*(8A+9B+10C)+1//5*a^2*d^-1*(8A+9B+10C)*sin(c+d*x)+1//6*A*d^-1*(a+a*sec(c+d*x))^2*cos(c+d*x)^5*sin(c+d*x)+1//15*d^-1*cos(c+d*x)^4*(A+3B)*(a^2+a^2*sec(c+d*x))*sin(c+d*x)+1//16*a^2*d^-1*(11A+12B+14C)*cos(c+d*x)*sin(c+d*x)+1//40*a^2*d^-1*cos(c+d*x)^3*(9A+10C+12B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//16*a^3*d^-1*(21C+23B+26A)*arctanh(sin(c+d*x))+1//35*a^3*d^-1*(108C+119B+133A)*tan(c+d*x)+1//105*a^3*d^-1*tan(c+d*x)^3*(108C+119B+133A)+1//7*C*d^-1*(a+a*sec(c+d*x))^3*sec(c+d*x)^3*tan(c+d*x)+1//15*d^-1*sec(c+d*x)^3*(a^3+a^3*sec(c+d*x))*(3A+3C+4B)*tan(c+d*x)+1//16*a^3*d^-1*(21C+23B+26A)*sec(c+d*x)*tan(c+d*x)+1//280*a^3*d^-1*sec(c+d*x)^3*(129C+147B+154A)*tan(c+d*x)+1//42*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*sec(c+d*x)^3*(3C+7B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//10*a^3*d^-1*(23C+26B+30A)*tan(c+d*x)+1//16*a^3*d^-1*(23C+26B+30A)*arctanh(sin(c+d*x))+1//120*a^3*d^-1*tan(c+d*x)^3*(23C+26B+30A)+1//120*d^-1*(a+a*sec(c+d*x))^3*(-6B+7C+30A)*tan(c+d*x)+1//6*C*d^-1*(a+a*sec(c+d*x))^3*sec(c+d*x)^2*tan(c+d*x)+1//10*a^-1*d^-1*(a+a*sec(c+d*x))^4*(C+2B)*tan(c+d*x)+3//80*a^3*d^-1*(23C+26B+30A)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//5*a^3*d^-1*(13C+15B+20A)*tan(c+d*x)+1//8*a^3*d^-1*(13C+15B+20A)*arctanh(sin(c+d*x))+1//20*d^-1*(a+a*sec(c+d*x))^3*(-1C+5B)*tan(c+d*x)+1//60*a^3*d^-1*tan(c+d*x)^3*(13C+15B+20A)+1//5*C*a^-1*d^-1*(a+a*sec(c+d*x))^4*tan(c+d*x)+3//40*a^3*d^-1*(13C+15B+20A)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(A*x*a^3+1//4*C*d^-1*(a+a*sec(c+d*x))^3*tan(c+d*x)+1//8*a^3*d^-1*(15C+20B+28A)*arctanh(sin(c+d*x))+1//24*d^-1*(a^3+a^3*sec(c+d*x))*(12A+15C+20B)*tan(c+d*x)+5//8*a^3*d^-1*(3C+4A+4B)*tan(c+d*x)+1//12*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*(3C+4B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(x*a^3*(B+3A)+A*d^-1*(a+a*sec(c+d*x))^3*sin(c+d*x)+(1/2)*a^3*d^-1*(5C+6A+7B)*arctanh(sin(c+d*x))+-1//6*d^-1*(a^3+a^3*sec(c+d*x))*(-5C+-3B+6A)*tan(c+d*x)+5//2*a^3*d^-1*(B+C)*tan(c+d*x)+-1//3*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*(-1C+3A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*x*a^3*(2C+6B+7A)+(1/2)*a^3*d^-1*(2A+6B+7C)*arctanh(sin(c+d*x))+-1//2*d^-1*(a^3+a^3*sec(c+d*x))*(A+-4C+-2B)*sin(c+d*x)+5//2*a^3*d^-1*(A+-1C)*sin(c+d*x)+(1/2)*A*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)*sin(c+d*x)+-1//2*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*(A+-1C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*x*a^3*(5A+6C+7B)+a^3*d^-1*(B+3C)*arctanh(sin(c+d*x))+-1//6*d^-1*(a^3+a^3*sec(c+d*x))*(-6C+3B+5A)*sin(c+d*x)+5//2*a^3*d^-1*(A+B)*sin(c+d*x)+1//3*A*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)^2*sin(c+d*x)+(1/2)*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*(A+B)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//8*x*a^3*(15A+20B+28C)+C*a^3*d^-1*arctanh(sin(c+d*x))+5//8*a^3*d^-1*(3A+4B+4C)*sin(c+d*x)+1//4*A*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)^3*sin(c+d*x)+1//24*d^-1*(a^3+a^3*sec(c+d*x))*(12C+15A+20B)*cos(c+d*x)*sin(c+d*x)+1//12*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*cos(c+d*x)^2*(3A+4B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^5*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//8*x*a^3*(13A+15B+20C)+-1//60*a^3*d^-1*sin(c+d*x)^3*(13A+15B+20C)+1//5*a^3*d^-1*(13A+15B+20C)*sin(c+d*x)+1//5*A*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)^4*sin(c+d*x)+1//20*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)^3*(3A+5B)*sin(c+d*x)+3//40*a^3*d^-1*(13A+15B+20C)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^6*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//16*x*a^3*(23A+26B+30C)+1//15*a^3*d^-1*(34A+38B+45C)*sin(c+d*x)+1//6*A*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)^5*sin(c+d*x)+1//16*a^3*d^-1*(23A+26B+30C)*cos(c+d*x)*sin(c+d*x)+1//120*a^3*d^-1*cos(c+d*x)^2*(73A+86B+90C)*sin(c+d*x)+1//120*d^-1*cos(c+d*x)^3*(a^3+a^3*sec(c+d*x))*(30C+31A+42B)*sin(c+d*x)+1//10*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*cos(c+d*x)^4*(A+2B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^7*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//16*x*a^3*(21A+23B+26C)+-1//105*a^3*d^-1*sin(c+d*x)^3*(108A+119B+133C)+1//35*a^3*d^-1*(108A+119B+133C)*sin(c+d*x)+1//7*A*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)^6*sin(c+d*x)+1//15*d^-1*cos(c+d*x)^4*(a^3+a^3*sec(c+d*x))*(3A+3C+4B)*sin(c+d*x)+1//16*a^3*d^-1*(21A+23B+26C)*cos(c+d*x)*sin(c+d*x)+1//280*a^3*d^-1*cos(c+d*x)^3*(129A+147B+154C)*sin(c+d*x)+1//42*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*cos(c+d*x)^5*(3A+7B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*sec(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//16*a^4*d^-1*(44C+49B+56A)*arctanh(sin(c+d*x))+1//210*d^-1*(a+a*sec(c+d*x))^4*(-7B+8C+42A)*tan(c+d*x)+2//105*a^4*d^-1*tan(c+d*x)^3*(44C+49B+56A)+4//35*a^4*d^-1*(44C+49B+56A)*tan(c+d*x)+1//7*C*d^-1*(a+a*sec(c+d*x))^4*sec(c+d*x)^2*tan(c+d*x)+1//42*a^-1*d^-1*(a+a*sec(c+d*x))^5*(4C+7B)*tan(c+d*x)+1//280*a^4*d^-1*sec(c+d*x)^3*(44C+49B+56A)*tan(c+d*x)+27//560*a^4*d^-1*(44C+49B+56A)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//30*d^-1*(a+a*sec(c+d*x))^4*(-1C+6B)*tan(c+d*x)+2//15*a^4*d^-1*tan(c+d*x)^3*(7C+8B+10A)+4//5*a^4*d^-1*(7C+8B+10A)*tan(c+d*x)+7//16*a^4*d^-1*(7C+8B+10A)*arctanh(sin(c+d*x))+1//6*C*a^-1*d^-1*(a+a*sec(c+d*x))^5*tan(c+d*x)+1//40*a^4*d^-1*sec(c+d*x)^3*(7C+8B+10A)*tan(c+d*x)+27//80*a^4*d^-1*(7C+8B+10A)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(A*x*a^4+1//5*C*d^-1*(a+a*sec(c+d*x))^4*tan(c+d*x)+1//8*a^4*d^-1*(28C+35B+40A)*tan(c+d*x)+1//8*a^4*d^-1*(28C+35B+48A)*arctanh(sin(c+d*x))+1//24*d^-1*(a^4+a^4*sec(c+d*x))*(28C+32A+35B)*tan(c+d*x)+1//60*d^-1*(a^2+a^2*sec(c+d*x))^2*(20A+28C+35B)*tan(c+d*x)+1//20*a*d^-1*(a+a*sec(c+d*x))^3*(4C+5B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(x*a^4*(B+4A)+A*d^-1*(a+a*sec(c+d*x))^4*sin(c+d*x)+-1//12*d^-1*(a^2+a^2*sec(c+d*x))^2*(-7C+-4B+12A)*tan(c+d*x)+-1//24*d^-1*(a^4+a^4*sec(c+d*x))*(-35C+-32B+12A)*tan(c+d*x)+1//8*a^4*d^-1*(35C+48B+52A)*arctanh(sin(c+d*x))+5//8*a^4*d^-1*(4A+7C+8B)*tan(c+d*x)+-1//4*a*d^-1*(a+a*sec(c+d*x))^3*(-1C+4A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*x*a^4*(2C+8B+13A)+(1/2)*a^4*d^-1*(8A+12C+13B)*arctanh(sin(c+d*x))+-1//2*d^-1*(a^2+a^2*sec(c+d*x))^2*(A+-1B+-2C)*sin(c+d*x)+1//6*d^-1*(a^4+a^4*sec(c+d*x))*(3A+18B+22C)*sin(c+d*x)+5//2*a^4*d^-1*(A+-1B+-2C)*sin(c+d*x)+(1/2)*A*d^-1*(a+a*sec(c+d*x))^4*cos(c+d*x)*sin(c+d*x)+-1//6*a*d^-1*(a+a*sec(c+d*x))^3*(-2C+3A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*x*a^4*(8C+12A+13B)+(1/2)*a^4*d^-1*(2A+8B+13C)*arctanh(sin(c+d*x))+-1//2*d^-1*(a^2+a^2*sec(c+d*x))^2*(B+-1C+2A)*sin(c+d*x)+-1//6*d^-1*(a^4+a^4*sec(c+d*x))*(-18C+-3B+8A)*sin(c+d*x)+5//2*a^4*d^-1*(B+-1C+2A)*sin(c+d*x)+1//3*A*d^-1*(a+a*sec(c+d*x))^4*cos(c+d*x)^2*sin(c+d*x)+1//6*a*d^-1*(a+a*sec(c+d*x))^3*(3B+4A)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//8*x*a^4*(35A+48B+52C)+a^4*d^-1*(B+4C)*arctanh(sin(c+d*x))+-1//24*d^-1*(a^4+a^4*sec(c+d*x))*(-12C+32B+35A)*sin(c+d*x)+5//8*a^4*d^-1*(4C+7A+8B)*sin(c+d*x)+1//4*A*d^-1*(a+a*sec(c+d*x))^4*cos(c+d*x)^3*sin(c+d*x)+1//8*d^-1*(a^2+a^2*sec(c+d*x))^2*(4C+7A+8B)*cos(c+d*x)*sin(c+d*x)+1//3*a*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)^2*(A+B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^5*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//8*x*a^4*(28A+35B+48C)+C*a^4*d^-1*arctanh(sin(c+d*x))+1//8*a^4*d^-1*(28A+35B+40C)*sin(c+d*x)+1//5*A*d^-1*(a+a*sec(c+d*x))^4*cos(c+d*x)^4*sin(c+d*x)+1//24*d^-1*(a^4+a^4*sec(c+d*x))*(28A+32C+35B)*cos(c+d*x)*sin(c+d*x)+1//60*d^-1*(a^2+a^2*sec(c+d*x))^2*cos(c+d*x)^2*(20C+28A+35B)*sin(c+d*x)+1//20*a*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)^3*(4A+5B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^6*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(7//16*x*a^4*(7A+8B+10C)+-2//15*a^4*d^-1*sin(c+d*x)^3*(7A+8B+10C)+4//5*a^4*d^-1*(7A+8B+10C)*sin(c+d*x)+1//6*A*d^-1*(a+a*sec(c+d*x))^4*cos(c+d*x)^5*sin(c+d*x)+1//15*d^-1*(a+a*sec(c+d*x))^4*cos(c+d*x)^4*(2A+3B)*sin(c+d*x)+1//40*a^4*d^-1*cos(c+d*x)^3*(7A+8B+10C)*sin(c+d*x)+27//80*a^4*d^-1*(7A+8B+10C)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^7*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//16*x*a^4*(44A+49B+56C)+1//105*a^4*d^-1*(454A+504B+581C)*sin(c+d*x)+1//7*A*d^-1*(a+a*sec(c+d*x))^4*cos(c+d*x)^6*sin(c+d*x)+1//16*a^4*d^-1*(44A+49B+56C)*cos(c+d*x)*sin(c+d*x)+1//70*d^-1*(a^2+a^2*sec(c+d*x))^2*cos(c+d*x)^4*(14C+16A+21B)*sin(c+d*x)+1//840*a^4*d^-1*cos(c+d*x)^2*(988A+1113B+1232C)*sin(c+d*x)+1//840*d^-1*cos(c+d*x)^3*(a^4+a^4*sec(c+d*x))*(436A+504C+511B)*sin(c+d*x)+1//42*a*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)^5*(4A+7B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^8*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//128*x*a^4*(323A+352B+392C)+-1//105*a^4*d^-1*sin(c+d*x)^3*(208A+227B+252C)+1//35*a^4*d^-1*(208A+227B+252C)*sin(c+d*x)+1//8*A*d^-1*(a+a*sec(c+d*x))^4*cos(c+d*x)^7*sin(c+d*x)+1//120*d^-1*cos(c+d*x)^4*(a^4+a^4*sec(c+d*x))*(49A+56B+56C)*sin(c+d*x)+1//128*a^4*d^-1*(323A+352B+392C)*cos(c+d*x)*sin(c+d*x)+1//336*d^-1*(a^2+a^2*sec(c+d*x))^2*cos(c+d*x)^5*(56C+61A+80B)*sin(c+d*x)+1//2240*a^4*d^-1*cos(c+d*x)^3*(2007A+2208B+2408C)*sin(c+d*x)+1//14*a*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)^6*(A+2B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1*a^-1*d^-1*(-4B+3A+4C)*tan(c+d*x)+-1//3*a^-1*d^-1*tan(c+d*x)^3*(-4B+3A+4C)+1//8*a^-1*d^-1*(-12B+12A+15C)*arctanh(sin(c+d*x))+-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^4*(A+C+-1B)*tan(c+d*x)+1//4*a^-1*d^-1*sec(c+d*x)^3*(-4B+4A+5C)*tan(c+d*x)+1//8*a^-1*d^-1*(-12B+12A+15C)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^-1*d^-1*(-3B+3A+4C)*tan(c+d*x)+-1//2*a^-1*d^-1*(-3B+2A+3C)*arctanh(sin(c+d*x))+1//3*a^-1*d^-1*tan(c+d*x)^3*(-3B+3A+4C)+-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^3*(A+C+-1B)*tan(c+d*x)+-1//2*a^-1*d^-1*(-3B+2A+3C)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*a^-1*d^-1*(-2B+2A+3C)*arctanh(sin(c+d*x))+-1*a^-1*d^-1*(A+-2B+2C)*tan(c+d*x)+(1/2)*a^-1*d^-1*(-2B+2A+3C)*sec(c+d*x)*tan(c+d*x)+-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^2*(A+C+-1B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(C*a^-1*d^-1*tan(c+d*x)+a^-1*d^-1*(B+-1C)*arctanh(sin(c+d*x))+a^-1*d^-1*(1+sec(c+d*x))^-1*(A+C+-1B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(A*x*a^-1+C*a^-1*d^-1*arctanh(sin(c+d*x))+-1*a^-1*d^-1*(1+sec(c+d*x))^-1*(A+C+-1B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(-1*x*a^-1*(A+-1B)+a^-1*d^-1*(C+-1B+2A)*sin(c+d*x)+-1*d^-1*(a+a*sec(c+d*x))^-1*(A+C+-1B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*x*a^-1*(-2B+2C+3A)+-1*a^-1*d^-1*(C+-2B+2A)*sin(c+d*x)+(1/2)*a^-1*d^-1*(-2B+2C+3A)*cos(c+d*x)*sin(c+d*x)+-1*d^-1*(a+a*sec(c+d*x))^-1*(A+C+-1B)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//2*x*a^-1*(-3B+2C+3A)+a^-1*d^-1*(-3B+3C+4A)*sin(c+d*x)+-1//3*a^-1*d^-1*sin(c+d*x)^3*(-3B+3C+4A)+-1*d^-1*(a+a*sec(c+d*x))^-1*cos(c+d*x)^2*(A+C+-1B)*sin(c+d*x)+-1//2*a^-1*d^-1*(-3B+2C+3A)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//8*x*a^-1*(-12B+12C+15A)+-1*a^-1*d^-1*(-4B+3C+4A)*sin(c+d*x)+1//3*a^-1*d^-1*sin(c+d*x)^3*(-4B+3C+4A)+-1*d^-1*(a+a*sec(c+d*x))^-1*cos(c+d*x)^3*(A+C+-1B)*sin(c+d*x)+1//4*a^-1*d^-1*cos(c+d*x)^3*(-4B+4C+5A)*sin(c+d*x)+1//8*a^-1*d^-1*(-12B+12C+15A)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^-2*d^-1*(-8B+5A+12C)*tan(c+d*x)+-1//2*a^-2*d^-1*(-7B+4A+10C)*arctanh(sin(c+d*x))+1//3*a^-2*d^-1*tan(c+d*x)^3*(-8B+5A+12C)+-1//2*a^-2*d^-1*(-7B+4A+10C)*sec(c+d*x)*tan(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^4*(A+C+-1B)*tan(c+d*x)+-1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^3*(-7B+4A+10C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*a^-2*d^-1*(-4B+2A+7C)*arctanh(sin(c+d*x))+-1//3*a^-2*d^-1*(-10B+4A+16C)*tan(c+d*x)+(1/2)*a^-2*d^-1*(-4B+2A+7C)*sec(c+d*x)*tan(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^3*(A+C+-1B)*tan(c+d*x)+-1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^2*(-5B+2A+8C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^-2*d^-1*(B+-2C)*arctanh(sin(c+d*x))+1//3*a^-2*d^-1*(A+-1B+4C)*tan(c+d*x)+-1*a^-2*d^-1*(1+sec(c+d*x))^-1*(B+-2C)*tan(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^2*(A+C+-1B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(A*x*a^-2+-1//3*d^-1*(a+a*sec(c+d*x))^-2*(A+C+-1B)*tan(c+d*x)+-1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*(-1B+-2C+4A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(-1*x*a^-2*(-1B+2A)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*(A+C+-1B)*sin(c+d*x)+1//3*a^-2*d^-1*(C+-4B+10A)*sin(c+d*x)+-1*a^-2*d^-1*(1+sec(c+d*x))^-1*(-1B+2A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*x*a^-2*(-4B+2C+7A)+-1//3*a^-2*d^-1*(-10B+4C+16A)*sin(c+d*x)+(1/2)*a^-2*d^-1*(-4B+2C+7A)*cos(c+d*x)*sin(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*(A+C+-1B)*cos(c+d*x)*sin(c+d*x)+-1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*(-5B+2C+8A)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//2*x*a^-2*(-7B+4C+10A)+a^-2*d^-1*(-8B+5C+12A)*sin(c+d*x)+-1//3*a^-2*d^-1*sin(c+d*x)^3*(-8B+5C+12A)+-1//2*a^-2*d^-1*(-7B+4C+10A)*cos(c+d*x)*sin(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)^2*(A+C+-1B)*sin(c+d*x)+-1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*cos(c+d*x)^2*(-7B+4C+10A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*a^-3*d^-1*(-6B+2A+13C)*arctanh(sin(c+d*x))+-1//15*a^-3*d^-1*(-72B+22A+152C)*tan(c+d*x)+(1/2)*a^-3*d^-1*(-6B+2A+13C)*sec(c+d*x)*tan(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^4*(A+C+-1B)*tan(c+d*x)+-1//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^2*(-36B+11A+76C)*tan(c+d*x)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^3*(A+-6B+11C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^-3*d^-1*(B+-3C)*arctanh(sin(c+d*x))+-1*d^-1*(a^3+a^3*sec(c+d*x))^-1*(B+-3C)*tan(c+d*x)+1//15*a^-3*d^-1*(-7B+2A+27C)*tan(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^3*(A+C+-1B)*tan(c+d*x)+1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^2*(A+-9C+4B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(C*a^-3*d^-1*arctanh(sin(c+d*x))+1//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*(-29C+4B+6A)*tan(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^2*(A+C+-1B)*tan(c+d*x)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*(-7C+2B+3A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*(2A+3B+7C)*tan(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*(A+C+-1B)*sec(c+d*x)*tan(c+d*x)+1//3*a^-1*d^-1*(a+a*sec(c+d*x))^-2*(A+-1C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(A*x*a^-3+-1//5*d^-1*(a+a*sec(c+d*x))^-3*(A+C+-1B)*tan(c+d*x)+-1//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*(-3C+-2B+22A)*tan(c+d*x)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*(-3C+-2B+7A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(-1*x*a^-3*(-1B+3A)+-1*d^-1*(a^3+a^3*sec(c+d*x))^-1*(-1B+3A)*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*(A+C+-1B)*sin(c+d*x)+1//15*a^-3*d^-1*(-22B+2C+72A)*sin(c+d*x)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*(-1C+-4B+9A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*x*a^-3*(-6B+2C+13A)+-1//15*a^-3*d^-1*(-72B+22C+152A)*sin(c+d*x)+(1/2)*a^-3*d^-1*(-6B+2C+13A)*cos(c+d*x)*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*(A+C+-1B)*cos(c+d*x)*sin(c+d*x)+-1//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*(-36B+11C+76A)*cos(c+d*x)*sin(c+d*x)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*(C+-6B+11A)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//2*x*a^-3*(-13B+6C+23A)+-1//15*a^-3*d^-1*sin(c+d*x)^3*(-76B+36C+136A)+1//5*a^-3*d^-1*(-76B+36C+136A)*sin(c+d*x)+-1//2*a^-3*d^-1*(-13B+6C+23A)*cos(c+d*x)*sin(c+d*x)+-1//3*d^-1*(a^3+a^3*sec(c+d*x))^-1*cos(c+d*x)^2*(-13B+6C+23A)*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*cos(c+d*x)^2*(A+C+-1B)*sin(c+d*x)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)^2*(-8B+3C+13A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*sec(c+d*x)^5*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*a^-4*d^-1*(-8B+2A+21C)*arctanh(sin(c+d*x))+-1//105*a^-4*d^-1*(-664B+160A+1728C)*tan(c+d*x)+(1/2)*a^-4*d^-1*(-8B+2A+21C)*sec(c+d*x)*tan(c+d*x)+-1//7*d^-1*(a+a*sec(c+d*x))^-4*sec(c+d*x)^5*(A+C+-1B)*tan(c+d*x)+-1//105*a^-4*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^2*(-332B+80A+864C)*tan(c+d*x)+-1//105*a^-4*d^-1*(1+sec(c+d*x))^-2*sec(c+d*x)^3*(-52B+10A+129C)*tan(c+d*x)+1//5*a^-1*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^4*(B+-2C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*sec(c+d*x)^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^-4*d^-1*(B+-4C)*arctanh(sin(c+d*x))+1//105*a^-4*d^-1*(-55B+6A+244C)*tan(c+d*x)+-1*a^-4*d^-1*(1+sec(c+d*x))^-1*(B+-4C)*tan(c+d*x)+-1//7*d^-1*(a+a*sec(c+d*x))^-4*sec(c+d*x)^4*(A+C+-1B)*tan(c+d*x)+1//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^3*(-12C+2A+5B)*tan(c+d*x)+1//105*a^-4*d^-1*(1+sec(c+d*x))^-2*sec(c+d*x)^2*(-88C+3A+25B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*sec(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(C*a^-4*d^-1*arctanh(sin(c+d*x))+-1//7*d^-1*(a+a*sec(c+d*x))^-4*sec(c+d*x)^3*(A+C+-1B)*tan(c+d*x)+-1//105*a^-4*d^-1*(1+sec(c+d*x))^-2*(-55C+6B+8A)*tan(c+d*x)+1//105*a^-4*d^-1*(1+sec(c+d*x))^-1*(-215C+12B+16A)*tan(c+d*x)+1//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^2*(-10C+3B+4A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*sec(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//7*d^-1*(a+a*sec(c+d*x))^-4*sec(c+d*x)^2*(A+C+-1B)*tan(c+d*x)+-1//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*(B+-8C+6A)*tan(c+d*x)+1//105*a^-4*d^-1*(1+sec(c+d*x))^-1*(8A+13B+36C)*tan(c+d*x)+1//105*a^-4*d^-1*(1+sec(c+d*x))^-2*(-54C+-2B+23A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//105*d^-1*(a^2+a^2*sec(c+d*x))^-2*(6A+8B+13C)*tan(c+d*x)+1//105*d^-1*(a^4+a^4*sec(c+d*x))^-1*(6A+8B+13C)*tan(c+d*x)+-1//7*d^-1*(a+a*sec(c+d*x))^-4*(A+C+-1B)*sec(c+d*x)*tan(c+d*x)+1//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*(-1B+-6C+8A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(A*x*a^-4+-1//7*d^-1*(a+a*sec(c+d*x))^-4*(A+C+-1B)*tan(c+d*x)+-1//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*(-4C+-3B+10A)*tan(c+d*x)+-1//105*a^-4*d^-1*(1+sec(c+d*x))^-1*(-8C+-6B+160A)*tan(c+d*x)+-1//105*a^-4*d^-1*(1+sec(c+d*x))^-2*(-8C+-6B+55A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(-1*x*a^-4*(-1B+4A)+-1//7*d^-1*(a+a*sec(c+d*x))^-4*(A+C+-1B)*sin(c+d*x)+1//105*a^-4*d^-1*(-160B+6C+664A)*sin(c+d*x)+-1*a^-4*d^-1*(1+sec(c+d*x))^-1*(-1B+4A)*sin(c+d*x)+-1//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*(-5B+-2C+12A)*sin(c+d*x)+-1//105*a^-4*d^-1*(1+sec(c+d*x))^-2*(-25B+-3C+88A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*cos(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*x*a^-4*(-8B+2C+21A)+-1//105*a^-4*d^-1*(-664B+160C+1728A)*sin(c+d*x)+(1/2)*a^-4*d^-1*(-8B+2C+21A)*cos(c+d*x)*sin(c+d*x)+-1//7*d^-1*(a+a*sec(c+d*x))^-4*(A+C+-1B)*cos(c+d*x)*sin(c+d*x)+-1//5*a^-1*d^-1*(a+a*sec(c+d*x))^-3*(-1B+2A)*cos(c+d*x)*sin(c+d*x)+-1//105*a^-4*d^-1*(1+sec(c+d*x))^-1*(-332B+80C+864A)*cos(c+d*x)*sin(c+d*x)+-1//105*a^-4*d^-1*(1+sec(c+d*x))^-2*(-52B+10C+129A)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//3465*d^-1*(a+a*sec(c+d*x))^(1/2)*(640C+704B+792A)*tan(c+d*x)+1//1155*a^-1*d^-1*(a+a*sec(c+d*x))^3//2*(320C+352B+396A)*tan(c+d*x)+2//11*C*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^4*tan(c+d*x)+4//495*a*d^-1*(a+a*sec(c+d*x))^-1//2*(80C+88B+99A)*tan(c+d*x)+2//99*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^4*(C+11B)*tan(c+d*x)+2//693*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*(80C+88B+99A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//315*d^-1*(a+a*sec(c+d*x))^(1/2)*(64C+72B+84A)*tan(c+d*x)+1//105*a^-1*d^-1*(a+a*sec(c+d*x))^3//2*(32C+36B+42A)*tan(c+d*x)+2//9*C*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3*tan(c+d*x)+2//45*a*d^-1*(a+a*sec(c+d*x))^-1//2*(16C+18B+21A)*tan(c+d*x)+2//63*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*(C+9B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//105*d^-1*(a+a*sec(c+d*x))^(1/2)*(-28B+36C+70A)*tan(c+d*x)+1//35*a^-1*d^-1*(a+a*sec(c+d*x))^3//2*(2C+14B)*tan(c+d*x)+2//7*C*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^2*tan(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^-1//2*(27C+35A+49B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//15*d^-1*(a+a*sec(c+d*x))^(1/2)*(-4C+10B)*tan(c+d*x)+2//5*C*a^-1*d^-1*(a+a*sec(c+d*x))^3//2*tan(c+d*x)+2//15*a*d^-1*(a+a*sec(c+d*x))^-1//2*(5B+7C+15A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2*A*a^(1/2)*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//3*C*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x)+2//3*a*d^-1*(a+a*sec(c+d*x))^-1//2*(C+3B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(A*d^-1*(a+a*sec(c+d*x))^(1/2)*sin(c+d*x)+a^(1/2)*d^-1*(A+2B)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1*a*d^-1*(a+a*sec(c+d*x))^-1//2*(A+-2C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//4*a^(1/2)*d^-1*(3A+4B+8C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*A*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)*sin(c+d*x)+1//4*a*d^-1*(a+a*sec(c+d*x))^-1//2*(A+4B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//8*a^(1/2)*d^-1*(5A+6B+8C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//3*A*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^2*sin(c+d*x)+1//8*a*d^-1*(a+a*sec(c+d*x))^-1//2*(5A+6B+8C)*sin(c+d*x)+1//12*a*d^-1*(a+a*sec(c+d*x))^-1//2*(A+6B)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//64*a^(1/2)*d^-1*(35A+40B+48C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//4*A*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^3*sin(c+d*x)+1//64*a*d^-1*(a+a*sec(c+d*x))^-1//2*(35A+40B+48C)*sin(c+d*x)+1//24*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*(A+8B)*sin(c+d*x)+1//96*a*d^-1*(a+a*sec(c+d*x))^-1//2*(35A+40B+48C)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//1155*d^-1*(a+a*sec(c+d*x))^3//2*(672C+748B+858A)*tan(c+d*x)+-4//3465*a*d^-1*(a+a*sec(c+d*x))^(1/2)*(336C+374B+429A)*tan(c+d*x)+2//11*C*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^3*tan(c+d*x)+2//495*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(336C+374B+429A)*tan(c+d*x)+2//99*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3*(3C+11B)*tan(c+d*x)+2//693*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*(84C+99A+110B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//315*d^-1*(a+a*sec(c+d*x))^3//2*(-36B+44C+126A)*tan(c+d*x)+1//21*a^-1*d^-1*(a+a*sec(c+d*x))^5//2*(2C+6B)*tan(c+d*x)+2//9*C*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^2*tan(c+d*x)+2//315*a*d^-1*(a+a*sec(c+d*x))^(1/2)*(47C+57B+63A)*tan(c+d*x)+8//315*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(47C+57B+63A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//35*d^-1*(a+a*sec(c+d*x))^3//2*(-4C+14B)*tan(c+d*x)+2//7*C*a^-1*d^-1*(a+a*sec(c+d*x))^5//2*tan(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^(1/2)*(19C+21B+35A)*tan(c+d*x)+8//105*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(19C+21B+35A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2*A*a^3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//5*C*d^-1*(a+a*sec(c+d*x))^3//2*tan(c+d*x)+2//15*a*d^-1*(a+a*sec(c+d*x))^(1/2)*(3C+5B)*tan(c+d*x)+2//15*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(12C+15A+20B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(A*d^-1*(a+a*sec(c+d*x))^3//2*sin(c+d*x)+a^3//2*d^-1*(2B+3A)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//3*a*d^-1*(a+a*sec(c+d*x))^(1/2)*(-2C+3A)*tan(c+d*x)+-1//3*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(-8C+-6B+3A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//4*a^3//2*d^-1*(7A+8C+12B)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*A*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)*sin(c+d*x)+-1//2*a*d^-1*(a+a*sec(c+d*x))^(1/2)*(A+-4C)*sin(c+d*x)+1//4*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(-8C+4B+5A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//8*a^3//2*d^-1*(11A+14B+24C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//3*A*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^2*sin(c+d*x)+1//24*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(19A+24C+30B)*sin(c+d*x)+1//4*a*d^-1*(a+a*sec(c+d*x))^(1/2)*(A+2B)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//64*a^3//2*d^-1*(75A+88B+112C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//4*A*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^3*sin(c+d*x)+1//64*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(75A+88B+112C)*sin(c+d*x)+1//24*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^2*(3A+8B)*sin(c+d*x)+1//96*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(39A+48C+56B)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^5*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//128*a^3//2*d^-1*(133A+150B+176C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//5*A*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^4*sin(c+d*x)+1//128*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(133A+150B+176C)*sin(c+d*x)+1//40*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^3*(3A+10B)*sin(c+d*x)+1//192*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(133A+150B+176C)*cos(c+d*x)*sin(c+d*x)+1//240*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*(67A+80C+90B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-4//45045*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(8368C+9230B+10439A)*tan(c+d*x)+2//13*C*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^3*tan(c+d*x)+2//6435*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(8368C+9230B+10439A)*tan(c+d*x)+2//15015*a*d^-1*(a+a*sec(c+d*x))^3//2*(8368C+9230B+10439A)*tan(c+d*x)+2//143*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^3*(5C+13B)*tan(c+d*x)+2//1287*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3*(136C+143A+182B)*tan(c+d*x)+2//9009*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*(2224C+2522B+2717A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//693*d^-1*(a+a*sec(c+d*x))^5//2*(-44B+52C+198A)*tan(c+d*x)+1//99*a^-1*d^-1*(a+a*sec(c+d*x))^7//2*(10C+22B)*tan(c+d*x)+2//11*C*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^2*tan(c+d*x)+2//1155*a*d^-1*(a+a*sec(c+d*x))^3//2*(125C+143B+165A)*tan(c+d*x)+16//3465*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(125C+143B+165A)*tan(c+d*x)+64//3465*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(125C+143B+165A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//63*d^-1*(a+a*sec(c+d*x))^5//2*(-4C+18B)*tan(c+d*x)+2//9*C*a^-1*d^-1*(a+a*sec(c+d*x))^7//2*tan(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^3//2*(13C+15B+21A)*tan(c+d*x)+16//315*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(13C+15B+21A)*tan(c+d*x)+64//315*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(13C+15B+21A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2*A*a^5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//7*C*d^-1*(a+a*sec(c+d*x))^5//2*tan(c+d*x)+2//35*a*d^-1*(a+a*sec(c+d*x))^3//2*(5C+7B)*tan(c+d*x)+2//105*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(35A+40C+56B)*tan(c+d*x)+2//105*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(160C+224B+245A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(A*d^-1*(a+a*sec(c+d*x))^5//2*sin(c+d*x)+a^5//2*d^-1*(2B+5A)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//5*a*d^-1*(a+a*sec(c+d*x))^3//2*(-2C+5A)*tan(c+d*x)+-1//15*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(-16C+-10B+15A)*tan(c+d*x)+1//15*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(15A+64C+70B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//4*a^5//2*d^-1*(8C+19A+20B)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*A*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)*sin(c+d*x)+-1//2*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(A+-8C+-4B)*sin(c+d*x)+-1//6*a*d^-1*(a+a*sec(c+d*x))^3//2*(-4C+3A)*sin(c+d*x)+1//12*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(-56C+-12B+27A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//8*a^5//2*d^-1*(25A+38B+40C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(-8C+2B+3A)*sin(c+d*x)+1//3*A*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^2*sin(c+d*x)+1//24*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(-24C+49A+54B)*sin(c+d*x)+1//12*a*d^-1*(a+a*sec(c+d*x))^3//2*(5A+6B)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//64*a^5//2*d^-1*(163A+200B+304C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//4*A*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^3*sin(c+d*x)+1//192*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(299A+392B+432C)*sin(c+d*x)+1//24*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^2*(5A+8B)*sin(c+d*x)+1//32*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(16C+17A+24B)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^5*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//128*a^5//2*d^-1*(283A+326B+400C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//5*A*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^4*sin(c+d*x)+1//128*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(283A+326B+400C)*sin(c+d*x)+1//8*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^3*(A+2B)*sin(c+d*x)+1//240*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^2*(79A+80C+110B)*sin(c+d*x)+1//960*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(787A+950B+1040C)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^6*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//512*a^5//2*d^-1*(1015A+1132B+1304C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//6*A*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^5*sin(c+d*x)+1//512*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(1015A+1132B+1304C)*sin(c+d*x)+1//60*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^4*(5A+12B)*sin(c+d*x)+1//480*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^3*(115A+120C+156B)*sin(c+d*x)+1//768*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(1015A+1132B+1304C)*cos(c+d*x)*sin(c+d*x)+1//960*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*(545A+628B+680C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//315*d^-1*(a+a*sec(c+d*x))^-1//2*(-444B+572C+588A)*tan(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*(A+C+-1B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//315*a^-1*d^-1*(a+a*sec(c+d*x))^(1/2)*(-186B+42A+58C)*tan(c+d*x)+1//63*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*(-2C+18B)*tan(c+d*x)+1//105*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*(-6B+38C+42A)*tan(c+d*x)+2//9*C*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^4*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//105*d^-1*(a+a*sec(c+d*x))^-1//2*(-196B+140A+148C)*tan(c+d*x)+2^(1/2)*a^-1//2*d^-1*(A+C+-1B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//35*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*(-2C+14B)*tan(c+d*x)+1//105*a^-1*d^-1*(a+a*sec(c+d*x))^(1/2)*(-14B+62C+70A)*tan(c+d*x)+2//7*C*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//15*d^-1*(a+a*sec(c+d*x))^-1//2*(-20B+28C+30A)*tan(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*(A+C+-1B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//15*a^-1*d^-1*(a+a*sec(c+d*x))^(1/2)*(-2C+10B)*tan(c+d*x)+2//5*C*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//3*d^-1*(a+a*sec(c+d*x))^-1//2*(-4C+6B)*tan(c+d*x)+2^(1/2)*a^-1//2*d^-1*(A+C+-1B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//3*C*a^-1*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2*A*a^-1//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2*C*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*(A+C+-1B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(A*d^-1*(a+a*sec(c+d*x))^-1//2*sin(c+d*x)+-1*a^-1//2*d^-1*(A+-2B)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2^(1/2)*a^-1//2*d^-1*(A+C+-1B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-1//2*(A+-4B)*sin(c+d*x)+1//4*a^-1//2*d^-1*(-4B+7A+8C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*A*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)*sin(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*(A+C+-1B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//8*a^-1//2*d^-1*(-14B+8C+9A)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//8*d^-1*(a+a*sec(c+d*x))^-1//2*(-2B+7A+8C)*sin(c+d*x)+2^(1/2)*a^-1//2*d^-1*(A+C+-1B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//12*d^-1*(a+a*sec(c+d*x))^-1//2*(A+-6B)*cos(c+d*x)*sin(c+d*x)+1//3*A*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//64*d^-1*(a+a*sec(c+d*x))^-1//2*(-56B+16C+21A)*sin(c+d*x)+1//64*a^-1//2*d^-1*(-72B+107A+112C)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1*2^(1/2)*a^-1//2*d^-1*(A+C+-1B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//24*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*(A+-8B)*sin(c+d*x)+1//4*A*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3*sin(c+d*x)+1//96*d^-1*(a+a*sec(c+d*x))^-1//2*(-8B+43A+48C)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^4*(A+C+-1B)*tan(c+d*x)+-1//105*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(-651B+455A+799C)*tan(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(-15B+11A+19C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//210*a^-2*d^-1*(a+a*sec(c+d*x))^(1/2)*(-273B+245A+397C)*tan(c+d*x)+-1//70*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*(-63B+35A+67C)*tan(c+d*x)+1//14*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*(-7B+7A+11C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3*(A+C+-1B)*tan(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*(-11B+7A+15C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//30*a^-2*d^-1*(a+a*sec(c+d*x))^(1/2)*(-35B+15A+39C)*tan(c+d*x)+1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(-65B+45A+93C)*tan(c+d*x)+1//10*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*(-5B+5A+9C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^2*(A+C+-1B)*tan(c+d*x)+-1//3*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(-9B+3A+13C)*tan(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(-7B+3A+11C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//6*a^-2*d^-1*(a+a*sec(c+d*x))^(1/2)*(-3B+3A+7C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2*A*a^-3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*(A+C+-1B)*tan(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*(-1B+-3C+5A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(-1*a^-3//2*d^-1*(-2B+3A)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*(A+C+-1B)*sin(c+d*x)+(1/2)*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(C+-1B+3A)*sin(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(C+-5B+9A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//4*a^-3//2*d^-1*(-12B+8C+19A)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*(A+C+-1B)*cos(c+d*x)*sin(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*(-9B+5C+13A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(-6B+2C+7A)*sin(c+d*x)+(1/2)*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(C+-1B+2A)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//8*a^-3//2*d^-1*(-38B+24C+47A)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^2*(A+C+-1B)*sin(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(-13B+9C+17A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//8*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(-14B+12C+21A)*sin(c+d*x)+-1//12*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(-12B+6C+13A)*cos(c+d*x)*sin(c+d*x)+1//6*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*(-3B+3C+5A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^4*(A+C+-1B)*tan(c+d*x)+-1//32*2^(1/2)*a^-5//2*d^-1*(-163B+75A+283C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//240*a^-3*d^-1*(a+a*sec(c+d*x))^(1/2)*(-475B+195A+787C)*tan(c+d*x)+1//120*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*(-985B+465A+1729C)*tan(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3*(-13B+5A+21C)*tan(c+d*x)+1//80*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*(-85B+45A+157C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^3*(A+C+-1B)*tan(c+d*x)+-1//24*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*(-93B+21A+197C)*tan(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(-75B+19A+163C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//48*a^-3*d^-1*(a+a*sec(c+d*x))^(1/2)*(-39B+15A+95C)*tan(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^2*(A+-9B+17C)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^2*(A+C+-1B)*tan(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*(-13C+3A+5B)*tan(c+d*x)+1//4*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*(A+-1B+9C)*tan(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(-75C+5A+19B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*(A+C+-1B)*sec(c+d*x)*tan(c+d*x)+1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*(B+-9C+7A)*tan(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(3A+5B+19C)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2*A*a^-5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*(A+C+-1B)*tan(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*(-5C+-3B+11A)*tan(c+d*x)+-1//32*2^(1/2)*a^-5//2*d^-1*(-5C+-3B+43A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(-1*a^-5//2*d^-1*(-2B+5A)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*(A+C+-1B)*sin(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*(-1C+-7B+15A)*sin(c+d*x)+1//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*(-11B+3C+35A)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(-43B+3C+115A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//4*a^-5//2*d^-1*(-20B+8C+39A)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*(A+C+-1B)*cos(c+d*x)*sin(c+d*x)+-1//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*(-35B+11C+63A)*sin(c+d*x)+-1//32*2^(1/2)*a^-5//2*d^-1*(-115B+43C+219A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*(-11B+3C+19A)*cos(c+d*x)*sin(c+d*x)+1//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*(-15B+7C+31A)*cos(c+d*x)*sin(c+d*x))
@test integrate(sec(c+d*x)^3//2*(a+a*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//5*a*d^-1*sec(c+d*x)^(1/2)*(3B+3C+5A)*sin(c+d*x)+2//5*a*d^-1*sec(c+d*x)^5//2*(B+C)*sin(c+d*x)+2//7*C*a*d^-1*sec(c+d*x)^7//2*sin(c+d*x)+2//21*a*d^-1*sec(c+d*x)^3//2*(5C+7A+7B)*sin(c+d*x)+-2//5*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3B+3C+5A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//21*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5C+7A+7B)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^(1/2)*(a+a*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//3*a*d^-1*sec(c+d*x)^3//2*(B+C)*sin(c+d*x)+2//5*C*a*d^-1*sec(c+d*x)^5//2*sin(c+d*x)+2//5*a*d^-1*sec(c+d*x)^(1/2)*(3C+5A+5B)*sin(c+d*x)+-2//5*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3C+5A+5B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(B+C+3A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^-1//2*(a+a*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2*a*d^-1*sec(c+d*x)^(1/2)*(B+C)*sin(c+d*x)+2//3*C*a*d^-1*sec(c+d*x)^3//2*sin(c+d*x)+2*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1B+-1C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(C+3A+3B)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^-3//2*(a+a*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2*C*a*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+2//3*A*a*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+2*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+B+-1C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+3B+3C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^-5//2*(a+a*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//3*a*d^-1*sec(c+d*x)^-1//2*(A+B)*sin(c+d*x)+2//5*A*a*d^-1*sec(c+d*x)^-3//2*sin(c+d*x)+2//3*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+B+3C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3A+5B+5C)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^-7//2*(a+a*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//5*a*d^-1*sec(c+d*x)^-3//2*(A+B)*sin(c+d*x)+2//7*A*a*d^-1*sec(c+d*x)^-5//2*sin(c+d*x)+2//21*a*d^-1*sec(c+d*x)^-1//2*(5A+7B+7C)*sin(c+d*x)+2//5*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3A+3B+5C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//21*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5A+7B+7C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^-9//2*(a+a*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//7*a*d^-1*sec(c+d*x)^-5//2*(A+B)*sin(c+d*x)+2//9*A*a*d^-1*sec(c+d*x)^-7//2*sin(c+d*x)+2//21*a*d^-1*sec(c+d*x)^-1//2*(5A+5B+7C)*sin(c+d*x)+2//45*a*d^-1*sec(c+d*x)^-3//2*(7A+9B+9C)*sin(c+d*x)+2//15*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(7A+9B+9C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//21*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5A+5B+7C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//63*d^-1*sec(c+d*x)^5//2*(a^2+a^2*sec(c+d*x))*(8C+18B)*sin(c+d*x)+2//9*C*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^5//2*sin(c+d*x)+2//105*a^2*d^-1*sec(c+d*x)^5//2*(19C+21A+27B)*sin(c+d*x)+4//15*a^2*d^-1*sec(c+d*x)^(1/2)*(8C+9B+12A)*sin(c+d*x)+4//21*a^2*d^-1*sec(c+d*x)^3//2*(5C+6B+7A)*sin(c+d*x)+-4//15*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(8C+9B+12A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5C+6B+7A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//35*d^-1*sec(c+d*x)^3//2*(a^2+a^2*sec(c+d*x))*(8C+14B)*sin(c+d*x)+2//7*C*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^3//2*sin(c+d*x)+2//105*a^2*d^-1*sec(c+d*x)^3//2*(33C+35A+49B)*sin(c+d*x)+4//5*a^2*d^-1*sec(c+d*x)^(1/2)*(3C+4B+5A)*sin(c+d*x)+-4//5*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3C+4B+5A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(6C+7B+14A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//15*d^-1*sec(c+d*x)^(1/2)*(a^2+a^2*sec(c+d*x))*(8C+10B)*sin(c+d*x)+2//5*C*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^(1/2)*sin(c+d*x)+2//15*a^2*d^-1*sec(c+d*x)^(1/2)*(15A+17C+25B)*sin(c+d*x)+-4//5*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(4C+5B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//3*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(C+2B+3A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-2//3*a^2*d^-1*sec(c+d*x)^(1/2)*(A+-5C+-3B)*sin(c+d*x)+-1//3*d^-1*sec(c+d*x)^(1/2)*(a^2+a^2*sec(c+d*x))*(-2C+2A)*sin(c+d*x)+2//3*A*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^-1//2*sin(c+d*x)+4*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//3*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2A+2C+3B)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-2//15*a^2*d^-1*sec(c+d*x)^(1/2)*(-15C+5B+7A)*sin(c+d*x)+1//15*d^-1*sec(c+d*x)^-1//2*(a^2+a^2*sec(c+d*x))*(8A+10B)*sin(c+d*x)+2//5*A*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^-3//2*sin(c+d*x)+4//3*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+2B+3C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+4//5*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(4A+5B)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^-7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//35*d^-1*sec(c+d*x)^-3//2*(a^2+a^2*sec(c+d*x))*(8A+14B)*sin(c+d*x)+2//7*A*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^-5//2*sin(c+d*x)+2//105*a^2*d^-1*sec(c+d*x)^-1//2*(33A+35C+49B)*sin(c+d*x)+4//5*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3A+4B+5C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(6A+7B+14C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^-9//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//63*d^-1*sec(c+d*x)^-5//2*(a^2+a^2*sec(c+d*x))*(8A+18B)*sin(c+d*x)+2//9*A*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^-7//2*sin(c+d*x)+2//105*a^2*d^-1*sec(c+d*x)^-3//2*(19A+21C+27B)*sin(c+d*x)+4//21*a^2*d^-1*sec(c+d*x)^-1//2*(5A+6B+7C)*sin(c+d*x)+4//15*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(8A+9B+12C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5A+6B+7C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^-11//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//99*d^-1*sec(c+d*x)^-7//2*(a^2+a^2*sec(c+d*x))*(8A+22B)*sin(c+d*x)+2//11*A*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^-9//2*sin(c+d*x)+2//693*a^2*d^-1*sec(c+d*x)^-5//2*(89A+99C+121B)*sin(c+d*x)+4//45*a^2*d^-1*sec(c+d*x)^-3//2*(7A+8B+9C)*sin(c+d*x)+4//231*a^2*d^-1*sec(c+d*x)^-1//2*(50A+55B+66C)*sin(c+d*x)+4//15*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(7A+8B+9C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//231*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(50A+55B+66C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//693*d^-1*sec(c+d*x)^5//2*(a^3+a^3*sec(c+d*x))*(198A+210C+286B)*sin(c+d*x)+2//11*C*d^-1*(a+a*sec(c+d*x))^3*sec(c+d*x)^5//2*sin(c+d*x)+4//15*a^3*d^-1*sec(c+d*x)^(1/2)*(15C+17B+21A)*sin(c+d*x)+4//231*a^3*d^-1*sec(c+d*x)^3//2*(105C+121B+143A)*sin(c+d*x)+4//1155*a^3*d^-1*sec(c+d*x)^5//2*(210C+253B+264A)*sin(c+d*x)+-4//15*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(15C+17B+21A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//99*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*sec(c+d*x)^5//2*(12C+22B)*sin(c+d*x)+4//231*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(105C+121B+143A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//315*d^-1*sec(c+d*x)^3//2*(a^3+a^3*sec(c+d*x))*(126A+146C+198B)*sin(c+d*x)+2//9*C*d^-1*(a+a*sec(c+d*x))^3*sec(c+d*x)^3//2*sin(c+d*x)+4//15*a^3*d^-1*sec(c+d*x)^(1/2)*(17C+21B+27A)*sin(c+d*x)+4//105*a^3*d^-1*sec(c+d*x)^3//2*(32C+41B+42A)*sin(c+d*x)+-4//15*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(17C+21B+27A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*sec(c+d*x)^3//2*(4C+6B)*sin(c+d*x)+4//21*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(11C+13B+21A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//15*d^-1*sec(c+d*x)^(1/2)*(a^3+a^3*sec(c+d*x))*(10A+14C+18B)*sin(c+d*x)+2//7*C*d^-1*(a+a*sec(c+d*x))^3*sec(c+d*x)^(1/2)*sin(c+d*x)+4//105*a^3*d^-1*sec(c+d*x)^(1/2)*(106C+140A+147B)*sin(c+d*x)+-4//5*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5A+7C+9B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//35*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*sec(c+d*x)^(1/2)*(12C+14B)*sin(c+d*x)+4//21*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(13C+21B+35A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//15*d^-1*sec(c+d*x)^(1/2)*(a^3+a^3*sec(c+d*x))*(-18C+-10B+10A)*sin(c+d*x)+2//3*A*d^-1*(a+a*sec(c+d*x))^3*sec(c+d*x)^-1//2*sin(c+d*x)+4//15*a^3*d^-1*sec(c+d*x)^(1/2)*(5A+20B+21C)*sin(c+d*x)+-1//15*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*sec(c+d*x)^(1/2)*(-6C+10A)*sin(c+d*x)+4//3*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3C+5A+5B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+4//5*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-9C+-5B+5A)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-4//15*a^3*d^-1*sec(c+d*x)^(1/2)*(-20C+-5B+6A)*sin(c+d*x)+-1//15*d^-1*sec(c+d*x)^(1/2)*(a^3+a^3*sec(c+d*x))*(-10C+10B+18A)*sin(c+d*x)+2//5*A*d^-1*(a+a*sec(c+d*x))^3*sec(c+d*x)^-3//2*sin(c+d*x)+1//15*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*sec(c+d*x)^-1//2*(10B+12A)*sin(c+d*x)+4//3*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3A+5B+5C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+4//5*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-5C+5B+9A)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^-7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-4//105*a^3*d^-1*sec(c+d*x)^(1/2)*(-35C+41A+42B)*sin(c+d*x)+1//15*d^-1*sec(c+d*x)^-1//2*(a^3+a^3*sec(c+d*x))*(10C+14A+18B)*sin(c+d*x)+2//7*A*d^-1*(a+a*sec(c+d*x))^3*sec(c+d*x)^-5//2*sin(c+d*x)+1//35*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*sec(c+d*x)^-3//2*(12A+14B)*sin(c+d*x)+4//5*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5C+7A+9B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(13A+21B+35C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^-9//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//315*d^-1*sec(c+d*x)^-3//2*(a^3+a^3*sec(c+d*x))*(126C+146A+198B)*sin(c+d*x)+2//9*A*d^-1*(a+a*sec(c+d*x))^3*sec(c+d*x)^-7//2*sin(c+d*x)+4//105*a^3*d^-1*sec(c+d*x)^-1//2*(32A+41B+42C)*sin(c+d*x)+1//21*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*sec(c+d*x)^-5//2*(4A+6B)*sin(c+d*x)+4//15*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(17A+21B+27C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(11A+13B+21C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^-11//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//693*d^-1*sec(c+d*x)^-5//2*(a^3+a^3*sec(c+d*x))*(198C+210A+286B)*sin(c+d*x)+2//11*A*d^-1*(a+a*sec(c+d*x))^3*sec(c+d*x)^-9//2*sin(c+d*x)+4//231*a^3*d^-1*sec(c+d*x)^-1//2*(105A+121B+143C)*sin(c+d*x)+4//1155*a^3*d^-1*sec(c+d*x)^-3//2*(210A+253B+264C)*sin(c+d*x)+1//99*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*sec(c+d*x)^-7//2*(12A+22B)*sin(c+d*x)+4//15*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(15A+17B+21C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//231*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(105A+121B+143C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^-13//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//1287*d^-1*sec(c+d*x)^-7//2*(a^3+a^3*sec(c+d*x))*(286C+290A+390B)*sin(c+d*x)+2//13*A*d^-1*(a+a*sec(c+d*x))^3*sec(c+d*x)^-11//2*sin(c+d*x)+4//231*a^3*d^-1*sec(c+d*x)^-1//2*(95A+105B+121C)*sin(c+d*x)+4//585*a^3*d^-1*sec(c+d*x)^-3//2*(175A+195B+221C)*sin(c+d*x)+20//9009*a^3*d^-1*sec(c+d*x)^-5//2*(236A+273B+286C)*sin(c+d*x)+1//143*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^2*sec(c+d*x)^-9//2*(12A+26B)*sin(c+d*x)+4//195*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(175A+195B+221C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//231*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(95A+105B+121C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^7//2*(A+C+-1B)*sin(c+d*x)+-1//3*a^-1*d^-1*sec(c+d*x)^3//2*(-5B+3A+5C)*sin(c+d*x)+1//5*a^-1*d^-1*sec(c+d*x)^(1/2)*(-15B+15A+21C)*sin(c+d*x)+1//5*a^-1*d^-1*sec(c+d*x)^5//2*(-5B+5A+7C)*sin(c+d*x)+-1//3*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-5B+3A+5C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-21C+-15A+15B)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1*a^-1*d^-1*sec(c+d*x)^(1/2)*(A+-3B+3C)*sin(c+d*x)+-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^5//2*(A+C+-1B)*sin(c+d*x)+1//3*a^-1*d^-1*sec(c+d*x)^3//2*(-3B+3A+5C)*sin(c+d*x)+a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-3B+3C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-3B+3A+5C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^-1*d^-1*sec(c+d*x)^(1/2)*(A+-1B+3C)*sin(c+d*x)+-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^3//2*(A+C+-1B)*sin(c+d*x)+a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+B+-1C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1B+3C)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^(1/2)*(A+C+-1B)*sin(c+d*x)+a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(C+-1B+3A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1B+-1C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^-1//2*(A+C+-1B)*sin(c+d*x)+1//3*a^-1*d^-1*sec(c+d*x)^-1//2*(-3B+3C+5A)*sin(c+d*x)+-1*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(C+-3B+3A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-3B+3C+5A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^-3//2*(A+C+-1B)*sin(c+d*x)+-1//3*a^-1*d^-1*sec(c+d*x)^-1//2*(-5B+3C+5A)*sin(c+d*x)+1//5*a^-1*d^-1*sec(c+d*x)^-3//2*(-5B+5C+7A)*sin(c+d*x)+-1//3*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-5B+3C+5A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-15B+15C+21A)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^-7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^-5//2*(A+C+-1B)*sin(c+d*x)+-1//5*a^-1*d^-1*sec(c+d*x)^-3//2*(-7B+5C+7A)*sin(c+d*x)+1//7*a^-1*d^-1*sec(c+d*x)^-5//2*(-7B+7C+9A)*sin(c+d*x)+1//21*a^-1*d^-1*sec(c+d*x)^-1//2*(-35B+35C+45A)*sin(c+d*x)+-1//5*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-21B+15C+21A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-35B+35C+45A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1*a^-2*d^-1*sec(c+d*x)^(1/2)*(A+-4B+7C)*sin(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^7//2*(A+C+-1B)*sin(c+d*x)+1//3*a^-2*d^-1*sec(c+d*x)^3//2*(-5B+2A+10C)*sin(c+d*x)+a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-4B+7C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^5//2*(A+-4B+7C)*sin(c+d*x)+1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-5B+2A+10C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1*a^-2*d^-1*sec(c+d*x)^(1/2)*(B+-4C)*sin(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^5//2*(A+C+-1B)*sin(c+d*x)+a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(B+-4C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^3//2*(A+-5C+2B)*sin(c+d*x)+1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-5C+2B)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^3//2*(A+C+-1B)*sin(c+d*x)+a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^(1/2)*(A+-1C)*sin(c+d*x)+-1*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(B+2A+2C)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^(1/2)*(A+C+-1B)*sin(c+d*x)+a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-1B+4A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^(1/2)*(-1C+-2B+5A)*sin(c+d*x)+-1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-1C+-2B+5A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^-1//2*(A+C+-1B)*sin(c+d*x)+1//3*a^-2*d^-1*sec(c+d*x)^-1//2*(-5B+2C+10A)*sin(c+d*x)+-1*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(C+-4B+7A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^-1//2*(C+-4B+7A)*sin(c+d*x)+1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-5B+2C+10A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//3*a^-2*d^-1*sec(c+d*x)^-1//2*(-10B+5C+15A)*sin(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^-3//2*(A+C+-1B)*sin(c+d*x)+1//15*a^-2*d^-1*sec(c+d*x)^-3//2*(-35B+20C+56A)*sin(c+d*x)+-1*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^-3//2*(C+-2B+3A)*sin(c+d*x)+-1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-10B+5C+15A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-35B+20C+56A)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^9//2*(A+C+-1B)*sin(c+d*x)+-1//10*a^-3*d^-1*sec(c+d*x)^(1/2)*(-49B+9A+119C)*sin(c+d*x)+-1//30*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^5//2*(-49B+9A+119C)*sin(c+d*x)+1//6*a^-3*d^-1*sec(c+d*x)^3//2*(-13B+3A+33C)*sin(c+d*x)+1//3*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^7//2*(B+-2C)*sin(c+d*x)+1//6*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-13B+3A+33C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-49B+9A+119C)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^7//2*(A+C+-1B)*sin(c+d*x)+-1//10*a^-3*d^-1*sec(c+d*x)^(1/2)*(A+-49C+9B)*sin(c+d*x)+1//6*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^3//2*(A+-13C+3B)*sin(c+d*x)+1//6*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-13C+3B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-49C+9B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^5//2*(-8C+2A+3B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^5//2*(A+C+-1B)*sin(c+d*x)+1//10*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^(1/2)*(A+-1B+-9C)*sin(c+d*x)+-1//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1B+-9C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//6*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+B+3C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^3//2*(B+-6C+4A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^3//2*(A+C+-1B)*sin(c+d*x)+1//6*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^(1/2)*(B+C+3A)*sin(c+d*x)+-1//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(B+-1C+9A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//6*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(B+C+3A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^(1/2)*(-1B+-4C+6A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^(1/2)*(A+C+-1B)*sin(c+d*x)+-1//6*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^(1/2)*(-1C+-3B+13A)*sin(c+d*x)+-1//6*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-1C+-3B+13A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^(1/2)*(-3B+-2C+8A)*sin(c+d*x)+1//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-1C+-9B+49A)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^-1//2*(A+C+-1B)*sin(c+d*x)+-1//30*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^-1//2*(-49B+9C+119A)*sin(c+d*x)+1//6*a^-3*d^-1*sec(c+d*x)^-1//2*(-13B+3C+33A)*sin(c+d*x)+-1//3*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^-1//2*(-1B+2A)*sin(c+d*x)+-1//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-49B+9C+119A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//6*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-13B+3C+33A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^-3//2*(A+C+-1B)*sin(c+d*x)+-1//6*a^-3*d^-1*sec(c+d*x)^-1//2*(-33B+13C+63A)*sin(c+d*x)+-1//10*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^-3//2*(-33B+13C+63A)*sin(c+d*x)+1//30*a^-3*d^-1*sec(c+d*x)^-3//2*(-119B+49C+231A)*sin(c+d*x)+-1//6*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-33B+13C+63A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^-3//2*(-7B+2C+12A)*sin(c+d*x)+1//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-119B+49C+231A)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//64*a^(1/2)*d^-1*(35C+40B+48A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//4*C*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^7//2*sin(c+d*x)+1//24*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^7//2*(C+8B)*sin(c+d*x)+1//64*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(35C+40B+48A)*sin(c+d*x)+1//96*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*(35C+40B+48A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//8*a^(1/2)*d^-1*(5C+6B+8A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//3*C*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^5//2*sin(c+d*x)+1//8*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(5C+6B+8A)*sin(c+d*x)+1//12*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*(C+6B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//4*a^(1/2)*d^-1*(3C+4B+8A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*C*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3//2*sin(c+d*x)+1//4*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(C+4B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^(1/2)*d^-1*(C+2B)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+C*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*sin(c+d*x)+a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-1C+2A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2*C*a^(1/2)*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//3*A*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*sin(c+d*x)+2//3*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(A+3B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//15*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(2A+10B)*sin(c+d*x)+2//5*A*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*sin(c+d*x)+2//15*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(5B+7A+15C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//7*A*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*sin(c+d*x)+2//35*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(A+7B)*sin(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(24A+28B+35C)*sin(c+d*x)+4//105*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(24A+28B+35C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-9//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//9*A*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-7//2*sin(c+d*x)+2//63*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-5//2*(A+9B)*sin(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(16A+18B+21C)*sin(c+d*x)+8//315*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(16A+18B+21C)*sin(c+d*x)+16//315*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(16A+18B+21C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//128*a^3//2*d^-1*(133C+150B+176A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//5*C*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^7//2*sin(c+d*x)+1//40*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^7//2*(3C+10B)*sin(c+d*x)+1//128*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(133C+150B+176A)*sin(c+d*x)+1//192*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*(133C+150B+176A)*sin(c+d*x)+1//240*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^7//2*(67C+80A+90B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//64*a^3//2*d^-1*(75C+88B+112A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//4*C*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^5//2*sin(c+d*x)+1//24*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^5//2*(3C+8B)*sin(c+d*x)+1//64*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(75C+88B+112A)*sin(c+d*x)+1//96*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*(39C+48A+56B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//8*a^3//2*d^-1*(11C+14B+24A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//3*C*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^3//2*sin(c+d*x)+1//4*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3//2*(C+2B)*sin(c+d*x)+1//24*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(19C+24A+30B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//4*a^3//2*d^-1*(7C+8A+12B)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*C*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^(1/2)*sin(c+d*x)+1//4*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*(3C+4B)*sin(c+d*x)+1//4*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-5C+-4B+8A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^3//2*d^-1*(2B+3C)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//3*A*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-1//2*sin(c+d*x)+-1//3*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*(-3C+2A)*sin(c+d*x)+1//3*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-3C+6B+8A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2*C*a^3//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//5*A*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-3//2*sin(c+d*x)+2//15*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(3A+5B)*sin(c+d*x)+2//15*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(12A+15C+20B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^-7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//35*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-3//2*(6A+14B)*sin(c+d*x)+2//7*A*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-5//2*sin(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(19A+21B+35C)*sin(c+d*x)+8//105*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(19A+21B+35C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^-9//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//9*A*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-7//2*sin(c+d*x)+2//21*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*(A+3B)*sin(c+d*x)+2//315*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(52A+63C+72B)*sin(c+d*x)+2//315*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(136A+156B+189C)*sin(c+d*x)+4//315*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(136A+156B+189C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^-11//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//11*A*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-9//2*sin(c+d*x)+2//99*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-7//2*(3A+11B)*sin(c+d*x)+2//693*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-5//2*(84A+99C+110B)*sin(c+d*x)+2//1155*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(336A+374B+429C)*sin(c+d*x)+8//3465*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(336A+374B+429C)*sin(c+d*x)+16//3465*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(336A+374B+429C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//512*a^5//2*d^-1*(1015C+1132B+1304A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//6*C*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^7//2*sin(c+d*x)+1//60*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^7//2*(5C+12B)*sin(c+d*x)+1//480*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^7//2*(115C+120A+156B)*sin(c+d*x)+1//512*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(1015C+1132B+1304A)*sin(c+d*x)+1//768*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*(1015C+1132B+1304A)*sin(c+d*x)+1//960*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^7//2*(545C+628B+680A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//128*a^5//2*d^-1*(283C+326B+400A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//5*C*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^5//2*sin(c+d*x)+1//8*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^5//2*(C+2B)*sin(c+d*x)+1//128*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(283C+326B+400A)*sin(c+d*x)+1//240*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^5//2*(79C+80A+110B)*sin(c+d*x)+1//960*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*(787C+950B+1040A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//64*a^5//2*d^-1*(163C+200B+304A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//4*C*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^3//2*sin(c+d*x)+1//24*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^3//2*(5C+8B)*sin(c+d*x)+1//32*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3//2*(16A+17C+24B)*sin(c+d*x)+1//192*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(299C+392B+432A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//8*a^5//2*d^-1*(25C+38B+40A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//3*C*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^(1/2)*sin(c+d*x)+1//12*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^(1/2)*(5C+6B)*sin(c+d*x)+1//24*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*(24A+31C+42B)*sin(c+d*x)+1//24*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-54B+-49C+24A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//4*a^5//2*d^-1*(8A+19C+20B)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//3*A*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^-1//2*sin(c+d*x)+-1//6*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^(1/2)*(-3C+4A)*sin(c+d*x)+-1//12*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*(-21C+-12B+8A)*sin(c+d*x)+1//12*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-27C+12B+56A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^5//2*d^-1*(2B+5C)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//5*A*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^-3//2*sin(c+d*x)+-1//15*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*(-15C+10B+16A)*sin(c+d*x)+1//15*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(15C+64A+70B)*sin(c+d*x)+2//3*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-1//2*(A+B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2*C*a^5//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//7*A*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^-5//2*sin(c+d*x)+2//35*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-3//2*(5A+7B)*sin(c+d*x)+2//105*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(35C+40A+56B)*sin(c+d*x)+2//105*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(160A+224B+245C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-9//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//63*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^-5//2*(10A+18B)*sin(c+d*x)+2//9*A*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^-7//2*sin(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-3//2*(13A+15B+21C)*sin(c+d*x)+16//315*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(13A+15B+21C)*sin(c+d*x)+64//315*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(13A+15B+21C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-11//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//11*A*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^-9//2*sin(c+d*x)+2//99*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-7//2*(5A+11B)*sin(c+d*x)+2//231*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*(32A+33C+44B)*sin(c+d*x)+2//3465*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(1160A+1364B+1485C)*sin(c+d*x)+2//3465*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(2840A+3212B+3795C)*sin(c+d*x)+4//3465*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(2840A+3212B+3795C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-13//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//13*A*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^-11//2*sin(c+d*x)+2//143*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-9//2*(5A+13B)*sin(c+d*x)+2//1287*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-7//2*(136A+143C+182B)*sin(c+d*x)+2//9009*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-5//2*(2224A+2522B+2717C)*sin(c+d*x)+2//15015*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(8368A+9230B+10439C)*sin(c+d*x)+8//45045*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(8368A+9230B+10439C)*sin(c+d*x)+16//45045*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(8368A+9230B+10439C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//8*a^-1//2*d^-1*(-14B+8A+9C)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2^(1/2)*a^-1//2*d^-1*(A+C+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+1//3*C*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^7//2*sin(c+d*x)+1//8*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(-2B+7C+8A)*sin(c+d*x)+1//12*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*(-1C+6B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//4*a^-1//2*d^-1*(-4B+7C+8A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*C*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*sin(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*(A+C+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+1//4*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(-1C+4B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^-1//2*d^-1*(-1C+2B)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+C*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x)+2^(1/2)*a^-1//2*d^-1*(A+C+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2*C*a^-1//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1*2^(1/2)*a^-1//2*d^-1*(A+C+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+2*A*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2^(1/2)*a^-1//2*d^-1*(A+C+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-6B+2A)*sin(c+d*x)+2//3*A*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1*2^(1/2)*a^-1//2*d^-1*(A+C+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//15*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(-10B+2A)*sin(c+d*x)+1//15*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-10B+26A+30C)*sin(c+d*x)+2//5*A*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2^(1/2)*a^-1//2*d^-1*(A+C+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//35*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(-14B+2A)*sin(c+d*x)+-1//105*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-182B+70C+86A)*sin(c+d*x)+1//105*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(-14B+62A+70C)*sin(c+d*x)+2//7*A*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-5//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(A*a+(A*b+B*a)*sec(c+d*x)+B*b*sec(c+d*x)^2), x) == :(a^-1//2*d^-1*(-1*B*b+2*A*b+2*B*a)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+B*b*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x)+2^(1/2)*a^-1//2*d^-1*(A+-1B)*(a+-1b)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//4*a^-3//2*d^-1*(-12B+8A+19C)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^7//2*(A+C+-1B)*sin(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*(-9B+5A+13C)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+(1/2)*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*(A+-1B+2C)*sin(c+d*x)+-1//4*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(-6B+2A+7C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^-3//2*d^-1*(-3C+2B)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^5//2*(A+C+-1B)*sin(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(A+-5B+9C)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+(1/2)*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(A+-1B+3C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2*C*a^-3//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3//2*(A+C+-1B)*sin(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(B+-5C+3A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^(1/2)*(A+C+-1B)*sin(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*(-1C+-3B+7A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+(1/2)*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(C+-1B+5A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-1//2*(A+C+-1B)*sin(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(-7B+3C+11A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//6*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-15B+3C+19A)*sin(c+d*x)+1//6*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(-3B+3C+7A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-3//2*(A+C+-1B)*sin(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*(-11B+7C+15A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//30*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(-35B+15C+39A)*sin(c+d*x)+1//10*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(-5B+5C+9A)*sin(c+d*x)+1//30*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-95B+75C+147A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^-5//2*d^-1*(-5C+2B)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^7//2*(A+C+-1B)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(-43B+3A+115C)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^5//2*(A+-15C+7B)*sin(c+d*x)+1//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(-11B+3A+35C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2*C*a^-5//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^5//2*(A+C+-1B)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(-43C+3B+5A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3//2*(-11C+3B+5A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^3//2*(A+C+-1B)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(3C+5B+19A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3//2*(-1B+-7C+9A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^(1/2)*(A+C+-1B)*sin(c+d*x)+-1//32*2^(1/2)*a^-5//2*d^-1*(-19B+-5C+75A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^(1/2)*(-5B+-3C+13A)*sin(c+d*x)+1//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(C+-9B+49A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^-1//2*(A+C+-1B)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(-75B+19C+163A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-1//2*(C+-9B+17A)*sin(c+d*x)+-1//48*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-147B+27C+299A)*sin(c+d*x)+1//48*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(-39B+15C+95A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^-3//2*(A+C+-1B)*sin(c+d*x)+-1//32*2^(1/2)*a^-5//2*d^-1*(-163B+75C+283A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-3//2*(-13B+5C+21A)*sin(c+d*x)+-1//240*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(-475B+195C+787A)*sin(c+d*x)+1//80*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(-85B+45C+157A)*sin(c+d*x)+1//240*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-1495B+735C+2671A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^n*sec(c+d*x)^(-1+-1n)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)+a^-1*(1+n)^-1*(a+a*sec(c+d*x))^n*sec(c+d*x)^(-1n)*(-1*a*(B+A*n+B*n)+-1*C*a*(1+n)*sec(c+d*x)), x) == :(A*d^-1*(1+n)^-1*(a+a*sec(c+d*x))^n*sec(c+d*x)^(-1n)*sin(c+d*x))
@test integrate(sec(c+d*x)^3*(A+C*sec(c+d*x)^2)*(a+b*sec(c+d*x)), x) == :(1//5*b*d^-1*(4C+5A)*tan(c+d*x)+1//8*a*d^-1*(3C+4A)*arctanh(sin(c+d*x))+1//15*b*d^-1*tan(c+d*x)^3*(4C+5A)+1//4*C*a*d^-1*sec(c+d*x)^3*tan(c+d*x)+1//5*C*b*d^-1*sec(c+d*x)^4*tan(c+d*x)+1//8*a*d^-1*(3C+4A)*sec(c+d*x)*tan(c+d*x))
@test integrate(sec(c+d*x)^2*(A+C*sec(c+d*x)^2)*(a+b*sec(c+d*x)), x) == :(1//3*a*d^-1*(2C+3A)*tan(c+d*x)+1//8*b*d^-1*(3C+4A)*arctanh(sin(c+d*x))+1//3*C*a*d^-1*sec(c+d*x)^2*tan(c+d*x)+1//4*C*b*d^-1*sec(c+d*x)^3*tan(c+d*x)+1//8*b*d^-1*(3C+4A)*sec(c+d*x)*tan(c+d*x))
@test integrate((A+C*sec(c+d*x)^2)*(a+b*sec(c+d*x))*sec(c+d*x), x) == :((1/2)*a*d^-1*(C+2A)*arctanh(sin(c+d*x))+1//3*b*d^-1*(2C+3A)*tan(c+d*x)+(1/2)*C*a*d^-1*sec(c+d*x)*tan(c+d*x)+1//3*C*b*d^-1*sec(c+d*x)^2*tan(c+d*x))
@test integrate((A+C*sec(c+d*x)^2)*(a+b*sec(c+d*x)), x) == :(A*a*x+C*a*d^-1*tan(c+d*x)+(1/2)*b*d^-1*(C+2A)*arctanh(sin(c+d*x))+(1/2)*C*b*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((A+C*sec(c+d*x)^2)*(a+b*sec(c+d*x))*cos(c+d*x), x) == :(A*b*x+A*a*d^-1*sin(c+d*x)+C*a*d^-1*arctanh(sin(c+d*x))+C*b*d^-1*tan(c+d*x))
@test integrate(cos(c+d*x)^2*(A+C*sec(c+d*x)^2)*(a+b*sec(c+d*x)), x) == :((1/2)*a*x*(A+2C)+A*b*d^-1*sin(c+d*x)+C*b*d^-1*arctanh(sin(c+d*x))+(1/2)*A*a*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^3*(A+C*sec(c+d*x)^2)*(a+b*sec(c+d*x)), x) == :((1/2)*b*x*(A+2C)+1//3*a*d^-1*(2A+3C)*sin(c+d*x)+(1/2)*A*b*d^-1*cos(c+d*x)*sin(c+d*x)+1//3*A*a*d^-1*cos(c+d*x)^2*sin(c+d*x))
@test integrate(cos(c+d*x)^4*(A+C*sec(c+d*x)^2)*(a+b*sec(c+d*x)), x) == :(1//8*a*x*(3A+4C)+b*d^-1*(A+C)*sin(c+d*x)+-1//3*A*b*d^-1*sin(c+d*x)^3+1//4*A*a*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//8*a*d^-1*(3A+4C)*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^5*(A+C*sec(c+d*x)^2)*(a+b*sec(c+d*x)), x) == :(1//8*b*x*(3A+4C)+-1//15*a*d^-1*sin(c+d*x)^3*(4A+5C)+1//5*a*d^-1*(4A+5C)*sin(c+d*x)+1//4*A*b*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//5*A*a*d^-1*cos(c+d*x)^4*sin(c+d*x)+1//8*b*d^-1*(3A+4C)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(1//15*b^-2*d^-1*(C*a^4+2*b^4*(4C+5A)+2*a^2*b^2*(3C+5A))*tan(c+d*x)+1//4*a*b*d^-1*(3C+4A)*arctanh(sin(c+d*x))+1//30*b^-2*d^-1*(a+b*sec(c+d*x))^2*(C*a^2+2*b^2*(4C+5A))*tan(c+d*x)+-1//10*C*a*b^-2*d^-1*(a+b*sec(c+d*x))^3*tan(c+d*x)+1//5*C*b^-1*d^-1*(a+b*sec(c+d*x))^3*sec(c+d*x)*tan(c+d*x)+1//60*a*b^-1*d^-1*(2*C*a^2+13*C*b^2+20*A*b^2)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*(A+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//8*d^-1*(b^2*(3C+4A)+4*a^2*(C+2A))*arctanh(sin(c+d*x))+-1//24*d^-1*(-3*b^2*(3C+4A)+2*C*a^2)*sec(c+d*x)*tan(c+d*x)+1//4*C*b^-1*d^-1*(a+b*sec(c+d*x))^3*tan(c+d*x)+1//6*a*b^-1*d^-1*(-1*C*a^2+8*C*b^2+12*A*b^2)*tan(c+d*x)+-1//12*C*a*b^-1*d^-1*(a+b*sec(c+d*x))^2*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*(A+C*sec(c+d*x)^2), x) == :(A*x*a^2+1//3*d^-1*(C*(2*a^2+2*b^2)+3*A*b^2)*tan(c+d*x)+1//3*C*d^-1*(a+b*sec(c+d*x))^2*tan(c+d*x)+a*b*d^-1*(C+2A)*arctanh(sin(c+d*x))+1//3*C*a*b*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*(A+C*sec(c+d*x)^2)*cos(c+d*x), x) == :((1/2)*d^-1*(C*(b^2+2*a^2)+2*A*b^2)*arctanh(sin(c+d*x))+A*d^-1*(a+b*sec(c+d*x))^2*sin(c+d*x)+2*A*a*b*x+-2*a*b*d^-1*(A+-1C)*tan(c+d*x)+-1//2*b^2*d^-1*(-1C+2A)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(x*(A*b^2+(1/2)*a^2*(A+2C))+-1//2*b^2*d^-1*(A+-2C)*tan(c+d*x)+A*a*b*d^-1*sin(c+d*x)+(1/2)*A*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)*sin(c+d*x)+2*C*a*b*d^-1*arctanh(sin(c+d*x)))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(1//3*d^-1*(a^2*(2A+3C)+2*A*b^2)*sin(c+d*x)+C*b^2*d^-1*arctanh(sin(c+d*x))+a*b*x*(A+2C)+1//3*A*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^2*sin(c+d*x)+1//3*A*a*b*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^4*(A+C*sec(c+d*x)^2), x) == :(x*((1/2)*b^2*(A+2C)+1//8*a^2*(3A+4C))+1//8*d^-1*(a^2*(3A+4C)+2*A*b^2)*cos(c+d*x)*sin(c+d*x)+1//4*A*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^3*sin(c+d*x)+2//3*a*b*d^-1*(2A+3C)*sin(c+d*x)+1//6*A*a*b*d^-1*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^5*(A+C*sec(c+d*x)^2), x) == :(-1//15*d^-1*sin(c+d*x)^3*(a^2*(4A+5C)+2*A*b^2)+1//4*a*b*x*(3A+4C)+1//5*d^-1*(a^2+b^2)*(4A+5C)*sin(c+d*x)+1//5*A*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^4*sin(c+d*x)+1//4*a*b*d^-1*(3A+4C)*cos(c+d*x)*sin(c+d*x)+1//10*A*a*b*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(1//16*b*d^-1*(b^2*(5C+6A)+6*a^2*(3C+4A))*arctanh(sin(c+d*x))+1//60*a*b^-2*d^-1*(2*C*a^4+24*b^4*(4C+5A)+a^2*b^2*(17C+30A))*tan(c+d*x)+1//120*b^-2*d^-1*(a+b*sec(c+d*x))^3*(2*C*a^2+5*b^2*(5C+6A))*tan(c+d*x)+1//240*b^-1*d^-1*(4*C*a^4+15*b^4*(5C+6A)+12*a^2*b^2*(3C+5A))*sec(c+d*x)*tan(c+d*x)+-1//15*C*a*b^-2*d^-1*(a+b*sec(c+d*x))^4*tan(c+d*x)+1//6*C*b^-1*d^-1*(a+b*sec(c+d*x))^4*sec(c+d*x)*tan(c+d*x)+1//120*a*b^-2*d^-1*(a+b*sec(c+d*x))^2*(2*C*a^2+21*C*b^2+30*A*b^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*(A+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(-1//30*b^-1*d^-1*(-4*b^4*(4C+5A)+3*C*a^4+-4*a^2*b^2*(13C+20A))*tan(c+d*x)+1//8*a*d^-1*(3*b^2*(3C+4A)+4*a^2*(C+2A))*arctanh(sin(c+d*x))+-1//60*b^-1*d^-1*(a+b*sec(c+d*x))^2*(-4*b^2*(4C+5A)+3*C*a^2)*tan(c+d*x)+1//5*C*b^-1*d^-1*(a+b*sec(c+d*x))^4*tan(c+d*x)+1//120*a*d^-1*(-6*C*a^2+71*C*b^2+100*A*b^2)*sec(c+d*x)*tan(c+d*x)+-1//20*C*a*b^-1*d^-1*(a+b*sec(c+d*x))^3*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*(A+C*sec(c+d*x)^2), x) == :(A*x*a^3+(1/2)*a*d^-1*(C*(a^2+4*b^2)+6*A*b^2)*tan(c+d*x)+1//4*C*d^-1*(a+b*sec(c+d*x))^3*tan(c+d*x)+1//8*b*d^-1*(b^2*(3C+4A)+12*a^2*(C+2A))*arctanh(sin(c+d*x))+1//4*C*a*d^-1*(a+b*sec(c+d*x))^2*tan(c+d*x)+1//8*b*d^-1*(b^2*(3C+4A)+2*C*a^2)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*(A+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(A*d^-1*(a+b*sec(c+d*x))^3*sin(c+d*x)+(1/2)*a*d^-1*(2*C*a^2+3*C*b^2+6*A*b^2)*arctanh(sin(c+d*x))+3*A*b*x*a^2+-1//3*b*d^-1*(a^2*(-8C+6A)+-1*b^2*(2C+3A))*tan(c+d*x)+-1//3*b*d^-1*(a+b*sec(c+d*x))^2*(-1C+3A)*tan(c+d*x)+-1//6*a*b^2*d^-1*(-5C+6A)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :((1/2)*a*x*(a^2*(A+2C)+6*A*b^2)+(1/2)*b*d^-1*(C*(b^2+6*a^2)+2*A*b^2)*arctanh(sin(c+d*x))+(1/2)*A*d^-1*(a+b*sec(c+d*x))^3*cos(c+d*x)*sin(c+d*x)+-3//2*a*b^2*d^-1*(-2C+3A)*tan(c+d*x)+-1//2*b^3*d^-1*(-1C+4A)*sec(c+d*x)*tan(c+d*x)+3//2*A*b*d^-1*(a+b*sec(c+d*x))^2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :((1/2)*b*x*(2*A*b^2+3*a^2*(A+2C))+-1//6*b^3*d^-1*(-6C+5A)*tan(c+d*x)+1//3*a*d^-1*(a^2*(2A+3C)+3*A*b^2)*sin(c+d*x)+3*C*a*b^2*d^-1*arctanh(sin(c+d*x))+1//3*A*d^-1*(a+b*sec(c+d*x))^3*cos(c+d*x)^2*sin(c+d*x)+(1/2)*A*b*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^4*(A+C*sec(c+d*x)^2), x) == :(1//8*a*x*(a^2*(3A+4C)+12*b^2*(A+2C))+C*b^3*d^-1*arctanh(sin(c+d*x))+(1/2)*b*d^-1*(A*b^2+a^2*(4A+6C))*sin(c+d*x)+1//4*A*d^-1*(a+b*sec(c+d*x))^3*cos(c+d*x)^3*sin(c+d*x)+1//8*a*d^-1*(a^2*(3A+4C)+2*A*b^2)*cos(c+d*x)*sin(c+d*x)+1//4*A*b*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^5*(A+C*sec(c+d*x)^2), x) == :(1//8*b*x*(3*a^2*(3A+4C)+4*b^2*(A+2C))+1//15*a*d^-1*(2*a^2*(4A+5C)+15*b^2*(2A+3C))*sin(c+d*x)+1//5*A*d^-1*(a+b*sec(c+d*x))^3*cos(c+d*x)^4*sin(c+d*x)+1//30*a*d^-1*cos(c+d*x)^2*(2*a^2*(4A+5C)+3*A*b^2)*sin(c+d*x)+3//40*b*d^-1*(2*A*b^2+5*a^2*(3A+4C))*cos(c+d*x)*sin(c+d*x)+3//20*A*b*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^6*(A+C*sec(c+d*x)^2), x) == :(1//16*a*x*(a^2*(5A+6C)+6*b^2*(3A+4C))+-1//15*b*d^-1*sin(c+d*x)^3*(A*b^2+3*a^2*(4A+5C))+1//15*b*d^-1*(b^2*(11A+15C)+9*a^2*(4A+5C))*sin(c+d*x)+1//6*A*d^-1*(a+b*sec(c+d*x))^3*cos(c+d*x)^5*sin(c+d*x)+1//16*a*d^-1*(a^2*(5A+6C)+6*b^2*(3A+4C))*cos(c+d*x)*sin(c+d*x)+1//120*a*d^-1*cos(c+d*x)^3*(5*a^2*(5A+6C)+6*A*b^2)*sin(c+d*x)+1//10*A*b*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^4*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(1//105*b^-2*d^-1*(2*C*a^6+8*b^6*(6C+7A)+a^4*b^2*(23C+42A)+8*a^2*b^4*(39C+49A))*tan(c+d*x)+1//4*a*b*d^-1*(a^2*(6C+8A)+b^2*(5C+6A))*arctanh(sin(c+d*x))+1//105*b^-2*d^-1*(a+b*sec(c+d*x))^4*(C*a^2+3*b^2*(6C+7A))*tan(c+d*x)+1//210*b^-2*d^-1*(a+b*sec(c+d*x))^2*(2*C*a^4+8*b^4*(6C+7A)+3*a^2*b^2*(9C+14A))*tan(c+d*x)+-1//21*C*a*b^-2*d^-1*(a+b*sec(c+d*x))^5*tan(c+d*x)+1//7*C*b^-1*d^-1*(a+b*sec(c+d*x))^5*sec(c+d*x)*tan(c+d*x)+1//210*a*b^-2*d^-1*(a+b*sec(c+d*x))^3*(2*C*a^2+31*C*b^2+42*A*b^2)*tan(c+d*x)+1//420*a*b^-1*d^-1*(b^4*(333C+406A)+4*C*a^4+12*a^2*b^2*(4C+7A))*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*(A+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//16*d^-1*(b^4*(5C+6A)+8*a^4*(C+2A)+12*a^2*b^2*(3C+4A))*arctanh(sin(c+d*x))+-1//240*d^-1*(-15*b^4*(5C+6A)+8*C*a^4+-2*a^2*b^2*(89C+130A))*sec(c+d*x)*tan(c+d*x)+-1//60*a*b^-1*d^-1*(-32*b^4*(4C+5A)+4*C*a^4+-1*a^2*b^2*(121C+190A))*tan(c+d*x)+-1//120*b^-1*d^-1*(a+b*sec(c+d*x))^3*(-5*b^2*(5C+6A)+4*C*a^2)*tan(c+d*x)+1//6*C*b^-1*d^-1*(a+b*sec(c+d*x))^5*tan(c+d*x)+-1//30*C*a*b^-1*d^-1*(a+b*sec(c+d*x))^4*tan(c+d*x)+1//120*a*b^-1*d^-1*(a+b*sec(c+d*x))^2*(-4*C*a^2+53*C*b^2+70*A*b^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*(A+C*sec(c+d*x)^2), x) == :(A*x*a^4+1//15*d^-1*(2*b^4*(4C+5A)+6*C*a^4+a^2*b^2*(56C+85A))*tan(c+d*x)+1//5*C*d^-1*(a+b*sec(c+d*x))^4*tan(c+d*x)+1//15*d^-1*(a+b*sec(c+d*x))^2*(b^2*(4C+5A)+3*C*a^2)*tan(c+d*x)+(1/2)*a*b*d^-1*(b^2*(3C+4A)+4*a^2*(C+2A))*arctanh(sin(c+d*x))+1//5*C*a*d^-1*(a+b*sec(c+d*x))^3*tan(c+d*x)+1//30*a*b*d^-1*(6*C*a^2+29*C*b^2+40*A*b^2)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*(A+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(1//8*d^-1*(b^4*(3C+4A)+8*C*a^4+24*a^2*b^2*(C+2A))*arctanh(sin(c+d*x))+A*d^-1*(a+b*sec(c+d*x))^4*sin(c+d*x)+4*A*b*x*a^3+-1//4*b*d^-1*(a+b*sec(c+d*x))^3*(-1C+4A)*tan(c+d*x)+-1//6*a*b*d^-1*(a^2*(-19C+12A)+-8*b^2*(2C+3A))*tan(c+d*x)+-1//24*b^2*d^-1*(a^2*(-26C+24A)+-3*b^2*(3C+4A))*sec(c+d*x)*tan(c+d*x)+-1//12*a*b*d^-1*(a+b*sec(c+d*x))^2*(-7C+12A)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :((1/2)*x*a^2*(a^2*(A+2C)+12*A*b^2)+-1//6*b^2*d^-1*(a^2*(-34C+39A)+-2*b^2*(2C+3A))*tan(c+d*x)+(1/2)*A*d^-1*(a+b*sec(c+d*x))^4*cos(c+d*x)*sin(c+d*x)+2*A*b*d^-1*(a+b*sec(c+d*x))^3*sin(c+d*x)+2*a*b*d^-1*(C*(b^2+2*a^2)+2*A*b^2)*arctanh(sin(c+d*x))+-1//6*b^2*d^-1*(a+b*sec(c+d*x))^2*(-2C+15A)*tan(c+d*x)+-1//3*a*b^3*d^-1*(-4C+9A)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :((1/2)*b^2*d^-1*(C*(b^2+12*a^2)+2*A*b^2)*arctanh(sin(c+d*x))+2*a*b*x*(a^2*(A+2C)+2*A*b^2)+1//3*d^-1*(a+b*sec(c+d*x))^2*(a^2*(2A+3C)+6*A*b^2)*sin(c+d*x)+-2//3*a*b*d^-1*(a^2*(2A+3C)+b^2*(-6C+11A))*tan(c+d*x)+-1//6*b^2*d^-1*(a^2*(4A+6C)+3*b^2*(-1C+6A))*sec(c+d*x)*tan(c+d*x)+1//3*A*d^-1*(a+b*sec(c+d*x))^4*cos(c+d*x)^2*sin(c+d*x)+2//3*A*b*d^-1*(a+b*sec(c+d*x))^3*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^4*(A+C*sec(c+d*x)^2), x) == :(x*(A*b^4+1//8*a^4*(3A+4C)+3*a^2*b^2*(A+2C))+-1//24*b^2*d^-1*(2*b^2*(-12C+13A)+3*a^2*(3A+4C))*tan(c+d*x)+4*C*a*b^3*d^-1*arctanh(sin(c+d*x))+1//4*A*d^-1*(a+b*sec(c+d*x))^4*cos(c+d*x)^3*sin(c+d*x)+1//8*d^-1*(a+b*sec(c+d*x))^2*(a^2*(3A+4C)+4*A*b^2)*cos(c+d*x)*sin(c+d*x)+1//12*a*b*d^-1*(a^2*(23A+36C)+12*A*b^2)*sin(c+d*x)+1//3*A*b*d^-1*(a+b*sec(c+d*x))^3*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^5*(A+C*sec(c+d*x)^2), x) == :(1//15*d^-1*(2*a^4*(4A+5C)+6*A*b^4+a^2*b^2*(56A+85C))*sin(c+d*x)+C*b^4*d^-1*arctanh(sin(c+d*x))+(1/2)*a*b*x*(a^2*(3A+4C)+4*b^2*(A+2C))+1//5*A*d^-1*(a+b*sec(c+d*x))^4*cos(c+d*x)^4*sin(c+d*x)+1//15*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^2*(a^2*(4A+5C)+3*A*b^2)*sin(c+d*x)+1//5*A*b*d^-1*(a+b*sec(c+d*x))^3*cos(c+d*x)^3*sin(c+d*x)+1//30*a*b*d^-1*(a^2*(29A+40C)+6*A*b^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^6*(A+C*sec(c+d*x)^2), x) == :(x*((1/2)*b^4*(A+2C)+1//16*a^4*(5A+6C)+3//4*a^2*b^2*(3A+4C))+1//240*d^-1*(15*a^4*(5A+6C)+24*A*b^4+10*a^2*b^2*(49A+66C))*cos(c+d*x)*sin(c+d*x)+1//6*A*d^-1*(a+b*sec(c+d*x))^4*cos(c+d*x)^5*sin(c+d*x)+1//120*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^3*(5*a^2*(5A+6C)+12*A*b^2)*sin(c+d*x)+4//15*a*b*d^-1*(2*a^2*(4A+5C)+5*b^2*(2A+3C))*sin(c+d*x)+1//60*a*b*d^-1*cos(c+d*x)^2*(a^2*(39A+50C)+4*A*b^2)*sin(c+d*x)+2//15*A*b*d^-1*(a+b*sec(c+d*x))^3*cos(c+d*x)^4*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^7*(A+C*sec(c+d*x)^2), x) == :(-1//105*d^-1*sin(c+d*x)^3*(4*A*b^4+4*a^4*(6A+7C)+3*a^2*b^2*(50A+63C))+1//105*d^-1*(b^4*(74A+105C)+12*a^4*(6A+7C)+3*a^2*b^2*(162A+203C))*sin(c+d*x)+1//4*a*b*x*(a^2*(5A+6C)+2*b^2*(3A+4C))+1//7*A*d^-1*(a+b*sec(c+d*x))^4*cos(c+d*x)^6*sin(c+d*x)+1//35*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^4*(a^2*(6A+7C)+2*A*b^2)*sin(c+d*x)+1//4*a*b*d^-1*(a^2*(5A+6C)+2*b^2*(3A+4C))*cos(c+d*x)*sin(c+d*x)+1//210*a*b*d^-1*cos(c+d*x)^3*(a^2*(103A+126C)+6*A*b^2)*sin(c+d*x)+2//21*A*b*d^-1*(a+b*sec(c+d*x))^3*cos(c+d*x)^5*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*(a^2+-1*b^2*sec(c+d*x)^2), x) == :(x*a^5+-1//4*b^2*d^-1*(a+b*sec(c+d*x))^3*tan(c+d*x)+1//8*b*d^-1*(-3*b^4+24*a^4+-8*a^2*b^2)*arctanh(sin(c+d*x))+(1/2)*a*b^2*d^-1*(-4*b^2+5*a^2)*tan(c+d*x)+-1//4*a*b^2*d^-1*(a+b*sec(c+d*x))^2*tan(c+d*x)+1//8*b^3*d^-1*(-3*b^2+2*a^2)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*(a^2+-1*b^2*sec(c+d*x)^2), x) == :(x*a^4+-1//3*b^2*d^-1*(a+b*sec(c+d*x))^2*tan(c+d*x)+1//3*b^2*d^-1*(a^2+-2*b^2)*tan(c+d*x)+a*b*d^-1*(-1*b^2+2*a^2)*arctanh(sin(c+d*x))+-1//3*a*b^3*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))*(a^2+-1*b^2*sec(c+d*x)^2), x) == :(x*a^3+(1/2)*b*d^-1*(-1*b^2+2*a^2)*arctanh(sin(c+d*x))+-1//2*a*b^2*d^-1*tan(c+d*x)+-1//2*b^2*d^-1*(a+b*sec(c+d*x))*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-1*sec(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(1//3*b^-3*d^-1*(b^2*(2C+3A)+3*C*a^2)*tan(c+d*x)+-1//2*a*b^-4*d^-1*(C*(b^2+2*a^2)+2*A*b^2)*arctanh(sin(c+d*x))+1//3*C*b^-1*d^-1*sec(c+d*x)^2*tan(c+d*x)+-1//2*C*a*b^-2*d^-1*sec(c+d*x)*tan(c+d*x)+2*a^2*b^-4*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(A*b^2+C*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :((1/2)*b^-3*d^-1*(b^2*(C+2A)+2*C*a^2)*arctanh(sin(c+d*x))+(1/2)*C*b^-1*d^-1*sec(c+d*x)*tan(c+d*x)+-1*C*a*b^-2*d^-1*tan(c+d*x)+-2*a*b^-3*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(A*b^2+C*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*(A+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(C*b^-1*d^-1*tan(c+d*x)+-1*C*a*b^-2*d^-1*arctanh(sin(c+d*x))+b^-2*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(2*A*b^2+2*C*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*(A+C*sec(c+d*x)^2), x) == :(A*x*a^-1+C*b^-1*d^-1*arctanh(sin(c+d*x))+-1*a^-1*b^-1*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(2*A*b^2+2*C*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*(A+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(A*a^-1*d^-1*sin(c+d*x)+-1*A*b*x*a^-2+a^-2*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(2*A*b^2+2*C*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*cos(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :((1/2)*x*a^-3*(a^2*(A+2C)+2*A*b^2)+(1/2)*A*a^-1*d^-1*cos(c+d*x)*sin(c+d*x)+-1*A*b*a^-2*d^-1*sin(c+d*x)+-2*b*a^-3*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(A*b^2+C*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*cos(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(-1//2*b*x*a^-4*(a^2*(A+2C)+2*A*b^2)+1//3*a^-3*d^-1*(a^2*(2A+3C)+3*A*b^2)*sin(c+d*x)+1//3*A*a^-1*d^-1*cos(c+d*x)^2*sin(c+d*x)+-1//2*A*b*a^-2*d^-1*cos(c+d*x)*sin(c+d*x)+2*a^-4*b^2*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(A*b^2+C*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*cos(c+d*x)^4*(A+C*sec(c+d*x)^2), x) == :(1//8*x*a^-5*(a^4*(3A+4C)+8*A*b^4+4*a^2*b^2*(A+2C))+-1//3*b*a^-4*d^-1*(a^2*(2A+3C)+3*A*b^2)*sin(c+d*x)+1//4*A*a^-1*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//8*a^-3*d^-1*(a^2*(3A+4C)+4*A*b^2)*cos(c+d*x)*sin(c+d*x)+-1//3*A*b*a^-2*d^-1*cos(c+d*x)^2*sin(c+d*x)+-2*a^-5*b^3*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(A*b^2+C*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-2*sec(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :((1/2)*b^-4*d^-1*(C*(b^2+6*a^2)+2*A*b^2)*arctanh(sin(c+d*x))+(1/2)*b^-2*d^-1*(a^2+-1*b^2)^-1*(-1*C*b^2+2*A*b^2+3*C*a^2)*sec(c+d*x)*tan(c+d*x)+-1*a*b^-3*d^-1*(a^2+-1*b^2)^-1*(A*b^2+-2*C*b^2+3*C*a^2)*tan(c+d*x)+-1*b^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*sec(c+d*x)^2*(A*b^2+C*a^2)*tan(c+d*x)+-2*a*b^-4*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-2*A*b^4+3*C*a^4+A*a^2*b^2+-4*C*a^2*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-2*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(C*b^-2*d^-1*tan(c+d*x)+-2*C*a*b^-3*d^-1*arctanh(sin(c+d*x))+-1*b^-3*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-4*C*a^4+2*A*b^4+6*C*a^2*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+a*b^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*(A*b^2+C*a^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-2*(A+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(C*b^-2*d^-1*arctanh(sin(c+d*x))+-1*b^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*(A*b^2+C*a^2)*tan(c+d*x)+2*a*b^-2*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(A*b^2+-1*C*a^2+2*C*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-2*(A+C*sec(c+d*x)^2), x) == :(A*x*a^-2+a^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*(A*b^2+C*a^2)*tan(c+d*x)+-2*b*a^-2*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(C*a^2+-1*A*b^2+2*A*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-2*(A+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(-2*A*b*x*a^-3+-1*a^-2*d^-1*(a^2+-1*b^2)^-1*(-1*a^2*(A+-1C)+2*A*b^2)*sin(c+d*x)+a^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*(A*b^2+C*a^2)*sin(c+d*x)+a^-3*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-4*A*b^4+2*C*a^4+6*A*a^2*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-2*cos(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :((1/2)*x*a^-4*(a^2*(A+2C)+6*A*b^2)+b*a^-3*d^-1*(a^2+-1*b^2)^-1*(-1*a^2*(-1C+2A)+3*A*b^2)*sin(c+d*x)+-1//2*a^-2*d^-1*(a^2+-1*b^2)^-1*(-1*a^2*(A+-2C)+3*A*b^2)*cos(c+d*x)*sin(c+d*x)+a^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*(A*b^2+C*a^2)*cos(c+d*x)*sin(c+d*x)+-2*b*a^-4*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-3*A*b^4+2*C*a^4+-1*C*a^2*b^2+4*A*a^2*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-2*cos(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(-1*b*x*a^-5*(a^2*(A+2C)+4*A*b^2)+-1//3*a^-4*d^-1*(a^2+-1*b^2)^-1*(-1*a^4*(2A+3C)+12*A*b^4+-1*a^2*b^2*(-6C+7A))*sin(c+d*x)+-1//3*a^-2*d^-1*(a^2+-1*b^2)^-1*cos(c+d*x)^2*(-1*a^2*(A+-3C)+4*A*b^2)*sin(c+d*x)+b*a^-3*d^-1*(a^2+-1*b^2)^-1*(-1*a^2*(A+-1C)+2*A*b^2)*cos(c+d*x)*sin(c+d*x)+a^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*cos(c+d*x)^2*(A*b^2+C*a^2)*sin(c+d*x)+2*a^-5*b^2*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-4*A*b^4+3*C*a^4+-2*C*a^2*b^2+5*A*a^2*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-3*sec(c+d*x)^4*(A+C*sec(c+d*x)^2), x) == :((1/2)*b^-5*d^-1*(C*(b^2+12*a^2)+2*A*b^2)*arctanh(sin(c+d*x))+(1/2)*b^-3*d^-1*(a^2+-1*b^2)^-2*(-1*b^4*(-1C+4A)+6*C*a^4+a^2*b^2*(A+-10C))*sec(c+d*x)*tan(c+d*x)+-1//2*a*b^-4*d^-1*(a^2+-1*b^2)^-2*(-1*b^4*(-6C+5A)+12*C*a^4+a^2*b^2*(-21C+2A))*tan(c+d*x)+(1/2)*b^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*sec(c+d*x)^2*(-4*C*a^4+3*A*b^4+7*C*a^2*b^2)*tan(c+d*x)+-1*a*b^-5*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(6*A*b^6+12*C*a^6+a^4*b^2*(-29C+2A)+-5*a^2*b^4*(A+-4C))*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1//2*b^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*sec(c+d*x)^3*(A*b^2+C*a^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*sec(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :((1/2)*b^-3*d^-1*(a^2+-1*b^2)^-1*(A*b^2+-2*C*b^2+3*C*a^2)*tan(c+d*x)+-3*C*a*b^-4*d^-1*arctanh(sin(c+d*x))+b^-4*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(2*A*b^6+6*C*a^6+a^2*b^4*(A+12C)+-15*C*a^4*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1//2*a*b^-3*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-3*C*a^4+2*A*b^4+a^2*b^2*(A+6C))*tan(c+d*x)+-1//2*b^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*sec(c+d*x)^2*(A*b^2+C*a^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(C*b^-3*d^-1*arctanh(sin(c+d*x))+(1/2)*b^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-3*C*a^4+2*A*b^4+a^2*b^2*(A+6C))*tan(c+d*x)+(1/2)*a*b^-2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*(A*b^2+C*a^2)*tan(c+d*x)+-1*a*b^-3*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(C*(2*a^4+6*b^4+-5*a^2*b^2)+3*A*b^4)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-3*(A+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(a^2*(C+2A)+b^2*(A+2C))*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1//2*b^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*(A*b^2+C*a^2)*tan(c+d*x)+-1//2*a*b^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-1*C*a^2+3*A*b^2+4*C*b^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*(A+C*sec(c+d*x)^2), x) == :(A*x*a^-3+(1/2)*a^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*(A*b^2+C*a^2)*tan(c+d*x)+-1//2*a^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-1*C*a^4+2*A*b^4+-1*a^2*b^2*(2C+5A))*tan(c+d*x)+b*a^-3*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(-3*a^4*(C+2A)+-2*A*b^4+5*A*a^2*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-3*(A+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(-3*A*b*x*a^-4+-1//2*a^-3*d^-1*(a^2+-1*b^2)^-2*(-1*a^4*(-3C+2A)+-6*A*b^4+11*A*a^2*b^2)*sin(c+d*x)+(1/2)*a^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*(A*b^2+C*a^2)*sin(c+d*x)+-1*a^-4*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(-6*A*b^6+-2*C*a^6+-1*a^4*b^2*(C+12A)+15*A*a^2*b^4)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1//2*a^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-2*C*a^4+3*A*b^4+-1*a^2*b^2*(C+6A))*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*cos(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :((1/2)*x*a^-5*(a^2*(A+2C)+12*A*b^2)+(1/2)*a^-3*d^-1*(a^2+-1*b^2)^-2*(a^4*(A+-4C)+6*A*b^4+-1*a^2*b^2*(-1C+10A))*cos(c+d*x)*sin(c+d*x)+-1//2*b*a^-4*d^-1*(a^2+-1*b^2)^-2*(a^4*(-5C+6A)+12*A*b^4+-1*a^2*b^2*(-2C+21A))*sin(c+d*x)+(1/2)*a^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*(A*b^2+C*a^2)*cos(c+d*x)*sin(c+d*x)+(1/2)*a^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-4*A*b^4+3*C*a^4+7*A*a^2*b^2)*cos(c+d*x)*sin(c+d*x)+-1*b*a^-5*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(6*C*a^6+12*A*b^6+-1*a^2*b^4*(-2C+29A)+5*a^4*b^2*(-1C+4A))*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-4*sec(c+d*x)^4*(A+C*sec(c+d*x)^2), x) == :(-4*C*a*b^-5*d^-1*arctanh(sin(c+d*x))+-1//6*b^-4*d^-1*(a^2+-1*b^2)^-2*(-1*C*(6*b^4+12*a^4+-23*a^2*b^2)+5*A*b^4)*tan(c+d*x)+-1*b^-5*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(-8*C*a^8+2*A*b^8+a^2*b^6*(3A+20C)+-35*C*a^4*b^4+28*C*a^6*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+(1/2)*a*b^-4*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(2*A*b^6+4*C*a^6+-11*C*a^4*b^2+3*a^2*b^4*(A+4C))*tan(c+d*x)+-1//3*b^-1*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*sec(c+d*x)^3*(A*b^2+C*a^2)*tan(c+d*x)+1//6*b^-2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*sec(c+d*x)^2*(-4*C*a^4+3*A*b^4+a^2*b^2*(2A+9C))*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*sec(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(C*b^-4*d^-1*arctanh(sin(c+d*x))+-1//6*b^-3*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(4*A*b^6+9*C*a^6+-1*a^4*b^2*(3A+28C)+2*a^2*b^4*(7A+17C))*tan(c+d*x)+a*b^-4*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(-2*C*a^6+4*b^6*(A+2C)+a^2*b^4*(A+-8C)+7*C*a^4*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1//3*b^-1*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*sec(c+d*x)^2*(A*b^2+C*a^2)*tan(c+d*x)+-1//6*a*b^-3*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(-3*C*a^4+2*A*b^4+a^2*b^2*(3A+8C))*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(-1*b*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(a^2*(3C+4A)+b^2*(A+2C))*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+1//6*b^-2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(-4*C*a^4+3*A*b^4+a^2*b^2*(2A+9C))*tan(c+d*x)+1//3*a*b^-2*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*(A*b^2+C*a^2)*tan(c+d*x)+1//6*a*b^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(b^4*(13A+18C)+2*C*a^4+a^2*b^2*(-5C+2A))*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*(A+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(a*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(a^2*(C+2A)+b^2*(3A+4C))*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1//3*b^-1*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*(A*b^2+C*a^2)*tan(c+d*x)+1//6*b^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(C*a^4+-2*b^4*(2A+3C)+-1*a^2*b^2*(10C+11A))*tan(c+d*x)+-1//6*a*b^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(-1*C*a^2+5*A*b^2+6*C*b^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*(A+C*sec(c+d*x)^2), x) == :(A*x*a^-4+-1//6*a^-3*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(-6*A*b^6+-2*C*a^6+-13*a^4*b^2*(C+2A)+17*A*a^2*b^4)*tan(c+d*x)+-1//6*a^-2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(-2*C*a^4+3*A*b^4+-1*a^2*b^2*(3C+8A))*tan(c+d*x)+1//3*a^-1*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*(A*b^2+C*a^2)*tan(c+d*x)+-1*b*a^-4*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(-2*A*b^6+4*a^6*(C+2A)+-1*a^4*b^2*(-1C+8A)+7*A*a^2*b^4)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-4*(A+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(-4*A*b*x*a^-5+1//6*a^-4*d^-1*(a^2+-1*b^2)^-3*(a^6*(-11C+6A)+-24*A*b^6+-1*a^4*b^2*(4C+65A)+68*A*a^2*b^4)*sin(c+d*x)+-1*a^-5*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(-2*C*a^8+8*A*b^8+-1*a^6*b^2*(3C+20A)+-28*A*a^2*b^6+35*A*a^4*b^4)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1//2*a^-3*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(-4*A*b^6+-2*C*a^6+-3*a^4*b^2*(C+4A)+11*A*a^2*b^4)*sin(c+d*x)+-1//6*a^-2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(-3*C*a^4+4*A*b^4+-1*a^2*b^2*(2C+9A))*sin(c+d*x)+1//3*a^-1*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*(A*b^2+C*a^2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*cos(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :((1/2)*x*a^-6*(a^2*(A+2C)+20*A*b^2)+-1//2*a^-4*d^-1*(a^2+-1*b^2)^-3*(-1*a^6*(A+-6C)+10*A*b^6+a^4*b^2*(-2C+23A)+-1*a^2*b^4*(-1C+27A))*cos(c+d*x)*sin(c+d*x)+1//6*b*a^-5*d^-1*(a^2+-1*b^2)^-3*(-1*a^6*(-26C+24A)+60*A*b^6+a^4*b^2*(-17C+146A)+-1*a^2*b^4*(-6C+167A))*sin(c+d*x)+a^-6*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(a^2+-1*b^2)^-3*(20*A*b^9+-1*a^2*b^7*(-2C+69A)+-8*C*b*a^8+-8*a^6*b^3*(-1C+5A)+7*a^4*b^5*(-1C+12A))*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1//6*a^-2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(-4*C*a^4+5*A*b^4+-1*a^2*b^2*(C+10A))*cos(c+d*x)*sin(c+d*x)+1//3*a^-1*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*(A*b^2+C*a^2)*cos(c+d*x)*sin(c+d*x)+1//6*a^-3*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(12*C*a^6+20*A*b^6+a^4*b^2*(C+48A)+-1*a^2*b^4*(-2C+53A))*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-1*(a^2+-1*b^2*sec(c+d*x)^2), x) == :(a*x+-1*b*d^-1*arctanh(sin(c+d*x)))
@test integrate((a+b*sec(c+d*x))^-2*(a^2+-1*b^2*sec(c+d*x)^2), x) == :(x+-4*b*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-3*(a^2+-1*b^2*sec(c+d*x)^2), x) == :(x*a^-1+2*b^2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*tan(c+d*x)+-2*b*a^-1*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-1*b^2+3*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-4*(a^2+-1*b^2*sec(c+d*x)^2), x) == :(x*a^-2+b^2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*tan(c+d*x)+a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-1*b^2+4*a^2)*tan(c+d*x)+-2*b*a^-2*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(b^4+4*a^4+-2*a^2*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(2//9*C*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^3*tan(c+d*x)+-1//315*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(-14*b^2*(7C+9A)+12*C*a^2)*sec(c+d*x)*tan(c+d*x)+2//315*a*b^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(8*C*a^2+13*C*b^2+21*A*b^2)*tan(c+d*x)+2//63*C*a*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^2*tan(c+d*x)+1//315*b^-5*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-21*b^4*(7C+9A)+16*C*a^4+6*a^2*b^2*(4C+7A))*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//315*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(16*C*a^3+21*b^3*(7C+9A)+6*a*b^2*(6C+7A)+12*C*b*a^2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(1//105*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(10*b^2*(5C+7A)+16*C*a^2)*tan(c+d*x)+-8//35*C*a*b^-2*d^-1*(a+b*sec(c+d*x))^3//2*tan(c+d*x)+2//7*C*b^-1*d^-1*(a+b*sec(c+d*x))^3//2*sec(c+d*x)*tan(c+d*x)+-1//105*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(C*(8*a^2+25*b^2+6*a*b)+35*A*b^2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+-2//105*a*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(a+-1b)*(8*C*a^2+19*C*b^2+35*A*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^(1/2)*(A+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(2//5*C*b^-1*d^-1*(a+b*sec(c+d*x))^3//2*tan(c+d*x)+-4//15*C*a*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*tan(c+d*x)+1//15*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-3*b^2*(3C+5A)+2*C*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//15*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(2*C*a+9*C*b+15*A*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^3//2*sec(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(1//1155*b^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(16*C*a^4+50*b^4*(9C+11A)+2*a^2*b^2*(19C+33A))*tan(c+d*x)+2//11*C*d^-1*(a+b*sec(c+d*x))^3//2*sec(c+d*x)^3*tan(c+d*x)+1//231*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^2*(2*C*a^2+6*b^2*(9C+11A))*tan(c+d*x)+2//33*C*a*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^3*tan(c+d*x)+4//1155*a*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(-3*C*a^2+101*C*b^2+132*A*b^2)*sec(c+d*x)*tan(c+d*x)+1//1155*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-25*b^4*(9C+11A)+16*C*a^4+3*a*b^3*(157C+209A)+6*a^2*b^2*(8C+11A)+12*C*b*a^3)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+4//1155*a*b^-5*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(a+-1b)*(-1*b^4*(348C+451A)+8*C*a^4+3*a^2*b^2*(6C+11A))*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^3//2*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(1//315*b^-2*d^-1*(a+b*sec(c+d*x))^3//2*(14*b^2*(7C+9A)+16*C*a^2)*tan(c+d*x)+-8//63*C*a*b^-2*d^-1*(a+b*sec(c+d*x))^5//2*tan(c+d*x)+2//9*C*b^-1*d^-1*(a+b*sec(c+d*x))^5//2*sec(c+d*x)*tan(c+d*x)+2//315*a*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(8*C*a^2+39*C*b^2+63*A*b^2)*tan(c+d*x)+-1//315*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-21*b^3*(7C+9A)+8*C*a^3+3*a*b^2*(13C+21A)+6*C*b*a^2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//315*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(8*C*a^4+21*b^4*(7C+9A)+3*a^2*b^2*(11C+21A))*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^3//2*(A+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(-1//105*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*(-10*b^2*(5C+7A)+12*C*a^2)*tan(c+d*x)+2//7*C*b^-1*d^-1*(a+b*sec(c+d*x))^5//2*tan(c+d*x)+-4//35*C*a*b^-1*d^-1*(a+b*sec(c+d*x))^3//2*tan(c+d*x)+1//105*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-35*A*b^2+-25*C*b^2+6*C*a^2+57*C*a*b+105*A*a*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+-4//105*a*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(a+-1b)*(-3*C*a^2+41*C*b^2+70*A*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^5//2*sec(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(1//1287*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^3*(22*b^2*(11C+13A)+30*C*a^2)*tan(c+d*x)+2//13*C*d^-1*(a+b*sec(c+d*x))^5//2*sec(c+d*x)^3*tan(c+d*x)+-1//45045*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(-1078*b^4*(11C+13A)+180*C*a^4+-30*a^2*b^2*(543C+715A))*sec(c+d*x)*tan(c+d*x)+2//45045*a*b^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(b^4*(18973C+23309A)+120*C*a^4+5*a^2*b^2*(79C+143A))*tan(c+d*x)+10//143*C*a*d^-1*(a+b*sec(c+d*x))^3//2*sec(c+d*x)^3*tan(c+d*x)+2//9009*a*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^2*(15*C*a^2+2209*C*b^2+2717*A*b^2)*tan(c+d*x)+1//45045*b^-5*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-1617*b^6*(11C+13A)+240*C*a^6+-3*a^2*b^4*(10223C+13299A)+10*a^4*b^2*(76C+143A))*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//45045*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(240*C*a^5+1617*b^5*(11C+13A)+-6*a*b^4*(2174C+2717A)+10*a^3*b^2*(94C+143A)+15*a^2*b^3*(1175C+1573A)+180*C*b*a^4)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^5//2*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(1//693*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(16*C*a^4+30*b^4*(9C+11A)+6*a^2*b^2*(19C+33A))*tan(c+d*x)+1//693*b^-2*d^-1*(a+b*sec(c+d*x))^5//2*(16*C*a^2+18*b^2*(9C+11A))*tan(c+d*x)+-8//99*C*a*b^-2*d^-1*(a+b*sec(c+d*x))^7//2*tan(c+d*x)+2//11*C*b^-1*d^-1*(a+b*sec(c+d*x))^7//2*sec(c+d*x)*tan(c+d*x)+2//693*a*b^-2*d^-1*(a+b*sec(c+d*x))^3//2*(8*C*a^2+67*C*b^2+99*A*b^2)*tan(c+d*x)+-1//693*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(8*C*a^4+15*b^4*(9C+11A)+-6*a*b^3*(101C+132A)+3*a^2*b^2*(19C+33A)+6*C*b*a^3)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+-2//693*a*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(a+-1b)*(3*b^4*(247C+319A)+8*C*a^4+3*a^2*b^2*(17C+33A))*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^5//2*(A+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(-1//315*b^-1*d^-1*(a+b*sec(c+d*x))^3//2*(-14*b^2*(7C+9A)+20*C*a^2)*tan(c+d*x)+2//9*C*b^-1*d^-1*(a+b*sec(c+d*x))^7//2*tan(c+d*x)+-4//63*C*a*b^-1*d^-1*(a+b*sec(c+d*x))^5//2*tan(c+d*x)+4//315*a*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*(-5*C*a^2+57*C*b^2+84*A*b^2)*tan(c+d*x)+1//315*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-21*b^4*(7C+9A)+10*C*a^4+-3*a^2*b^2*(93C+161A))*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//315*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(10*C*a^3+21*b^3*(7C+9A)+-6*a*b^2*(19C+28A)+15*b*a^2*(11C+21A))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-1//2*sec(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(1//105*b^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(10*b^2*(5C+7A)+48*C*a^2)*tan(c+d*x)+2//7*C*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^2*tan(c+d*x)+-12//35*C*a*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)*tan(c+d*x)+2//105*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(5*b^3*(5C+7A)+48*C*a^3+-12*C*b*a^2+2*a*b^2*(22C+35A))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+4//105*a*b^-5*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(a+-1b)*(22*C*b^2+24*C*a^2+35*A*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-1//2*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(-8//15*C*a*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*tan(c+d*x)+2//5*C*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)*tan(c+d*x)+-2//15*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(3*b^2*(3C+5A)+8*C*a^2+-2*C*a*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//15*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(3*b^2*(3C+5A)+8*C*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-1//2*(A+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(2//3*C*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*tan(c+d*x)+2//3*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(C*(b+2a)+3*A*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+4//3*C*a*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(a+-1b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3//2*sec(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(-1*b^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^2*(2*A*b^2+2*C*a^2)*tan(c+d*x)+-2//5*a*b^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*(-3*C*b^2+5*A*b^2+8*C*a^2)*tan(c+d*x)+1//5*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*(-2*C*b^2+10*A*b^2+12*C*a^2)*sec(c+d*x)*tan(c+d*x)+-1//5*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(2*b^3*(3C+5A)+32*C*a^3+4*a*b^2*(2C+5A)+24*C*b*a^2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//5*b^-5*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(-32*C*a^4+2*b^4*(3C+5A)+-4*a^2*b^2*(-4C+5A))*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3//2*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(2//3*C*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*tan(c+d*x)+2*a*b^-2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*(A*b^2+C*a^2)*tan(c+d*x)+1//3*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(2*C*(b^2+8*a^2+6*a*b)+6*A*b^2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+2//3*a*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(-5*C*b^2+3*A*b^2+8*C*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3//2*(A+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(-1*b^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*(2*A*b^2+2*C*a^2)*tan(c+d*x)+b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(-4*C*a^2+-2*A*b^2+2*C*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(-2*C*(b+2a)+2*A*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^3*(A+C*sec(c+d*x)^2), x) == :(1//3*b^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*(-2*C*b^2+2*A*b^2+4*C*a^2)*tan(c+d*x)+-4//3*a*b^-3*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*(-3*C*a^4+2*A*b^4+5*C*a^2*b^2)*tan(c+d*x)+-1//3*b^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*sec(c+d*x)^2*(2*A*b^2+2*C*a^2)*tan(c+d*x)+1//3*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(a^2+-1*b^2)^-1*(-2*b^4*(C+3A)+32*C*a^4+4*a^2*b^2*(A+-8C)+6*a*b^3*(A+-3C)+24*C*b*a^3)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+4//3*a*b^-5*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(a^2+-1*b^2)^-1*(-1*b^4*(-4C+3A)+8*C*a^4+a^2*b^2*(A+-14C))*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^2*(A+C*sec(c+d*x)^2), x) == :(1//3*b^-2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*(-10*C*a^4+6*A*b^4+2*a^2*b^2*(A+9C))*tan(c+d*x)+2//3*a*b^-2*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*(A*b^2+C*a^2)*tan(c+d*x)+-1//3*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(a^2+-1*b^2)^-1*(6*b^3*(A+-1C)+16*C*a^3+-2*a*b^2*(A+9C)+12*C*b*a^2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//3*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(a^2+-1*b^2)^-1*(-16*C*a^4+6*b^4*(A+-1C)+2*a^2*b^2*(A+15C))*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*(A+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(-1//3*b^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*(2*A*b^2+2*C*a^2)*tan(c+d*x)+-4//3*a*b^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*(-1*C*a^2+2*A*b^2+3*C*b^2)*tan(c+d*x)+1//3*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(a^2+-1*b^2)^-1*(-2*b^2*(A+3C)+4*C*a^2+6*a*b*(A+C))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+-4*a*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(-3b+3a)^-1*(-1*C*a^2+2*A*b^2+3*C*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate(sec(c+d*x)^3*(a+b*sec(c+d*x))*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//5*d^-1*(4*C*b+5*B*a)*tan(c+d*x)+1//8*d^-1*(3*B*b+3*C*a)*arctanh(sin(c+d*x))+1//15*d^-1*tan(c+d*x)^3*(4*C*b+5*B*a)+1//4*d^-1*sec(c+d*x)^3*(B*b+C*a)*tan(c+d*x)+1//8*d^-1*(3*B*b+3*C*a)*sec(c+d*x)*tan(c+d*x)+1//5*C*b*d^-1*sec(c+d*x)^4*tan(c+d*x))
@test integrate(sec(c+d*x)^2*(a+b*sec(c+d*x))*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(d^-1*(B*b+C*a)*tan(c+d*x)+1//3*d^-1*tan(c+d*x)^3*(B*b+C*a)+1//8*d^-1*(3*C*b+4*B*a)*arctanh(sin(c+d*x))+1//8*d^-1*(3*C*b+4*B*a)*sec(c+d*x)*tan(c+d*x)+1//4*C*b*d^-1*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))*(B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :((1/2)*d^-1*(B*b+C*a)*arctanh(sin(c+d*x))+1//3*d^-1*(2*C*b+3*B*a)*tan(c+d*x)+(1/2)*d^-1*(B*b+C*a)*sec(c+d*x)*tan(c+d*x)+1//3*C*b*d^-1*sec(c+d*x)^2*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(d^-1*(B*b+C*a)*tan(c+d*x)+(1/2)*d^-1*(C*b+2*B*a)*arctanh(sin(c+d*x))+(1/2)*C*b*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))*(B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(B*a*x+d^-1*(B*b+C*a)*arctanh(sin(c+d*x))+C*b*d^-1*tan(c+d*x))
@test integrate(cos(c+d*x)^2*(a+b*sec(c+d*x))*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*(B*b+C*a)+B*a*d^-1*sin(c+d*x)+C*b*d^-1*arctanh(sin(c+d*x)))
@test integrate(cos(c+d*x)^3*(a+b*sec(c+d*x))*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*(C*b+(1/2)*B*a)+d^-1*(B*b+C*a)*sin(c+d*x)+(1/2)*B*a*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^4*(a+b*sec(c+d*x))*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*((1/2)*B*b+(1/2)*C*a)+1//3*d^-1*(2*B*a+3*C*b)*sin(c+d*x)+(1/2)*d^-1*(B*b+C*a)*cos(c+d*x)*sin(c+d*x)+1//3*B*a*d^-1*cos(c+d*x)^2*sin(c+d*x))
@test integrate(cos(c+d*x)^5*(a+b*sec(c+d*x))*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*((1/2)*C*b+3//8*B*a)+d^-1*(B*b+C*a)*sin(c+d*x)+-1//3*d^-1*sin(c+d*x)^3*(B*b+C*a)+1//8*d^-1*(3*B*a+4*C*b)*cos(c+d*x)*sin(c+d*x)+1//4*B*a*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate(cos(c+d*x)^6*(a+b*sec(c+d*x))*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*(3//8*B*b+3//8*C*a)+-1//15*d^-1*sin(c+d*x)^3*(4*B*a+5*C*b)+1//5*d^-1*(4*B*a+5*C*b)*sin(c+d*x)+1//4*d^-1*cos(c+d*x)^3*(B*b+C*a)*sin(c+d*x)+1//8*d^-1*(3*B*b+3*C*a)*cos(c+d*x)*sin(c+d*x)+1//5*B*a*d^-1*cos(c+d*x)^4*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//5*d^-1*(4*C*b^2+5*a*(C*a+2*B*b))*tan(c+d*x)+1//8*d^-1*(3*B*b^2+4*B*a^2+6*C*a*b)*arctanh(sin(c+d*x))+1//15*d^-1*tan(c+d*x)^3*(4*C*b^2+5*a*(C*a+2*B*b))+1//8*d^-1*(3*B*b^2+4*B*a^2+6*C*a*b)*sec(c+d*x)*tan(c+d*x)+1//20*b*d^-1*sec(c+d*x)^3*(5*B*b+6*C*a)*tan(c+d*x)+1//5*C*b*d^-1*sec(c+d*x)^3*(a+b*sec(c+d*x))*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*(B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//8*d^-1*(3*C*b^2+4*C*a^2+8*B*a*b)*arctanh(sin(c+d*x))+1//6*b^-1*d^-1*(-1*C*a^3+4*B*b^3+4*B*b*a^2+8*C*a*b^2)*tan(c+d*x)+1//24*d^-1*(-2*C*a^2+9*C*b^2+8*B*a*b)*sec(c+d*x)*tan(c+d*x)+1//4*C*b^-1*d^-1*(a+b*sec(c+d*x))^3*tan(c+d*x)+1//12*b^-1*d^-1*(a+b*sec(c+d*x))^2*(-1*C*a+4*B*b)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*d^-1*(B*b^2+2*B*a^2+2*C*a*b)*arctanh(sin(c+d*x))+1//3*d^-1*(2*C*a^2+2*C*b^2+6*B*a*b)*tan(c+d*x)+1//3*C*d^-1*(a+b*sec(c+d*x))^2*tan(c+d*x)+1//6*b*d^-1*(2*C*a+3*B*b)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*(B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(B*x*a^2+(1/2)*d^-1*(C*b^2+2*C*a^2+4*B*a*b)*arctanh(sin(c+d*x))+(1/2)*b*d^-1*(2*B*b+3*C*a)*tan(c+d*x)+(1/2)*C*b*d^-1*(a+b*sec(c+d*x))*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a*x*(C*a+2*B*b)+B*a^2*d^-1*sin(c+d*x)+C*b^2*d^-1*tan(c+d*x)+b*d^-1*(B*b+2*C*a)*arctanh(sin(c+d*x)))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*(B*b^2+(1/2)*B*a^2+2*C*a*b)+C*b^2*d^-1*arctanh(sin(c+d*x))+a*d^-1*(C*a+2*B*b)*sin(c+d*x)+(1/2)*B*a^2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^4*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*(C*b^2+(1/2)*C*a^2+B*a*b)+1//3*d^-1*(2*B*a^2+3*B*b^2+6*C*a*b)*sin(c+d*x)+(1/2)*a*d^-1*(C*a+2*B*b)*cos(c+d*x)*sin(c+d*x)+1//3*B*a^2*d^-1*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^5*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*((1/2)*B*b^2+3//8*B*a^2+C*a*b)+d^-1*(C*a^2+C*b^2+2*B*a*b)*sin(c+d*x)+-1//3*a*d^-1*sin(c+d*x)^3*(C*a+2*B*b)+1//8*d^-1*(3*B*a^2+4*B*b^2+8*C*a*b)*cos(c+d*x)*sin(c+d*x)+1//4*B*a^2*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^6*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*((1/2)*C*b^2+3//8*C*a^2+3//4*B*a*b)+-1//15*d^-1*sin(c+d*x)^3*(4*B*a^2+5*B*b^2+10*C*a*b)+1//5*d^-1*(4*B*a^2+5*B*b^2+10*C*a*b)*sin(c+d*x)+1//8*d^-1*(3*C*a^2+4*C*b^2+6*B*a*b)*cos(c+d*x)*sin(c+d*x)+1//4*a*d^-1*cos(c+d*x)^3*(C*a+2*B*b)*sin(c+d*x)+1//5*B*a^2*d^-1*cos(c+d*x)^4*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//5*d^-1*(4*B*b^3+5*C*a^3+12*C*a*b^2+15*B*b*a^2)*tan(c+d*x)+1//15*d^-1*tan(c+d*x)^3*(4*B*b^3+5*C*a^3+12*C*a*b^2+15*B*b*a^2)+1//16*d^-1*(5*C*b^3+8*B*a^3+18*B*a*b^2+18*C*b*a^2)*arctanh(sin(c+d*x))+1//16*d^-1*(5*C*b^3+8*B*a^3+18*B*a*b^2+18*C*b*a^2)*sec(c+d*x)*tan(c+d*x)+1//15*b^2*d^-1*sec(c+d*x)^4*(3*B*b+4*C*a)*tan(c+d*x)+1//24*b*d^-1*sec(c+d*x)^3*(5*C*b^2+14*C*a^2+18*B*a*b)*tan(c+d*x)+1//6*C*b*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*(B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//8*d^-1*(3*B*b^3+4*C*a^3+9*C*a*b^2+12*B*b*a^2)*arctanh(sin(c+d*x))+1//30*b^-1*d^-1*(-3*C*a^4+16*C*b^4+15*B*b*a^3+52*C*a^2*b^2+60*B*a*b^3)*tan(c+d*x)+1//120*d^-1*(-6*C*a^3+45*B*b^3+30*B*b*a^2+71*C*a*b^2)*sec(c+d*x)*tan(c+d*x)+1//5*C*b^-1*d^-1*(a+b*sec(c+d*x))^4*tan(c+d*x)+1//20*b^-1*d^-1*(a+b*sec(c+d*x))^3*(-1*C*a+5*B*b)*tan(c+d*x)+1//60*b^-1*d^-1*(a+b*sec(c+d*x))^2*(-3*C*a^2+16*C*b^2+15*B*a*b)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//6*d^-1*(3*C*a^3+4*B*b^3+12*C*a*b^2+16*B*b*a^2)*tan(c+d*x)+1//8*d^-1*(3*C*b^3+8*B*a^3+12*B*a*b^2+12*C*b*a^2)*arctanh(sin(c+d*x))+1//4*C*d^-1*(a+b*sec(c+d*x))^3*tan(c+d*x)+1//12*d^-1*(a+b*sec(c+d*x))^2*(3*C*a+4*B*b)*tan(c+d*x)+1//24*b*d^-1*(6*C*a^2+9*C*b^2+20*B*a*b)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*(B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(B*x*a^3+(1/2)*d^-1*(B*b^3+2*C*a^3+3*C*a*b^2+6*B*b*a^2)*arctanh(sin(c+d*x))+1//3*b*d^-1*(2*C*b^2+8*C*a^2+9*B*a*b)*tan(c+d*x)+1//3*C*b*d^-1*(a+b*sec(c+d*x))^2*tan(c+d*x)+1//6*b^2*d^-1*(3*B*b+5*C*a)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*a^2*(C*a+3*B*b)+(1/2)*b*d^-1*(C*b^2+6*C*a^2+6*B*a*b)*arctanh(sin(c+d*x))+-1*b*d^-1*(-1*B*b^2+2*B*a^2+-3*C*a*b)*tan(c+d*x)+B*a*d^-1*(a+b*sec(c+d*x))^2*sin(c+d*x)+-1//2*b^2*d^-1*(-1*C*b+2*B*a)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*a*x*(B*a^2+6*B*b^2+6*C*a*b)+a^2*d^-1*(C*a+2*B*b)*sin(c+d*x)+b^2*d^-1*(B*b+3*C*a)*arctanh(sin(c+d*x))+-1//2*b^2*d^-1*(B*a+-2*C*b)*tan(c+d*x)+(1/2)*B*a*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^4*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*(B*b^3+(1/2)*C*a^3+3*C*a*b^2+3//2*B*b*a^2)+C*b^3*d^-1*arctanh(sin(c+d*x))+1//3*a*d^-1*(2*B*a^2+8*B*b^2+9*C*a*b)*sin(c+d*x)+1//6*a^2*d^-1*(3*C*a+5*B*b)*cos(c+d*x)*sin(c+d*x)+1//3*B*a*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^5*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*(C*b^3+3//8*B*a^3+3//2*B*a*b^2+3//2*C*b*a^2)+1//3*d^-1*(2*C*a^3+3*B*b^3+6*B*b*a^2+9*C*a*b^2)*sin(c+d*x)+1//6*a^2*d^-1*cos(c+d*x)^2*(2*C*a+3*B*b)*sin(c+d*x)+1//8*a*d^-1*(3*B*a^2+10*B*b^2+12*C*a*b)*cos(c+d*x)*sin(c+d*x)+1//4*B*a*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^6*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*((1/2)*B*b^3+3//8*C*a^3+3//2*C*a*b^2+9//8*B*b*a^2)+1//5*d^-1*(4*B*a^3+5*C*b^3+14*B*a*b^2+15*C*b*a^2)*sin(c+d*x)+-1//15*a*d^-1*sin(c+d*x)^3*(4*B*a^2+12*B*b^2+15*C*a*b)+1//8*d^-1*(3*C*a^3+4*B*b^3+9*B*b*a^2+12*C*a*b^2)*cos(c+d*x)*sin(c+d*x)+1//20*a^2*d^-1*cos(c+d*x)^3*(5*C*a+7*B*b)*sin(c+d*x)+1//5*B*a*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^4*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-1*sec(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//3*b^-3*d^-1*(-3*C*a^2+-2*C*b^2+3*B*a*b)*tan(c+d*x)+(1/2)*b^-4*d^-1*(b^2+2*a^2)*(B*b+-1*C*a)*arctanh(sin(c+d*x))+(1/2)*b^-2*d^-1*(B*b+-1*C*a)*sec(c+d*x)*tan(c+d*x)+1//3*C*b^-1*d^-1*sec(c+d*x)^2*tan(c+d*x)+-2*a^3*b^-4*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(B*b+-1*C*a)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*sec(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(b^-2*d^-1*(B*b+-1*C*a)*tan(c+d*x)+-1//2*b^-3*d^-1*(-1*C*b^2+-2*C*a^2+2*B*a*b)*arctanh(sin(c+d*x))+(1/2)*C*b^-1*d^-1*sec(c+d*x)*tan(c+d*x)+2*a^2*b^-3*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(B*b+-1*C*a)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*(B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(C*b^-1*d^-1*tan(c+d*x)+b^-2*d^-1*(B*b+-1*C*a)*arctanh(sin(c+d*x))+-2*a*b^-2*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(B*b+-1*C*a)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(C*b^-1*d^-1*arctanh(sin(c+d*x))+b^-1*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(-2*C*a+2*B*b)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*(B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(B*x*a^-1+-1*a^-1*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(-2*C*a+2*B*b)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*cos(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1*x*a^-2*(B*b+-1*C*a)+B*a^-1*d^-1*sin(c+d*x)+2*b*a^-2*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(B*b+-1*C*a)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*cos(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*x*a^-3*(B*a^2+2*B*b^2+-2*C*a*b)+-1*a^-2*d^-1*(B*b+-1*C*a)*sin(c+d*x)+(1/2)*B*a^-1*d^-1*cos(c+d*x)*sin(c+d*x)+-2*a^-3*b^2*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(B*b+-1*C*a)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*cos(c+d*x)^4*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//2*x*a^-4*(a^2+2*b^2)*(B*b+-1*C*a)+1//3*a^-3*d^-1*(2*B*a^2+3*B*b^2+-3*C*a*b)*sin(c+d*x)+-1//2*a^-2*d^-1*(B*b+-1*C*a)*cos(c+d*x)*sin(c+d*x)+1//3*B*a^-1*d^-1*cos(c+d*x)^2*sin(c+d*x)+2*a^-4*b^3*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(B*b+-1*C*a)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-2*sec(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//2*b^-4*d^-1*(-1*C*b^2+-6*C*a^2+4*B*a*b)*arctanh(sin(c+d*x))+b^-3*d^-1*(a^2+-1*b^2)^-1*(-1*B*b^3+-3*C*a^3+2*B*b*a^2+2*C*a*b^2)*tan(c+d*x)+-1//2*b^-2*d^-1*(a^2+-1*b^2)^-1*(C*b^2+-3*C*a^2+2*B*a*b)*sec(c+d*x)*tan(c+d*x)+2*a^2*b^-4*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-3*B*b^3+-3*C*a^3+2*B*b*a^2+4*C*a*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+a*b^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*sec(c+d*x)^2*(B*b+-1*C*a)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-2*sec(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(C*b^-2*d^-1*tan(c+d*x)+b^-3*d^-1*(B*b+-2*C*a)*arctanh(sin(c+d*x))+-1*a^2*b^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*(B*b+-1*C*a)*tan(c+d*x)+-2*a*b^-3*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-2*B*b^3+-2*C*a^3+B*b*a^2+3*C*a*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-2*(B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(C*b^-2*d^-1*arctanh(sin(c+d*x))+-1*b^-2*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(2*B*b^3+2*C*a^3+-4*C*a*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+a*b^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*(B*b+-1*C*a)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-2*C*b+2*B*a)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*(B*b+-1*C*a)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-2*(B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(B*x*a^-2+-1*a^-2*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-2*B*b^3+-2*C*a^3+4*B*b*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+b*a^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*(B*b+-1*C*a)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-2*cos(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1*x*a^-3*(-1*C*a+2*B*b)+a^-2*d^-1*(a^2+-1*b^2)^-1*(B*a^2+-2*B*b^2+C*a*b)*sin(c+d*x)+b*a^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*(B*b+-1*C*a)*sin(c+d*x)+2*b*a^-3*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-2*B*b^3+-2*C*a^3+C*a*b^2+3*B*b*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-2*cos(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*x*a^-4*(B*a^2+6*B*b^2+-4*C*a*b)+-1*a^-3*d^-1*(a^2+-1*b^2)^-1*(-1*C*a^3+-3*B*b^3+2*B*b*a^2+2*C*a*b^2)*sin(c+d*x)+(1/2)*a^-2*d^-1*(a^2+-1*b^2)^-1*(B*a^2+-3*B*b^2+2*C*a*b)*cos(c+d*x)*sin(c+d*x)+-2*a^-4*b^2*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-3*B*b^3+-3*C*a^3+2*C*a*b^2+4*B*b*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+b*a^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*(B*b+-1*C*a)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*sec(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(b^-4*d^-1*(B*b+-3*C*a)*arctanh(sin(c+d*x))+-1//2*b^-3*d^-1*(a^2+-1*b^2)^-1*(-3*C*a^2+2*C*b^2+B*a*b)*tan(c+d*x)+-1*a*b^-4*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(-6*C*a^5+6*B*b^5+-12*C*a*b^4+-5*B*a^2*b^3+2*B*b*a^4+15*C*a^3*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1//2*a^2*b^-3*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-4*B*b^3+-3*C*a^3+B*b*a^2+6*C*a*b^2)*tan(c+d*x)+(1/2)*a*b^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*sec(c+d*x)^2*(B*b+-1*C*a)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*sec(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(C*b^-3*d^-1*arctanh(sin(c+d*x))+b^-3*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(-2*C*a^5+2*B*b^5+B*a^2*b^3+-6*C*a*b^4+5*C*a^3*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+(1/2)*a*b^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-4*B*b^3+-3*C*a^3+B*b*a^2+6*C*a*b^2)*tan(c+d*x)+-1//2*a^2*b^-2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*(B*b+-1*C*a)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*(B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(-1*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(-1*C*a^2+-2*C*b^2+3*B*a*b)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+(1/2)*b^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(C*a^3+2*B*b^3+B*b*a^2+-4*C*a*b^2)*tan(c+d*x)+(1/2)*a*b^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*(B*b+-1*C*a)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(B*b^2+2*B*a^2+-3*C*a*b)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1*d^-1*(a+b*sec(c+d*x))^-2*(-2*b^2+2*a^2)^-1*(B*b+-1*C*a)*tan(c+d*x)+-1//2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-1*C*a^2+-2*C*b^2+3*B*a*b)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*(B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(B*x*a^-3+-1*a^-3*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(-2*C*a^5+2*B*b^5+-1*C*a^3*b^2+-5*B*a^2*b^3+6*B*b*a^4)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+(1/2)*b*a^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*(B*b+-1*C*a)*tan(c+d*x)+(1/2)*b*a^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-3*C*a^3+-2*B*b^3+5*B*b*a^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*cos(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1*x*a^-4*(-1*C*a+3*B*b)+(1/2)*a^-3*d^-1*(a^2+-1*b^2)^-2*(2*B*a^4+6*B*b^4+-11*B*a^2*b^2+-2*C*a*b^3+5*C*b*a^3)*sin(c+d*x)+b*a^-4*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(-6*C*a^5+6*B*b^5+-15*B*a^2*b^3+-2*C*a*b^4+5*C*a^3*b^2+12*B*b*a^4)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+(1/2)*b*a^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*(B*b+-1*C*a)*sin(c+d*x)+(1/2)*b*a^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-4*C*a^3+-3*B*b^3+C*a*b^2+6*B*b*a^2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//315*b^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(-150*B*b^3+-16*C*a^3+-26*C*a*b^2+24*B*b*a^2)*tan(c+d*x)+2//9*C*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^3*tan(c+d*x)+1//63*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^2*(2*C*a+18*B*b)*tan(c+d*x)+1//315*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(-12*C*a^2+98*C*b^2+18*B*a*b)*sec(c+d*x)*tan(c+d*x)+-1//315*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-16*C*a^3+3*b^3*(-49C+25B)+12*b*a^2*(-1C+2B)+18*a*b^2*(B+-2C))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//315*b^-5*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(-16*C*a^4+147*C*b^4+-24*C*a^2*b^2+24*B*b*a^3+57*B*a*b^3)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//105*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(-8*C*a^2+50*C*b^2+14*B*a*b)*tan(c+d*x)+2//7*C*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^2*tan(c+d*x)+1//35*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*(2*C*a+14*B*b)*sec(c+d*x)*tan(c+d*x)+1//105*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-63*B*b^3+-8*C*a^3+-19*C*a*b^2+14*B*b*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//105*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(b^2*(-25C+63B)+-8*C*a^2+2*a*b*(-3C+7B))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^(1/2)*(B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//15*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*(-4*C*a+10*B*b)*tan(c+d*x)+2//5*C*b^-1*d^-1*(a+b*sec(c+d*x))^3//2*tan(c+d*x)+-1//15*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-9*C*b+-2*C*a+5*B*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//15*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(-2*C*a^2+9*C*b^2+5*B*a*b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^(1/2)*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//3*C*d^-1*(a+b*sec(c+d*x))^(1/2)*tan(c+d*x)+1//3*b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-1C+3B)*(-2b+2a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//3*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(C*a+3*B*b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^3//2*sec(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//693*b^-3*d^-1*(a+b*sec(c+d*x))^5//2*(-162*C*b^2+-48*C*a^2+88*B*a*b)*tan(c+d*x)+1//3465*b^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(-96*C*a^4+1350*C*b^4+-288*C*a^2*b^2+176*B*b*a^3+858*B*a*b^3)*tan(c+d*x)+1//3465*b^-3*d^-1*(a+b*sec(c+d*x))^3//2*(-96*C*a^3+1078*B*b^3+-408*C*a*b^2+176*B*b*a^2)*tan(c+d*x)+1//99*b^-2*d^-1*(a+b*sec(c+d*x))^5//2*(-12*C*a+22*B*b)*sec(c+d*x)*tan(c+d*x)+2//11*C*b^-1*d^-1*(a+b*sec(c+d*x))^5//2*sec(c+d*x)^2*tan(c+d*x)+-1//3465*b^-5*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-48*C*a^5+1617*B*b^5+-108*C*a^3*b^2+88*B*b*a^4+363*B*a^2*b^3+2088*C*a*b^4)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+-1//3465*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-48*C*a^4+-3*b^4*(-225C+539B)+3*a*b^3*(-471C+143B)+4*b*a^3*(-9C+22B)+6*a^2*b^2*(-24C+11B))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^3//2*sec(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//315*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(-150*B*b^3+-16*C*a^3+-78*C*a*b^2+36*B*b*a^2)*tan(c+d*x)+-1//315*b^-2*d^-1*(a+b*sec(c+d*x))^3//2*(-98*C*b^2+-16*C*a^2+36*B*a*b)*tan(c+d*x)+1//63*b^-2*d^-1*(a+b*sec(c+d*x))^5//2*(-8*C*a+18*B*b)*tan(c+d*x)+2//9*C*b^-1*d^-1*(a+b*sec(c+d*x))^5//2*sec(c+d*x)*tan(c+d*x)+-1//315*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(3*b^3*(-49C+25B)+8*C*a^3+-6*b*a^2*(-1C+3B)+-3*a*b^2*(-13C+57B))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//315*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-147*C*b^4+-8*C*a^4+-246*B*a*b^3+-33*C*a^2*b^2+18*B*b*a^3)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^3//2*(B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//35*b^-1*d^-1*(a+b*sec(c+d*x))^3//2*(-4*C*a+14*B*b)*tan(c+d*x)+1//105*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*(-12*C*a^2+50*C*b^2+42*B*a*b)*tan(c+d*x)+2//7*C*b^-1*d^-1*(a+b*sec(c+d*x))^5//2*tan(c+d*x)+-1//105*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-1*b^2*(-25C+63B)+-6*C*a^2+a*b*(-57C+21B))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//105*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(-6*C*a^3+63*B*b^3+21*B*b*a^2+82*C*a*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^3//2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//15*d^-1*(a+b*sec(c+d*x))^(1/2)*(6*C*a+10*B*b)*tan(c+d*x)+2//5*C*d^-1*(a+b*sec(c+d*x))^3//2*tan(c+d*x)+1//15*b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-5*B*b+-3*C*a+9*C*b+15*B*a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//15*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(3*C*a^2+9*C*b^2+20*B*a*b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^5//2*sec(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//693*b^-2*d^-1*(a+b*sec(c+d*x))^5//2*(-162*C*b^2+-16*C*a^2+44*B*a*b)*tan(c+d*x)+-1//3465*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(-1350*C*b^4+-80*C*a^4+-2508*B*a*b^3+-570*C*a^2*b^2+220*B*b*a^3)*tan(c+d*x)+-1//3465*b^-2*d^-1*(a+b*sec(c+d*x))^3//2*(-1078*B*b^3+-80*C*a^3+-670*C*a*b^2+220*B*b*a^2)*tan(c+d*x)+1//99*b^-2*d^-1*(a+b*sec(c+d*x))^7//2*(-8*C*a+22*B*b)*tan(c+d*x)+2//11*C*b^-1*d^-1*(a+b*sec(c+d*x))^7//2*sec(c+d*x)*tan(c+d*x)+-1//3465*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-3*b^4*(-225C+539B)+40*C*a^4+-1*b*a^3*(-30C+110B)+-15*a^2*b^2*(-19C+121B)+6*a*b^3*(-505C+209B))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//3465*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-1617*B*b^5+-40*C*a^5+-3705*C*a*b^4+-3069*B*a^2*b^3+-255*C*a^3*b^2+110*B*b*a^4)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^5//2*(B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//63*b^-1*d^-1*(a+b*sec(c+d*x))^5//2*(-4*C*a+18*B*b)*tan(c+d*x)+1//315*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*(-20*C*a^3+150*B*b^3+90*B*b*a^2+228*C*a*b^2)*tan(c+d*x)+1//315*b^-1*d^-1*(a+b*sec(c+d*x))^3//2*(-20*C*a^2+98*C*b^2+90*B*a*b)*tan(c+d*x)+2//9*C*b^-1*d^-1*(a+b*sec(c+d*x))^7//2*tan(c+d*x)+-1//315*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-10*C*a^3+3*b^3*(-49C+25B)+-6*a*b^2*(-19C+60B)+15*b*a^2*(-11C+3B))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//315*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(-10*C*a^4+147*C*b^4+45*B*b*a^3+279*C*a^2*b^2+435*B*a*b^3)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^5//2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//35*d^-1*(a+b*sec(c+d*x))^3//2*(10*C*a+14*B*b)*tan(c+d*x)+1//105*d^-1*(a+b*sec(c+d*x))^(1/2)*(30*C*a^2+50*C*b^2+112*B*a*b)*tan(c+d*x)+2//7*C*d^-1*(a+b*sec(c+d*x))^5//2*tan(c+d*x)+1//105*b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(b^2*(-25C+63B)+15*a^2*(-1C+7B)+-8*a*b*(-15C+7B))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//105*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(15*C*a^3+63*B*b^3+145*C*a*b^2+161*B*b*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-1//2*sec(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//105*b^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(-50*C*b^2+-48*C*a^2+56*B*a*b)*tan(c+d*x)+1//35*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(-12*C*a+14*B*b)*sec(c+d*x)*tan(c+d*x)+2//7*C*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^2*tan(c+d*x)+-2//105*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(b^3*(-25C+63B)+-48*C*a^3+-2*a*b^2*(7B+22C)+4*b*a^2*(3C+14B))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//105*b^-5*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(-48*C*a^3+63*B*b^3+-44*C*a*b^2+56*B*b*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-1//2*sec(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//15*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(-8*C*a+10*B*b)*tan(c+d*x)+2//5*C*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)*tan(c+d*x)+2//15*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(b^2*(-9C+5B)+-8*C*a^2+2*a*b*(C+5B))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//15*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-9*C*b^2+-8*C*a^2+10*B*a*b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-1//2*(B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(2//3*C*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*tan(c+d*x)+-2//3*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-1*C*b+-2*C*a+3*B*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//3*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(-2*C*a+3*B*b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-1//2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2*b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(B+-1C)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+C*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3//2*sec(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//15*b^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*(-48*C*a^3+-10*B*b^3+18*C*a*b^2+40*B*b*a^2)*tan(c+d*x)+-1//5*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*(-12*C*a^2+2*C*b^2+10*B*a*b)*sec(c+d*x)*tan(c+d*x)+2*a*b^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^2*(B*b+-1*C*a)*tan(c+d*x)+1//15*b^-5*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(-96*C*a^4+18*C*b^4+-50*B*a*b^3+48*C*a^2*b^2+80*B*b*a^3)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//15*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(-96*C*a^3+2*b^3*(-9C+5B)+8*b*a^2*(-9C+10B)+12*a*b^2*(-2C+5B))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3//2*sec(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//3*C*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*tan(c+d*x)+-2*a^2*b^-2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*(B*b+-1*C*a)*tan(c+d*x)+1//3*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(6*B*b^3+16*C*a^3+-12*B*b*a^2+-10*C*a*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+-1//3*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(2b+4a)*(-1*C*b+-4*C*a+3*B*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3//2*(B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(2*a*b^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*(B*b+-1*C*a)*tan(c+d*x)+b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(-4*C*a^2+2*C*b^2+2*B*a*b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(-4*C*a+2*b*(B+-1C))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3//2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*(-2*C*a+2*B*b)*tan(c+d*x)+b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(2B+2C)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(-2*B*b+2*C*a)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^3*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//3*b^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*(-4*C*a^2+2*C*b^2+2*B*a*b)*tan(c+d*x)+-2//3*a^2*b^-3*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*(-7*B*b^3+-6*C*a^3+3*B*b*a^2+10*C*a*b^2)*tan(c+d*x)+2//3*a*b^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*sec(c+d*x)^2*(B*b+-1*C*a)*tan(c+d*x)+b^-5*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(-3b+3a)^-1*(-6*B*b^5+32*C*a^5+-56*C*a^3*b^2+-16*B*b*a^4+16*C*a*b^4+30*B*a^2*b^3)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+-1//3*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(a^2+-1*b^2)^-1*(-32*C*a^4+-2*b^4*(-1C+3B)+-18*a*b^3*(B+-1C)+2*b*a^3*(-12C+8B)+4*a^2*b^2*(3B+8C))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-2//3*a^2*b^-2*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*(B*b+-1*C*a)*tan(c+d*x)+2//3*a*b^-2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*(-6*B*b^3+-5*C*a^3+2*B*b*a^2+9*C*a*b^2)*tan(c+d*x)+b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(-3b+3a)^-1*(-16*C*a^4+-6*C*b^4+-12*B*a*b^3+4*B*b*a^3+30*C*a^2*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//3*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(a^2+-1*b^2)^-1*(-16*C*a^3+-6*b^3*(B+-1C)+4*b*a^2*(B+-3C)+6*a*b^2*(B+3C))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*(B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//3*b^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*(4*C*a^3+6*B*b^3+-12*C*a*b^2+2*B*b*a^2)*tan(c+d*x)+2//3*a*b^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*(B*b+-1*C*a)*tan(c+d*x)+b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(-3b+3a)^-1*(4*C*a^3+6*B*b^3+-12*C*a*b^2+2*B*b*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//3*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(a^2+-1*b^2)^-1*(-6*b^2*(B+C)+4*C*a^2+2*a*b*(B+3C))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1*d^-1*(a+b*sec(c+d*x))^-3//2*(-3*b^2+3*a^2)^-1*(-2*C*a+2*B*b)*tan(c+d*x)+-1//3*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*(-6*C*b^2+-2*C*a^2+8*B*a*b)*tan(c+d*x)+b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(-3b+3a)^-1*(-6*C*b+-2*B*b+2*C*a+6*B*a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(-3b+3a)^-1*(2*C*a^2+6*C*b^2+-8*B*a*b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-7//2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1*d^-1*(a+b*sec(c+d*x))^-5//2*(-5*b^2+5*a^2)^-1*(-2*C*a+2*B*b)*tan(c+d*x)+-1//15*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-2*(-10*C*b^2+-6*C*a^2+16*B*a*b)*tan(c+d*x)+-1//15*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-3*(-6*C*a^3+18*B*b^3+-58*C*a*b^2+46*B*b*a^2)*tan(c+d*x)+1//15*b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(a^2+-1*b^2)^-2*(2*b^2*(5C+9B)+6*a^2*(C+5B)+-16*a*b*(B+3C))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//15*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-5//2*(a+-1b)^-2*(-18*B*b^3+6*C*a^3+-46*B*b*a^2+58*C*a*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate(sec(c+d*x)^3*(a+b*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//5*d^-1*(4*C*b+5*A*b+5*B*a)*tan(c+d*x)+1//8*d^-1*(3*B*b+3*C*a+4*A*a)*arctanh(sin(c+d*x))+1//15*d^-1*tan(c+d*x)^3*(4*C*b+5*A*b+5*B*a)+1//4*d^-1*sec(c+d*x)^3*(B*b+C*a)*tan(c+d*x)+1//8*d^-1*(3*B*b+3*C*a+4*A*a)*sec(c+d*x)*tan(c+d*x)+1//5*C*b*d^-1*sec(c+d*x)^4*tan(c+d*x))
@test integrate(sec(c+d*x)^2*(a+b*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//3*d^-1*(2*B*b+2*C*a+3*A*a)*tan(c+d*x)+1//8*d^-1*(3*C*b+4*A*b+4*B*a)*arctanh(sin(c+d*x))+1//3*d^-1*sec(c+d*x)^2*(B*b+C*a)*tan(c+d*x)+1//8*d^-1*(3*C*b+4*A*b+4*B*a)*sec(c+d*x)*tan(c+d*x)+1//4*C*b*d^-1*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :((1/2)*d^-1*(B*b+a*(C+2A))*arctanh(sin(c+d*x))+1//3*d^-1*(2*C*b+3*A*b+3*B*a)*tan(c+d*x)+(1/2)*d^-1*(B*b+C*a)*sec(c+d*x)*tan(c+d*x)+1//3*C*b*d^-1*sec(c+d*x)^2*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(A*a*x+d^-1*(B*b+C*a)*tan(c+d*x)+(1/2)*d^-1*(C*b+2*A*b+2*B*a)*arctanh(sin(c+d*x))+(1/2)*C*b*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(x*(A*b+B*a)+d^-1*(B*b+C*a)*arctanh(sin(c+d*x))+A*a*d^-1*sin(c+d*x)+C*b*d^-1*tan(c+d*x))
@test integrate(cos(c+d*x)^2*(a+b*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*(B*b+(1/2)*a*(A+2C))+d^-1*(A*b+B*a)*sin(c+d*x)+C*b*d^-1*arctanh(sin(c+d*x))+(1/2)*A*a*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^3*(a+b*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*(C*b+(1/2)*A*b+(1/2)*B*a)+1//3*d^-1*(2*A*a+3*B*b+3*C*a)*sin(c+d*x)+(1/2)*d^-1*(A*b+B*a)*cos(c+d*x)*sin(c+d*x)+1//3*A*a*d^-1*cos(c+d*x)^2*sin(c+d*x))
@test integrate(cos(c+d*x)^4*(a+b*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*((1/2)*B*b+(1/2)*C*a+3//8*A*a)+d^-1*(A*b+B*a+C*b)*sin(c+d*x)+-1//3*d^-1*sin(c+d*x)^3*(A*b+B*a)+1//8*d^-1*(3*A*a+4*B*b+4*C*a)*cos(c+d*x)*sin(c+d*x)+1//4*A*a*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate(cos(c+d*x)^5*(a+b*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*((1/2)*C*b+3//8*A*b+3//8*B*a)+-1//15*d^-1*sin(c+d*x)^3*(4*A*a+5*B*b+5*C*a)+1//5*d^-1*(4*A*a+5*B*b+5*C*a)*sin(c+d*x)+1//4*d^-1*cos(c+d*x)^3*(A*b+B*a)*sin(c+d*x)+1//8*d^-1*(3*A*b+3*B*a+4*C*b)*cos(c+d*x)*sin(c+d*x)+1//5*A*a*d^-1*cos(c+d*x)^4*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//8*d^-1*(b^2*(3C+4A)+4*a^2*(C+2A)+8*B*a*b)*arctanh(sin(c+d*x))+1//6*b^-1*d^-1*(-1*C*a^3+4*B*b^3+4*B*b*a^2+4*a*b^2*(2C+3A))*tan(c+d*x)+1//24*d^-1*(-2*C*a^2+9*C*b^2+12*A*b^2+8*B*a*b)*sec(c+d*x)*tan(c+d*x)+1//4*C*b^-1*d^-1*(a+b*sec(c+d*x))^3*tan(c+d*x)+1//12*b^-1*d^-1*(a+b*sec(c+d*x))^2*(-1*C*a+4*B*b)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(A*x*a^2+(1/2)*d^-1*(B*b^2+2*B*a^2+2*a*b*(C+2A))*arctanh(sin(c+d*x))+1//3*d^-1*(2*C*a^2+2*C*b^2+3*A*b^2+6*B*a*b)*tan(c+d*x)+1//3*C*d^-1*(a+b*sec(c+d*x))^2*tan(c+d*x)+1//6*b*d^-1*(2*C*a+3*B*b)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(a*x*(B*a+2*A*b)+(1/2)*d^-1*(C*b^2+2*A*b^2+2*C*a^2+4*B*a*b)*arctanh(sin(c+d*x))+A*d^-1*(a+b*sec(c+d*x))^2*sin(c+d*x)+-1*b*d^-1*(-1*B*b+-2*C*a+2*A*a)*tan(c+d*x)+-1//2*b^2*d^-1*(-1C+2A)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*(A*b^2+(1/2)*a^2*(A+2C)+2*B*a*b)+a*d^-1*(A*b+B*a)*sin(c+d*x)+b*d^-1*(B*b+2*C*a)*arctanh(sin(c+d*x))+-1//2*b^2*d^-1*(A+-2C)*tan(c+d*x)+(1/2)*A*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*(B*b^2+(1/2)*B*a^2+a*b*(A+2C))+1//3*d^-1*(a^2*(2A+3C)+2*A*b^2+6*B*a*b)*sin(c+d*x)+C*b^2*d^-1*arctanh(sin(c+d*x))+1//3*A*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^2*sin(c+d*x)+1//6*a*d^-1*(2*A*b+3*B*a)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*((1/2)*b^2*(A+2C)+1//8*a^2*(3A+4C)+B*a*b)+1//3*d^-1*(2*B*a^2+3*B*b^2+4*A*a*b+6*C*a*b)*sin(c+d*x)+1//8*d^-1*(a^2*(3A+4C)+2*A*b^2+8*B*a*b)*cos(c+d*x)*sin(c+d*x)+1//4*A*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^3*sin(c+d*x)+1//6*a*d^-1*cos(c+d*x)^2*(A*b+2*B*a)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^5*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*((1/2)*B*b^2+3//8*B*a^2+C*a*b+3//4*A*a*b)+-1//15*d^-1*sin(c+d*x)^3*(a^2*(4A+5C)+2*A*b^2+10*B*a*b)+1//5*d^-1*(a^2*(4A+5C)+b^2*(4A+5C)+10*B*a*b)*sin(c+d*x)+1//8*d^-1*(3*B*a^2+4*B*b^2+6*A*a*b+8*C*a*b)*cos(c+d*x)*sin(c+d*x)+1//5*A*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^4*sin(c+d*x)+1//20*a*d^-1*cos(c+d*x)^3*(2*A*b+5*B*a)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//16*d^-1*(b^3*(5C+6A)+8*B*a^3+6*b*a^2*(3C+4A)+18*B*a*b^2)*arctanh(sin(c+d*x))+-1//60*b^-2*d^-1*(-32*B*b^5+-2*C*a^5+-1*a^3*b^2*(17C+30A)+-104*B*a^2*b^3+-24*a*b^4*(4C+5A)+6*B*b*a^4)*tan(c+d*x)+-1//120*b^-2*d^-1*(a+b*sec(c+d*x))^2*(-32*B*b^3+-2*C*a^3+-3*a*b^2*(7C+10A)+6*B*b*a^2)*tan(c+d*x)+-1//240*b^-1*d^-1*(-15*b^4*(5C+6A)+-4*C*a^4+-142*B*a*b^3+-12*a^2*b^2*(3C+5A)+12*B*b*a^3)*sec(c+d*x)*tan(c+d*x)+1//15*b^-2*d^-1*(a+b*sec(c+d*x))^4*(-1*C*a+3*B*b)*tan(c+d*x)+1//120*b^-2*d^-1*(a+b*sec(c+d*x))^3*(2*C*a^2+25*C*b^2+30*A*b^2+-6*B*a*b)*tan(c+d*x)+1//6*C*b^-1*d^-1*(a+b*sec(c+d*x))^4*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//8*d^-1*(3*B*b^3+4*a^3*(C+2A)+3*a*b^2*(3C+4A)+12*B*b*a^2)*arctanh(sin(c+d*x))+1//30*b^-1*d^-1*(-3*C*a^4+4*b^4*(4C+5A)+4*a^2*b^2*(13C+20A)+15*B*b*a^3+60*B*a*b^3)*tan(c+d*x)+1//120*d^-1*(-6*C*a^3+45*B*b^3+a*b^2*(71C+100A)+30*B*b*a^2)*sec(c+d*x)*tan(c+d*x)+1//5*C*b^-1*d^-1*(a+b*sec(c+d*x))^4*tan(c+d*x)+1//20*b^-1*d^-1*(a+b*sec(c+d*x))^3*(-1*C*a+5*B*b)*tan(c+d*x)+1//60*b^-1*d^-1*(a+b*sec(c+d*x))^2*(3*a*(-1*C*a+5*B*b)+4*b^2*(4C+5A))*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(A*x*a^3+1//6*d^-1*(3*C*a^3+4*B*b^3+6*a*b^2*(2C+3A)+16*B*b*a^2)*tan(c+d*x)+1//8*d^-1*(b^3*(3C+4A)+8*B*a^3+12*B*a*b^2+12*b*a^2*(C+2A))*arctanh(sin(c+d*x))+1//4*C*d^-1*(a+b*sec(c+d*x))^3*tan(c+d*x)+1//12*d^-1*(a+b*sec(c+d*x))^2*(3*C*a+4*B*b)*tan(c+d*x)+1//24*b*d^-1*(6*C*a^2+9*C*b^2+12*A*b^2+20*B*a*b)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(x*a^2*(B*a+3*A*b)+(1/2)*d^-1*(B*b^3+2*C*a^3+3*a*b^2*(C+2A)+6*B*b*a^2)*arctanh(sin(c+d*x))+A*d^-1*(a+b*sec(c+d*x))^3*sin(c+d*x)+1//3*b*d^-1*(b^2*(2C+3A)+-1*a^2*(-8C+6A)+9*B*a*b)*tan(c+d*x)+-1//3*b*d^-1*(a+b*sec(c+d*x))^2*(-1C+3A)*tan(c+d*x)+-1//6*b^2*d^-1*(-5*C*a+-3*B*b+6*A*a)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*a*x*(a^2*(A+2C)+6*A*b^2+6*B*a*b)+(1/2)*b*d^-1*(C*b^2+2*A*b^2+6*C*a^2+6*B*a*b)*arctanh(sin(c+d*x))+(1/2)*d^-1*(a+b*sec(c+d*x))^2*(2*B*a+3*A*b)*sin(c+d*x)+-1//2*b*d^-1*(-2*B*b^2+4*B*a^2+-6*C*a*b+9*A*a*b)*tan(c+d*x)+(1/2)*A*d^-1*(a+b*sec(c+d*x))^3*cos(c+d*x)*sin(c+d*x)+-1//2*b^2*d^-1*(-1*C*b+2*B*a+4*A*b)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*(A*b^3+(1/2)*B*a^3+3*B*a*b^2+3//2*b*a^2*(A+2C))+b^2*d^-1*(B*b+3*C*a)*arctanh(sin(c+d*x))+-1//6*b^2*d^-1*(-6*C*b+3*B*a+5*A*b)*tan(c+d*x)+1//3*a*d^-1*(a^2*(2A+3C)+3*A*b^2+6*B*a*b)*sin(c+d*x)+(1/2)*d^-1*(a+b*sec(c+d*x))^2*(A*b+B*a)*cos(c+d*x)*sin(c+d*x)+1//3*A*d^-1*(a+b*sec(c+d*x))^3*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*(B*b^3+1//8*a^3*(3A+4C)+3//2*B*b*a^2+3//2*a*b^2*(A+2C))+1//6*d^-1*(3*A*b^3+4*B*a^3+6*b*a^2*(2A+3C)+16*B*a*b^2)*sin(c+d*x)+C*b^3*d^-1*arctanh(sin(c+d*x))+1//4*A*d^-1*(a+b*sec(c+d*x))^3*cos(c+d*x)^3*sin(c+d*x)+1//12*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^2*(3*A*b+4*B*a)*sin(c+d*x)+1//24*a*d^-1*(3*a^2*(3A+4C)+6*A*b^2+20*B*a*b)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^5*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*((1/2)*b^3*(A+2C)+3//8*B*a^3+3//2*B*a*b^2+3//8*b*a^2*(3A+4C))+1//15*d^-1*(2*a^3*(4A+5C)+15*B*b^3+15*a*b^2*(2A+3C)+30*B*b*a^2)*sin(c+d*x)+1//40*d^-1*(6*A*b^3+15*B*a^3+15*b*a^2*(3A+4C)+50*B*a*b^2)*cos(c+d*x)*sin(c+d*x)+1//5*A*d^-1*(a+b*sec(c+d*x))^3*cos(c+d*x)^4*sin(c+d*x)+1//20*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^3*(3*A*b+5*B*a)*sin(c+d*x)+1//30*a*d^-1*cos(c+d*x)^2*(2*a^2*(4A+5C)+3*A*b^2+15*B*a*b)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^6*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*((1/2)*B*b^3+1//16*a^3*(5A+6C)+3//8*a*b^2*(3A+4C)+9//8*B*b*a^2)+-1//15*d^-1*sin(c+d*x)^3*(A*b^3+4*B*a^3+3*b*a^2*(4A+5C)+12*B*a*b^2)+1//15*d^-1*(b^3*(11A+15C)+12*B*a^3+9*b*a^2*(4A+5C)+42*B*a*b^2)*sin(c+d*x)+1//16*d^-1*(a^3*(5A+6C)+8*B*b^3+6*a*b^2*(3A+4C)+18*B*b*a^2)*cos(c+d*x)*sin(c+d*x)+1//6*A*d^-1*(a+b*sec(c+d*x))^3*cos(c+d*x)^5*sin(c+d*x)+1//10*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^4*(A*b+2*B*a)*sin(c+d*x)+1//120*a*d^-1*cos(c+d*x)^3*(5*a^2*(5A+6C)+6*A*b^2+42*B*a*b)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*sec(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//16*d^-1*(5*B*b^4+8*B*a^4+4*a*b^3*(5C+6A)+8*b*a^3*(3C+4A)+36*B*a^2*b^2)*arctanh(sin(c+d*x))+-1//420*b^-2*d^-1*(-32*b^6*(6C+7A)+-8*C*a^6+-896*B*a*b^5+-847*B*a^3*b^3+-32*a^2*b^4*(39C+49A)+-4*a^4*b^2*(23C+42A)+28*B*b*a^5)*tan(c+d*x)+-1//840*b^-2*d^-1*(a+b*sec(c+d*x))^2*(-32*b^4*(6C+7A)+-8*C*a^4+-371*B*a*b^3+-12*a^2*b^2*(9C+14A)+28*B*b*a^3)*tan(c+d*x)+-1//840*b^-2*d^-1*(a+b*sec(c+d*x))^3*(-175*B*b^3+-8*C*a^3+-4*a*b^2*(31C+42A)+28*B*b*a^2)*tan(c+d*x)+-1//1680*b^-1*d^-1*(-525*B*b^5+-16*C*a^5+-1246*B*a^2*b^3+-48*a^3*b^2*(4C+7A)+-4*a*b^4*(333C+406A)+56*B*b*a^4)*sec(c+d*x)*tan(c+d*x)+1//42*b^-2*d^-1*(a+b*sec(c+d*x))^5*(-2*C*a+7*B*b)*tan(c+d*x)+1//210*b^-2*d^-1*(a+b*sec(c+d*x))^4*(2*C*a^2+36*C*b^2+42*A*b^2+-7*B*a*b)*tan(c+d*x)+1//7*C*b^-1*d^-1*(a+b*sec(c+d*x))^5*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//16*d^-1*(b^4*(5C+6A)+8*a^4*(C+2A)+12*a^2*b^2*(3C+4A)+24*B*a*b^3+32*B*b*a^3)*arctanh(sin(c+d*x))+1//60*b^-1*d^-1*(-4*C*a^5+32*B*b^5+a^3*b^2*(121C+190A)+24*B*b*a^4+32*a*b^4*(4C+5A)+224*B*a^2*b^3)*tan(c+d*x)+1//240*d^-1*(-8*C*a^4+15*b^4*(5C+6A)+2*a^2*b^2*(89C+130A)+48*B*b*a^3+232*B*a*b^3)*sec(c+d*x)*tan(c+d*x)+1//6*C*b^-1*d^-1*(a+b*sec(c+d*x))^5*tan(c+d*x)+1//30*b^-1*d^-1*(a+b*sec(c+d*x))^4*(-1*C*a+6*B*b)*tan(c+d*x)+1//120*b^-1*d^-1*(a+b*sec(c+d*x))^2*(-4*C*a^3+32*B*b^3+a*b^2*(53C+70A)+24*B*b*a^2)*tan(c+d*x)+1//120*b^-1*d^-1*(a+b*sec(c+d*x))^3*(4*a*(-1*C*a+6*B*b)+5*b^2*(5C+6A))*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(A*x*a^4+1//8*d^-1*(3*B*b^4+8*B*a^4+4*a*b^3*(3C+4A)+16*b*a^3*(C+2A)+24*B*a^2*b^2)*arctanh(sin(c+d*x))+1//30*d^-1*(4*b^4*(4C+5A)+12*C*a^4+2*a^2*b^2*(56C+85A)+80*B*a*b^3+95*B*b*a^3)*tan(c+d*x)+1//5*C*d^-1*(a+b*sec(c+d*x))^4*tan(c+d*x)+1//20*d^-1*(a+b*sec(c+d*x))^3*(4*C*a+5*B*b)*tan(c+d*x)+1//60*d^-1*(a+b*sec(c+d*x))^2*(12*C*a^2+16*C*b^2+20*A*b^2+35*B*a*b)*tan(c+d*x)+1//120*b*d^-1*(24*C*a^3+45*B*b^3+4*a*b^2*(29C+40A)+130*B*b*a^2)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(x*a^3*(B*a+4*A*b)+1//8*d^-1*(b^4*(3C+4A)+8*C*a^4+16*B*a*b^3+24*a^2*b^2*(C+2A)+32*B*b*a^3)*arctanh(sin(c+d*x))+A*d^-1*(a+b*sec(c+d*x))^4*sin(c+d*x)+1//6*b*d^-1*(-1*a^3*(-19C+12A)+4*B*b^3+8*a*b^2*(2C+3A)+34*B*b*a^2)*tan(c+d*x)+-1//4*b*d^-1*(a+b*sec(c+d*x))^3*(-1C+4A)*tan(c+d*x)+-1//12*b*d^-1*(a+b*sec(c+d*x))^2*(-7*C*a+-4*B*b+12*A*a)*tan(c+d*x)+1//24*b^2*d^-1*(-1*a^2*(-26C+24A)+3*b^2*(3C+4A)+32*B*a*b)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*x*a^2*(a^2*(A+2C)+12*A*b^2+8*B*a*b)+d^-1*(a+b*sec(c+d*x))^3*(B*a+2*A*b)*sin(c+d*x)+(1/2)*b*d^-1*(B*b^3+8*C*a^3+4*a*b^2*(C+2A)+12*B*b*a^2)*arctanh(sin(c+d*x))+-1//6*b*d^-1*(-2*b^3*(2C+3A)+12*B*a^3+b*a^2*(-34C+39A)+-24*B*a*b^2)*tan(c+d*x)+(1/2)*A*d^-1*(a+b*sec(c+d*x))^4*cos(c+d*x)*sin(c+d*x)+-1//6*b*d^-1*(a+b*sec(c+d*x))^2*(-2*C*b+6*B*a+15*A*b)*tan(c+d*x)+-1//6*b^2*d^-1*(-3*B*b^2+6*B*a^2+2*a*b*(-4C+9A))*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*a*x*(B*a^3+8*A*b^3+4*b*a^2*(A+2C)+12*B*a*b^2)+(1/2)*b^2*d^-1*(C*b^2+2*A*b^2+12*C*a^2+8*B*a*b)*arctanh(sin(c+d*x))+-1//6*b*d^-1*(-6*B*b^3+4*a^3*(2A+3C)+4*a*b^2*(-6C+11A)+39*B*b*a^2)*tan(c+d*x)+1//6*d^-1*(a+b*sec(c+d*x))^2*(a^2*(4A+6C)+12*A*b^2+15*B*a*b)*sin(c+d*x)+-1//6*b^2*d^-1*(a^2*(4A+6C)+3*b^2*(-1C+6A)+18*B*a*b)*sec(c+d*x)*tan(c+d*x)+1//3*A*d^-1*(a+b*sec(c+d*x))^4*cos(c+d*x)^2*sin(c+d*x)+1//6*d^-1*(a+b*sec(c+d*x))^3*(3*B*a+4*A*b)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*(A*b^4+1//8*a^4*(3A+4C)+2*B*b*a^3+3*a^2*b^2*(A+2C)+4*B*a*b^3)+b^3*d^-1*(B*b+4*C*a)*arctanh(sin(c+d*x))+-1//24*b^2*d^-1*(2*b^2*(-12C+13A)+3*a^2*(3A+4C)+32*B*a*b)*tan(c+d*x)+1//12*a*d^-1*(8*B*a^3+12*A*b^3+b*a^2*(23A+36C)+36*B*a*b^2)*sin(c+d*x)+1//3*d^-1*(a+b*sec(c+d*x))^3*cos(c+d*x)^2*(A*b+B*a)*sin(c+d*x)+1//4*A*d^-1*(a+b*sec(c+d*x))^4*cos(c+d*x)^3*sin(c+d*x)+1//8*d^-1*(a+b*sec(c+d*x))^2*(a^2*(3A+4C)+4*A*b^2+8*B*a*b)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^5*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*(B*b^4+3//8*B*a^4+(1/2)*b*a^3*(3A+4C)+2*a*b^3*(A+2C)+3*B*a^2*b^2)+1//30*d^-1*(4*a^4*(4A+5C)+12*A*b^4+2*a^2*b^2*(56A+85C)+80*B*b*a^3+95*B*a*b^3)*sin(c+d*x)+C*b^4*d^-1*arctanh(sin(c+d*x))+1//5*A*d^-1*(a+b*sec(c+d*x))^4*cos(c+d*x)^4*sin(c+d*x)+1//20*d^-1*(a+b*sec(c+d*x))^3*cos(c+d*x)^3*(4*A*b+5*B*a)*sin(c+d*x)+1//60*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^2*(4*a^2*(4A+5C)+12*A*b^2+35*B*a*b)*sin(c+d*x)+1//120*a*d^-1*(24*A*b^3+45*B*a^3+4*b*a^2*(29A+40C)+130*B*a*b^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^6*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*((1/2)*b^4*(A+2C)+1//16*a^4*(5A+6C)+2*B*a*b^3+3//2*B*b*a^3+3//4*a^2*b^2*(3A+4C))+1//15*d^-1*(8*B*a^4+15*B*b^4+8*b*a^3*(4A+5C)+20*a*b^3*(2A+3C)+60*B*a^2*b^2)*sin(c+d*x)+1//240*d^-1*(15*a^4*(5A+6C)+24*A*b^4+10*a^2*b^2*(49A+66C)+336*B*a*b^3+360*B*b*a^3)*cos(c+d*x)*sin(c+d*x)+1//6*A*d^-1*(a+b*sec(c+d*x))^4*cos(c+d*x)^5*sin(c+d*x)+1//15*d^-1*(a+b*sec(c+d*x))^3*cos(c+d*x)^4*(2*A*b+3*B*a)*sin(c+d*x)+1//60*a*d^-1*cos(c+d*x)^2*(4*A*b^3+16*B*a^3+b*a^2*(39A+50C)+36*B*a*b^2)*sin(c+d*x)+1//120*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^3*(5*a^2*(5A+6C)+12*A*b^2+48*B*a*b)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^7*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(x*((1/2)*B*b^4+5//16*B*a^4+(1/2)*a*b^3*(3A+4C)+1//4*b*a^3*(5A+6C)+9//4*B*a^2*b^2)+-1//105*d^-1*sin(c+d*x)^3*(4*A*b^4+4*a^4*(6A+7C)+3*a^2*b^2*(50A+63C)+91*B*a*b^3+112*B*b*a^3)+1//105*d^-1*(b^4*(74A+105C)+12*a^4*(6A+7C)+3*a^2*b^2*(162A+203C)+336*B*b*a^3+371*B*a*b^3)*sin(c+d*x)+1//16*d^-1*(5*B*a^4+8*B*b^4+4*b*a^3*(5A+6C)+8*a*b^3*(3A+4C)+36*B*a^2*b^2)*cos(c+d*x)*sin(c+d*x)+1//7*A*d^-1*(a+b*sec(c+d*x))^4*cos(c+d*x)^6*sin(c+d*x)+1//42*d^-1*(a+b*sec(c+d*x))^3*cos(c+d*x)^5*(4*A*b+7*B*a)*sin(c+d*x)+1//70*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^4*(2*a^2*(6A+7C)+4*A*b^2+21*B*a*b)*sin(c+d*x)+1//840*a*d^-1*cos(c+d*x)^3*(a^2*(412*A*b+504*C*b)+24*A*b^3+175*B*a^3+336*B*a*b^2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*(-1*C*a^2+B*a*b+B*b^2*sec(c+d*x)+C*b^2*sec(c+d*x)^2), x) == :(x*a^4*(B*b+-1*C*a)+1//6*b^2*d^-1*(-15*C*a^3+4*B*b^3+12*C*a*b^2+34*B*b*a^2)*tan(c+d*x)+1//8*b*d^-1*(-24*C*a^4+3*C*b^4+8*C*a^2*b^2+16*B*a*b^3+32*B*b*a^3)*arctanh(sin(c+d*x))+1//4*C*b^2*d^-1*(a+b*sec(c+d*x))^3*tan(c+d*x)+1//12*b^2*d^-1*(a+b*sec(c+d*x))^2*(3*C*a+4*B*b)*tan(c+d*x)+1//24*b^3*d^-1*(-6*C*a^2+9*C*b^2+32*B*a*b)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*(-1*C*a^2+B*a*b+B*b^2*sec(c+d*x)+C*b^2*sec(c+d*x)^2), x) == :(x*a^3*(B*b+-1*C*a)+(1/2)*b*d^-1*(B*b^3+-4*C*a^3+2*C*a*b^2+6*B*b*a^2)*arctanh(sin(c+d*x))+1//3*b^2*d^-1*(-1*C*a^2+2*C*b^2+9*B*a*b)*tan(c+d*x)+1//3*C*b^2*d^-1*(a+b*sec(c+d*x))^2*tan(c+d*x)+1//6*b^3*d^-1*(2*C*a+3*B*b)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))*(-1*C*a^2+B*a*b+B*b^2*sec(c+d*x)+C*b^2*sec(c+d*x)^2), x) == :(x*a^2*(B*b+-1*C*a)+(1/2)*b*d^-1*(C*b^2+-2*C*a^2+4*B*a*b)*arctanh(sin(c+d*x))+(1/2)*b^2*d^-1*(C*a+2*B*b)*tan(c+d*x)+(1/2)*C*b^2*d^-1*(a+b*sec(c+d*x))*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-1*sec(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*b^-4*d^-1*(B*b^3+-2*C*a^3+-1*a*b^2*(C+2A)+2*B*b*a^2)*arctanh(sin(c+d*x))+1//3*b^-3*d^-1*(2*C*b^2+3*A*b^2+3*C*a^2+-3*B*a*b)*tan(c+d*x)+(1/2)*b^-2*d^-1*(B*b+-1*C*a)*sec(c+d*x)*tan(c+d*x)+1//3*C*b^-1*d^-1*sec(c+d*x)^2*tan(c+d*x)+2*a^2*b^-4*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(A*b^2+-1*a*(B*b+-1*C*a))*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*sec(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(b^-2*d^-1*(B*b+-1*C*a)*tan(c+d*x)+(1/2)*b^-3*d^-1*(b^2*(C+2A)+-2*a*(B*b+-1*C*a))*arctanh(sin(c+d*x))+(1/2)*C*b^-1*d^-1*sec(c+d*x)*tan(c+d*x)+-2*a*b^-3*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(A*b^2+-1*a*(B*b+-1*C*a))*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(C*b^-1*d^-1*tan(c+d*x)+b^-2*d^-1*(B*b+-1*C*a)*arctanh(sin(c+d*x))+b^-2*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(-2*a*(B*b+-1*C*a)+2*A*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(A*x*a^-1+C*b^-1*d^-1*arctanh(sin(c+d*x))+-1*a^-1*b^-1*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(-2*a*(B*b+-1*C*a)+2*A*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(-1*x*a^-2*(A*b+-1*B*a)+A*a^-1*d^-1*sin(c+d*x)+a^-2*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(-2*a*(B*b+-1*C*a)+2*A*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*cos(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*x*a^-3*(a^2*(A+2C)+2*A*b^2+-2*B*a*b)+-1*a^-2*d^-1*(A*b+-1*B*a)*sin(c+d*x)+(1/2)*A*a^-1*d^-1*cos(c+d*x)*sin(c+d*x)+-2*b*a^-3*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(A*b^2+-1*a*(B*b+-1*C*a))*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*cos(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//2*x*a^-4*(-1*B*a^3+2*A*b^3+b*a^2*(A+2C)+-2*B*a*b^2)+1//3*a^-3*d^-1*(a^2*(2A+3C)+3*A*b^2+-3*B*a*b)*sin(c+d*x)+-1//2*a^-2*d^-1*(A*b+-1*B*a)*cos(c+d*x)*sin(c+d*x)+1//3*A*a^-1*d^-1*cos(c+d*x)^2*sin(c+d*x)+2*a^-4*b^2*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(A*b^2+-1*a*(B*b+-1*C*a))*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*cos(c+d*x)^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//8*x*a^-5*(a^4*(3A+4C)+8*A*b^4+-8*B*a*b^3+-4*B*b*a^3+4*a^2*b^2*(A+2C))+-1//3*a^-4*d^-1*(-2*B*a^3+3*A*b^3+b*a^2*(2A+3C)+-3*B*a*b^2)*sin(c+d*x)+-1//3*a^-2*d^-1*cos(c+d*x)^2*(A*b+-1*B*a)*sin(c+d*x)+1//4*A*a^-1*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//8*a^-3*d^-1*(a^2*(3A+4C)+4*A*b^2+-4*B*a*b)*cos(c+d*x)*sin(c+d*x)+-2*a^-5*b^3*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(A*b^2+-1*a*(B*b+-1*C*a))*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-2*sec(c+d*x)^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*b^-5*d^-1*(B*b^3+-8*C*a^3+-2*a*b^2*(C+2A)+6*B*b*a^2)*arctanh(sin(c+d*x))+-1//3*b^-4*d^-1*(a^2+-1*b^2)^-1*(b^4*(2C+3A)+-12*C*a^4+-1*a^2*b^2*(-7C+6A)+-6*B*a*b^3+9*B*b*a^3)*tan(c+d*x)+(1/2)*b^-3*d^-1*(a^2+-1*b^2)^-1*(-1*B*b^3+-4*C*a^3+-2*a*b^2*(A+-1C)+3*B*b*a^2)*sec(c+d*x)*tan(c+d*x)+1//3*b^-2*d^-1*(a^2+-1*b^2)^-1*sec(c+d*x)^2*(-1*C*b^2+3*A*b^2+4*C*a^2+-3*B*a*b)*tan(c+d*x)+-1*b^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*sec(c+d*x)^3*(A*b^2+-1*a*(B*b+-1*C*a))*tan(c+d*x)+2*a^2*b^-5*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-3*A*b^4+4*C*a^4+-5*C*a^2*b^2+-3*B*b*a^3+2*A*a^2*b^2+4*B*a*b^3)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-2*sec(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*b^-4*d^-1*(C*b^2+2*A*b^2+6*C*a^2+-4*B*a*b)*arctanh(sin(c+d*x))+b^-3*d^-1*(a^2+-1*b^2)^-1*(-1*B*b^3+-3*C*a^3+-1*a*b^2*(A+-2C)+2*B*b*a^2)*tan(c+d*x)+(1/2)*b^-2*d^-1*(a^2+-1*b^2)^-1*(-1*C*b^2+2*A*b^2+3*C*a^2+-2*B*a*b)*sec(c+d*x)*tan(c+d*x)+-1*b^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*sec(c+d*x)^2*(A*b^2+-1*a*(B*b+-1*C*a))*tan(c+d*x)+-2*a*b^-4*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-2*A*b^4+3*C*a^4+A*a^2*b^2+-4*C*a^2*b^2+-2*B*b*a^3+3*B*a*b^3)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-2*sec(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(C*b^-2*d^-1*tan(c+d*x)+b^-3*d^-1*(B*b+-2*C*a)*arctanh(sin(c+d*x))+-1*b^-3*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-4*C*a^4+2*A*b^4+-4*B*a*b^3+2*B*b*a^3+6*C*a^2*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+a*b^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*(A*b^2+-1*a*(B*b+-1*C*a))*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(C*b^-2*d^-1*arctanh(sin(c+d*x))+b^-2*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-2*B*b^3+-2*C*a^3+2*A*a*b^2+4*C*a*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1*b^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*(A*b^2+-1*a*(B*b+-1*C*a))*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(A*x*a^-2+a^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*(A*b^2+-1*a*(B*b+-1*C*a))*tan(c+d*x)+-1*a^-2*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-2*A*b^3+-2*B*a^3+2*C*b*a^2+4*A*b*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(-1*x*a^-3*(-1*B*a+2*A*b)+-1*a^-2*d^-1*(a^2+-1*b^2)^-1*(-1*a^2*(A+-1C)+2*A*b^2+-1*B*a*b)*sin(c+d*x)+a^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*(A*b^2+-1*a*(B*b+-1*C*a))*sin(c+d*x)+a^-3*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-4*A*b^4+2*C*a^4+-4*B*b*a^3+2*B*a*b^3+6*A*a^2*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-2*cos(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*x*a^-4*(a^2*(A+2C)+6*A*b^2+-4*B*a*b)+a^-3*d^-1*(a^2+-1*b^2)^-1*(B*a^3+3*A*b^3+-1*b*a^2*(-1C+2A)+-2*B*a*b^2)*sin(c+d*x)+-1//2*a^-2*d^-1*(a^2+-1*b^2)^-1*(-1*a^2*(A+-2C)+3*A*b^2+-2*B*a*b)*cos(c+d*x)*sin(c+d*x)+a^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*(A*b^2+-1*a*(B*b+-1*C*a))*cos(c+d*x)*sin(c+d*x)+-2*b*a^-4*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-3*A*b^4+2*C*a^4+-1*C*a^2*b^2+-3*B*b*a^3+2*B*a*b^3+4*A*a^2*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-2*cos(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//2*x*a^-5*(-1*B*a^3+8*A*b^3+-6*B*a*b^2+2*b*a^2*(A+2C))+-1//3*a^-4*d^-1*(a^2+-1*b^2)^-1*(-1*a^4*(2A+3C)+12*A*b^4+-1*a^2*b^2*(-6C+7A)+-9*B*a*b^3+6*B*b*a^3)*sin(c+d*x)+(1/2)*a^-3*d^-1*(a^2+-1*b^2)^-1*(B*a^3+4*A*b^3+-3*B*a*b^2+-2*b*a^2*(A+-1C))*cos(c+d*x)*sin(c+d*x)+-1//3*a^-2*d^-1*(a^2+-1*b^2)^-1*cos(c+d*x)^2*(-1*a^2*(A+-3C)+4*A*b^2+-3*B*a*b)*sin(c+d*x)+a^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*cos(c+d*x)^2*(A*b^2+-1*a*(B*b+-1*C*a))*sin(c+d*x)+2*a^-5*b^2*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-4*A*b^4+3*C*a^4+-4*B*b*a^3+-2*C*a^2*b^2+3*B*a*b^3+5*A*a^2*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-3*sec(c+d*x)^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*b^-5*d^-1*(C*b^2+2*A*b^2+12*C*a^2+-6*B*a*b)*arctanh(sin(c+d*x))+(1/2)*b^-4*d^-1*(a^2+-1*b^2)^-2*(-12*C*a^5+2*B*b^5+a*b^4*(-6C+5A)+-1*a^3*b^2*(-21C+2A)+-11*B*a^2*b^3+6*B*b*a^4)*tan(c+d*x)+-1//2*b^-3*d^-1*(a^2+-1*b^2)^-2*(b^4*(-1C+4A)+-6*C*a^4+-1*a^2*b^2*(A+-10C)+-6*B*a*b^3+3*B*b*a^3)*sec(c+d*x)*tan(c+d*x)+(1/2)*b^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*sec(c+d*x)^2*(a*(-5*B*b^3+-4*C*a^3+2*B*b*a^2+7*C*a*b^2)+3*A*b^4)*tan(c+d*x)+-1*a*b^-5*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(6*A*b^6+12*C*a^6+a^4*b^2*(-29C+2A)+-12*B*a*b^5+-6*B*b*a^5+-5*a^2*b^4*(A+-4C)+15*B*a^3*b^3)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1//2*b^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*sec(c+d*x)^3*(A*b^2+-1*a*(B*b+-1*C*a))*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*sec(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(b^-4*d^-1*(B*b+-3*C*a)*arctanh(sin(c+d*x))+(1/2)*b^-3*d^-1*(a^2+-1*b^2)^-1*(A*b^2+-2*C*b^2+3*C*a^2+-1*B*a*b)*tan(c+d*x)+b^-4*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(2*A*b^6+6*C*a^6+a^2*b^4*(A+12C)+-15*C*a^4*b^2+-6*B*a*b^5+-2*B*b*a^5+5*B*a^3*b^3)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1//2*a*b^-3*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-3*C*a^4+2*A*b^4+B*b*a^3+a^2*b^2*(A+6C)+-4*B*a*b^3)*tan(c+d*x)+-1//2*b^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*sec(c+d*x)^2*(A*b^2+-1*a*(B*b+-1*C*a))*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*sec(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(C*b^-3*d^-1*arctanh(sin(c+d*x))+b^-3*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(-2*C*a^5+2*B*b^5+B*a^2*b^3+-3*a*b^4*(A+2C)+5*C*a^3*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+(1/2)*b^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-3*C*a^4+2*A*b^4+B*b*a^3+a^2*b^2*(A+6C)+-4*B*a*b^3)*tan(c+d*x)+(1/2)*a*b^-2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*(A*b^2+-1*a*(B*b+-1*C*a))*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(-1*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(-1*a^2*(C+2A)+-1*b^2*(A+2C)+3*B*a*b)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+(1/2)*b^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(C*a^3+2*B*b^3+B*b*a^2+-1*a*b^2*(3A+4C))*tan(c+d*x)+-1//2*b^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*(A*b^2+-1*a*(B*b+-1*C*a))*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(A*x*a^-3+a^-3*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(-2*A*b^5+2*B*a^5+B*a^3*b^2+-3*b*a^4*(C+2A)+5*A*a^2*b^3)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+(1/2)*a^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*(A*b^2+-1*a*(B*b+-1*C*a))*tan(c+d*x)+-1//2*a^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-1*C*a^4+2*A*b^4+-1*a^2*b^2*(2C+5A)+3*B*b*a^3)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(-1*x*a^-4*(-1*B*a+3*A*b)+-1//2*a^-3*d^-1*(a^2+-1*b^2)^-2*(-1*a^4*(-3C+2A)+-6*A*b^4+-5*B*b*a^3+2*B*a*b^3+11*A*a^2*b^2)*sin(c+d*x)+(1/2)*a^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*(A*b^2+-1*a*(B*b+-1*C*a))*sin(c+d*x)+-1*a^-4*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(-6*A*b^6+-2*C*a^6+-1*a^4*b^2*(C+12A)+-5*B*a^3*b^3+2*B*a*b^5+6*B*b*a^5+15*A*a^2*b^4)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1//2*a^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-2*C*a^4+3*A*b^4+-1*B*a*b^3+-1*a^2*b^2*(C+6A)+4*B*b*a^3)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*cos(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*x*a^-5*(a^2*(A+2C)+12*A*b^2+-6*B*a*b)+-1//2*a^-4*d^-1*(a^2+-1*b^2)^-2*(-2*B*a^5+12*A*b^5+b*a^4*(-5C+6A)+-1*a^2*b^3*(-2C+21A)+-6*B*a*b^4+11*B*a^3*b^2)*sin(c+d*x)+(1/2)*a^-3*d^-1*(a^2+-1*b^2)^-2*(a^4*(A+-4C)+6*A*b^4+-1*a^2*b^2*(-1C+10A)+-3*B*a*b^3+6*B*b*a^3)*cos(c+d*x)*sin(c+d*x)+(1/2)*a^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*(A*b^2+-1*a*(B*b+-1*C*a))*cos(c+d*x)*sin(c+d*x)+(1/2)*a^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-4*A*b^4+3*C*a^4+-5*B*b*a^3+2*B*a*b^3+7*A*a^2*b^2)*cos(c+d*x)*sin(c+d*x)+-1*b*a^-5*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(6*C*a^6+12*A*b^6+-1*a^2*b^4*(-2C+29A)+-12*B*b*a^5+-6*B*a*b^5+5*a^4*b^2*(-1C+4A)+15*B*a^3*b^3)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-4*sec(c+d*x)^4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(b^-5*d^-1*(B*b+-4*C*a)*arctanh(sin(c+d*x))+-1//6*b^-4*d^-1*(a^2+-1*b^2)^-2*(-12*C*a^4+-6*C*b^4+5*A*b^4+-8*B*a*b^3+3*B*b*a^3+23*C*a^2*b^2)*tan(c+d*x)+-1*b^-5*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(-8*C*a^8+2*A*b^8+a^2*b^6*(3A+20C)+-35*C*a^4*b^4+-8*B*a*b^7+-7*B*a^5*b^3+2*B*b*a^7+8*B*a^3*b^5+28*C*a^6*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+(1/2)*a*b^-4*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(2*A*b^6+4*C*a^6+-1*B*b*a^5+-11*C*a^4*b^2+-6*B*a*b^5+2*B*a^3*b^3+3*a^2*b^4*(A+4C))*tan(c+d*x)+-1//3*b^-1*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*sec(c+d*x)^3*(A*b^2+-1*a*(B*b+-1*C*a))*tan(c+d*x)+1//6*b^-2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*sec(c+d*x)^2*(-4*C*a^4+3*A*b^4+B*b*a^3+a^2*b^2*(2A+9C)+-6*B*a*b^3)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*sec(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(C*b^-4*d^-1*arctanh(sin(c+d*x))+-1*b^-4*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(2*B*b^7+2*C*a^7+-1*a^3*b^4*(A+-8C)+-7*C*a^5*b^2+-4*a*b^6*(A+2C)+3*B*a^2*b^5)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1//6*b^-3*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(4*A*b^6+9*C*a^6+B*a^3*b^3+-1*a^4*b^2*(3A+28C)+-16*B*a*b^5+2*a^2*b^4*(7A+17C))*tan(c+d*x)+-1//3*b^-1*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*sec(c+d*x)^2*(A*b^2+-1*a*(B*b+-1*C*a))*tan(c+d*x)+-1//6*a*b^-3*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(-3*C*a^4+2*A*b^4+a^2*b^2*(3A+8C)+-5*B*a*b^3)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*sec(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(B*a^3+-1*b^3*(A+2C)+-1*b*a^2*(3C+4A)+4*B*a*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+1//6*b^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(-6*B*b^5+2*C*a^5+B*b*a^4+a*b^4*(13A+18C)+a^3*b^2*(-5C+2A)+-10*B*a^2*b^3)*tan(c+d*x)+1//6*b^-2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(-4*C*a^4+3*A*b^4+B*b*a^3+a^2*b^2*(2A+9C)+-6*B*a*b^3)*tan(c+d*x)+1//3*a*b^-2*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*(A*b^2+-1*a*(B*b+-1*C*a))*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(-1*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(B*b^3+-1*a^3*(C+2A)+-1*a*b^2*(3A+4C)+4*B*b*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1//3*b^-1*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*(A*b^2+-1*a*(B*b+-1*C*a))*tan(c+d*x)+1//6*b^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(C*a^4+-2*b^4*(2A+3C)+-1*a^2*b^2*(10C+11A)+2*B*b*a^3+13*B*a*b^3)*tan(c+d*x)+1//6*b^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(C*a^3+3*B*b^3+-1*a*b^2*(5A+6C)+2*B*b*a^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(A*x*a^-4+-1*a^-4*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(-2*A*b^7+-2*B*a^7+-1*a^4*b^3*(-1C+8A)+-3*B*a^5*b^2+4*b*a^6*(C+2A)+7*A*a^2*b^5)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1//6*a^-3*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(-6*A*b^6+-2*C*a^6+-13*a^4*b^2*(C+2A)+4*B*a^3*b^3+11*B*b*a^5+17*A*a^2*b^4)*tan(c+d*x)+-1//6*a^-2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(-2*C*a^4+3*A*b^4+-1*a^2*b^2*(3C+8A)+5*B*b*a^3)*tan(c+d*x)+1//3*a^-1*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*(A*b^2+-1*a*(B*b+-1*C*a))*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*cos(c+d*x), x) == :(-1*x*a^-5*(-1*B*a+4*A*b)+1//6*a^-4*d^-1*(a^2+-1*b^2)^-3*(a^6*(-11C+6A)+-24*A*b^6+-1*a^4*b^2*(4C+65A)+-17*B*a^3*b^3+6*B*a*b^5+26*B*b*a^5+68*A*a^2*b^4)*sin(c+d*x)+-1*a^-5*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(-2*C*a^8+8*A*b^8+-1*a^6*b^2*(3C+20A)+-28*A*a^2*b^6+-8*B*a^5*b^3+-2*B*a*b^7+7*B*a^3*b^5+8*B*b*a^7+35*A*a^4*b^4)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1//2*a^-3*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(-4*A*b^6+-2*C*a^6+B*a*b^5+-3*a^4*b^2*(C+4A)+-2*B*a^3*b^3+6*B*b*a^5+11*A*a^2*b^4)*sin(c+d*x)+-1//6*a^-2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(-3*C*a^4+4*A*b^4+-1*B*a*b^3+-1*a^2*b^2*(2C+9A)+6*B*b*a^3)*sin(c+d*x)+1//3*a^-1*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*(A*b^2+-1*a*(B*b+-1*C*a))*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*cos(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*x*a^-6*(a^2*(A+2C)+20*A*b^2+-8*B*a*b)+1//6*a^-5*d^-1*(a^2+-1*b^2)^-3*(-1*a^6*(-26*C*b+24*A*b)+6*B*a^7+60*A*b^7+a^4*b^3*(-17C+146A)+-1*a^2*b^5*(-6C+167A)+-65*B*a^5*b^2+-24*B*a*b^6+68*B*a^3*b^4)*sin(c+d*x)+-1//2*a^-4*d^-1*(a^2+-1*b^2)^-3*(-1*a^6*(A+-6C)+10*A*b^6+a^4*b^2*(-2C+23A)+-1*a^2*b^4*(-1C+27A)+-12*B*b*a^5+-4*B*a*b^5+11*B*a^3*b^3)*cos(c+d*x)*sin(c+d*x)+-1//6*a^-2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(-4*C*a^4+5*A*b^4+-1*a^2*b^2*(C+10A)+-2*B*a*b^3+7*B*b*a^3)*cos(c+d*x)*sin(c+d*x)+1//3*a^-1*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*(A*b^2+-1*a*(B*b+-1*C*a))*cos(c+d*x)*sin(c+d*x)+1//6*a^-3*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(12*C*a^6+20*A*b^6+a^4*b^2*(C+48A)+-1*a^2*b^4*(-2C+53A)+-27*B*b*a^5+-8*B*a*b^5+20*B*a^3*b^3)*cos(c+d*x)*sin(c+d*x)+b*a^-6*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(a^2+-1*b^2)^-3*(-8*C*a^8+20*A*b^8+-1*a^2*b^6*(-2C+69A)+-35*B*a^5*b^3+-8*B*a*b^7+-8*a^6*b^2*(-1C+5A)+7*a^4*b^4*(-1C+12A)+20*B*b*a^7+28*B*a^3*b^5)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*(-1*C*a^2+B*a*b+B*b^2*sec(c+d*x)+C*b^2*sec(c+d*x)^2), x) == :(x*(B*b+-1*C*a)+C*b*d^-1*arctanh(sin(c+d*x)))
@test integrate((a+b*sec(c+d*x))^-2*(-1*C*a^2+B*a*b+B*b^2*sec(c+d*x)+C*b^2*sec(c+d*x)^2), x) == :(x*a^-1*(B*b+-1*C*a)+-2*b*a^-1*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(B*b+-2*C*a)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-3*(-1*C*a^2+B*a*b+B*b^2*sec(c+d*x)+C*b^2*sec(c+d*x)^2), x) == :(x*a^-2*(B*b+-1*C*a)+a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*(B*b+-2*C*a)*tan(c+d*x)+-2*b*a^-2*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-1*B*b^3+-3*C*a^3+C*a*b^2+2*B*b*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-4*(-1*C*a^2+B*a*b+B*b^2*sec(c+d*x)+C*b^2*sec(c+d*x)^2), x) == :(x*a^-3*(B*b+-1*C*a)+(1/2)*a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*(B*b+-2*C*a)*tan(c+d*x)+(1/2)*a^-2*b^2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-8*C*a^3+-2*B*b^3+2*C*a*b^2+5*B*b*a^2)*tan(c+d*x)+-1*b*a^-3*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(-8*C*a^5+2*B*b^5+-5*B*a^2*b^3+-2*C*a*b^4+4*C*a^3*b^2+6*B*b*a^4)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-5*(-1*C*a^2+B*a*b+B*b^2*sec(c+d*x)+C*b^2*sec(c+d*x)^2), x) == :(x*a^-4*(B*b+-1*C*a)+-1*b*a^-4*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(-10*C*a^7+-2*B*b^7+-8*B*a^4*b^3+-7*C*a^3*b^4+2*C*a*b^6+5*C*a^5*b^2+7*B*a^2*b^5+8*B*b*a^6)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+1//3*a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*(B*b+-2*C*a)*tan(c+d*x)+1//6*a^-3*b^2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(-37*C*a^5+6*B*b^5+-17*B*a^2*b^3+-6*C*a*b^4+13*C*a^3*b^2+26*B*b*a^4)*tan(c+d*x)+1//6*a^-2*b^2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(-13*C*a^3+-3*B*b^3+3*C*a*b^2+8*B*b*a^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//315*b^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(-150*B*b^3+-16*C*a^3+-2*a*b^2*(13C+21A)+24*B*b*a^2)*tan(c+d*x)+2//9*C*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^3*tan(c+d*x)+1//63*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^2*(2*C*a+18*B*b)*tan(c+d*x)+1//315*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(-12*C*a^2+98*C*b^2+126*A*b^2+18*B*a*b)*sec(c+d*x)*tan(c+d*x)+-1//315*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-16*C*a^3+-3*b^3*(-25B+49C+63A)+-6*a*b^2*(-3B+6C+7A)+12*b*a^2*(-1C+2B))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//315*b^-5*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(-16*C*a^4+21*b^4*(7C+9A)+-6*a^2*b^2*(4C+7A)+24*B*b*a^3+57*B*a*b^3)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//35*b^-2*d^-1*(a+b*sec(c+d*x))^3//2*(-8*C*a+14*B*b)*tan(c+d*x)+1//105*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(16*C*a^2+50*C*b^2+70*A*b^2+-28*B*a*b)*tan(c+d*x)+2//7*C*b^-1*d^-1*(a+b*sec(c+d*x))^3//2*sec(c+d*x)*tan(c+d*x)+-1//105*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-1*a*(-6*C*b+14*B*b)+-1*b^2*(-25C+63B)+8*C*a^2+35*A*b^2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//105*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-63*B*b^3+-8*C*a^3+-1*a*b^2*(19C+35A)+14*B*b*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//15*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*(-4*C*a+10*B*b)*tan(c+d*x)+2//5*C*b^-1*d^-1*(a+b*sec(c+d*x))^3//2*tan(c+d*x)+1//15*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(a*(-2*C*a+5*B*b)+3*b^2*(3C+5A))*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//15*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-5*B*b+2*C*a+9*C*b+15*A*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^3//2*sec(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//3465*b^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(-150*b^4*(9C+11A)+-48*C*a^4+-1936*B*a*b^3+-6*a^2*b^2*(19C+33A)+88*B*b*a^3)*tan(c+d*x)+1//99*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^3*(6*C*a+22*B*b)*tan(c+d*x)+2//11*C*d^-1*(a+b*sec(c+d*x))^3//2*sec(c+d*x)^3*tan(c+d*x)+1//693*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^2*(6*C*a^2+162*C*b^2+198*A*b^2+220*B*a*b)*tan(c+d*x)+1//3465*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(-36*C*a^3+1078*B*b^3+12*a*b^2*(101C+132A)+66*B*b*a^2)*sec(c+d*x)*tan(c+d*x)+-1//3465*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-48*C*a^4+3*b^4*(-539B+225C+275A)+-6*a^2*b^2*(-11B+24C+33A)+-3*a*b^3*(-143B+471C+627A)+4*b*a^3*(-9C+22B))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//3465*b^-5*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(-48*C*a^5+1617*B*b^5+-18*a^3*b^2*(6C+11A)+6*a*b^4*(348C+451A)+88*B*b*a^4+363*B*a^2*b^3)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^3//2*sec(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//315*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(-150*B*b^3+-16*C*a^3+-6*a*b^2*(13C+21A)+36*B*b*a^2)*tan(c+d*x)+1//63*b^-2*d^-1*(a+b*sec(c+d*x))^5//2*(-8*C*a+18*B*b)*tan(c+d*x)+1//315*b^-2*d^-1*(a+b*sec(c+d*x))^3//2*(16*C*a^2+98*C*b^2+126*A*b^2+-36*B*a*b)*tan(c+d*x)+2//9*C*b^-1*d^-1*(a+b*sec(c+d*x))^5//2*sec(c+d*x)*tan(c+d*x)+1//315*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-21*b^4*(7C+9A)+-8*C*a^4+-246*B*a*b^3+-3*a^2*b^2*(11C+21A)+18*B*b*a^3)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//315*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-8*C*a^3+3*b^3*(-25B+49C+63A)+-3*a*b^2*(-57B+13C+21A)+6*b*a^2*(-1C+3B))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//35*b^-1*d^-1*(a+b*sec(c+d*x))^3//2*(-4*C*a+14*B*b)*tan(c+d*x)+1//105*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*(-12*C*a^2+50*C*b^2+70*A*b^2+42*B*a*b)*tan(c+d*x)+2//7*C*b^-1*d^-1*(a+b*sec(c+d*x))^5//2*tan(c+d*x)+1//105*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(-6*C*a^3+63*B*b^3+2*a*b^2*(41C+70A)+21*B*b*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//105*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-1*b^2*(-63B+25C+35A)+6*C*a^2+3*a*b*(-7B+19C+35A))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^5//2*sec(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//3465*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(-150*b^4*(9C+11A)+-80*C*a^4+-2508*B*a*b^3+-30*a^2*b^2*(19C+33A)+220*B*b*a^3)*tan(c+d*x)+-1//3465*b^-2*d^-1*(a+b*sec(c+d*x))^3//2*(-1078*B*b^3+-80*C*a^3+-10*a*b^2*(67C+99A)+220*B*b*a^2)*tan(c+d*x)+1//99*b^-2*d^-1*(a+b*sec(c+d*x))^7//2*(-8*C*a+22*B*b)*tan(c+d*x)+1//693*b^-2*d^-1*(a+b*sec(c+d*x))^5//2*(16*C*a^2+162*C*b^2+198*A*b^2+-44*B*a*b)*tan(c+d*x)+2//11*C*b^-1*d^-1*(a+b*sec(c+d*x))^7//2*sec(c+d*x)*tan(c+d*x)+1//3465*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-1617*B*b^5+-40*C*a^5+-3069*B*a^2*b^3+-15*a*b^4*(247C+319A)+-15*a^3*b^2*(17C+33A)+110*B*b*a^4)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//3465*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-40*C*a^4+-3*b^4*(-539B+225C+275A)+-15*a^2*b^2*(-121B+19C+33A)+6*a*b^3*(-209B+505C+660A)+10*b*a^3*(-3C+11B))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(1//63*b^-1*d^-1*(a+b*sec(c+d*x))^5//2*(-4*C*a+18*B*b)*tan(c+d*x)+1//315*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*(-20*C*a^3+150*B*b^3+12*a*b^2*(19C+28A)+90*B*b*a^2)*tan(c+d*x)+1//315*b^-1*d^-1*(a+b*sec(c+d*x))^3//2*(-20*C*a^2+98*C*b^2+126*A*b^2+90*B*a*b)*tan(c+d*x)+2//9*C*b^-1*d^-1*(a+b*sec(c+d*x))^7//2*tan(c+d*x)+1//315*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(-10*C*a^4+21*b^4*(7C+9A)+3*a^2*b^2*(93C+161A)+45*B*b*a^3+435*B*a*b^3)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//315*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(3*b^3*(-25B+49C+63A)+10*C*a^3+-6*a*b^2*(-60B+19C+28A)+15*b*a^2*(-3B+11C+21A))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-1//2*sec(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//105*b^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(48*C*a^2+50*C*b^2+70*A*b^2+-56*B*a*b)*tan(c+d*x)+1//35*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(-12*C*a+14*B*b)*sec(c+d*x)*tan(c+d*x)+2//7*C*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^2*tan(c+d*x)+2//105*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(b^3*(-63B+25C+35A)+48*C*a^3+-4*b*a^2*(3C+14B)+2*a*b^2*(7B+22C+35A))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//105*b^-5*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(-48*C*a^3+63*B*b^3+-2*a*b^2*(22C+35A)+56*B*b*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-1//2*sec(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//15*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(-8*C*a+10*B*b)*tan(c+d*x)+2//5*C*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)*tan(c+d*x)+-2//15*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-1*b^2*(-9C+5B)+8*C*a^2+15*A*b^2+-2*a*b*(C+5B))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//15*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(8*C*a^2+9*C*b^2+15*A*b^2+-10*B*a*b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(2//3*C*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*tan(c+d*x)+2//3*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-1*b*(-1C+3B)+2*C*a+3*A*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//3*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(-2*C*a+3*B*b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3//2*sec(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//15*b^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*(-48*C*a^3+-10*B*b^3+-6*a*b^2*(-3C+5A)+40*B*b*a^2)*tan(c+d*x)+-1*b^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^2*(-2*a*(B*b+-1*C*a)+2*A*b^2)*tan(c+d*x)+1//5*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*(-2*C*b^2+10*A*b^2+12*C*a^2+-10*B*a*b)*sec(c+d*x)*tan(c+d*x)+1//15*b^-5*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(-96*C*a^4+6*b^4*(3C+5A)+-50*B*a*b^3+-12*a^2*b^2*(-4C+5A)+80*B*b*a^3)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//15*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(-96*C*a^3+-2*b^3*(-5B+9C+15A)+-12*a*b^2*(-5B+2C+5A)+2*b*a^2*(-36C+40B))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3//2*sec(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//3*C*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*tan(c+d*x)+2*a*b^-2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*(A*b^2+-1*a*(B*b+-1*C*a))*tan(c+d*x)+1//3*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(6*B*b^3+16*C*a^3+-12*B*b*a^2+2*a*b^2*(-5C+3A))*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//3*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(-2*(b+2a)*(b*(-1C+3B)+-4*C*a)+6*A*b^2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(-1*b^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*(-2*a*(B*b+-1*C*a)+2*A*b^2)*tan(c+d*x)+b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(-4*C*a^2+-2*A*b^2+2*C*b^2+2*B*a*b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(-4*C*a+2*A*b+2*b*(B+-1C))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^3*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//3*b^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*(-2*C*b^2+2*A*b^2+4*C*a^2+-2*B*a*b)*tan(c+d*x)+-2//3*a*b^-3*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*(a*(-7*B*b^3+-6*C*a^3+3*B*b*a^2+10*C*a*b^2)+4*A*b^4)*tan(c+d*x)+-1//3*b^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*sec(c+d*x)^2*(-2*a*(B*b+-1*C*a)+2*A*b^2)*tan(c+d*x)+-1//3*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(a^2+-1*b^2)^-1*(-32*C*a^4+2*b^4*(C+-3B+3A)+-6*a*b^3*(A+-3C+3B)+-4*a^2*b^2*(A+-8C+-3B)+2*b*a^3*(-12C+8B))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//3*b^-5*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(a^2+-1*b^2)^-1*(-6*B*b^5+32*C*a^5+-16*B*b*a^4+-4*a*b^4*(-4C+3A)+4*a^3*b^2*(A+-14C)+30*B*a^2*b^3)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//3*b^-2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*(-10*C*a^4+6*A*b^4+-12*B*a*b^3+2*a^2*b^2*(A+9C)+4*B*b*a^3)*tan(c+d*x)+2//3*a*b^-2*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*(A*b^2+-1*a*(B*b+-1*C*a))*tan(c+d*x)+1//3*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(a^2+-1*b^2)^-1*(-16*C*a^4+6*b^4*(A+-1C)+-12*B*a*b^3+2*a^2*b^2*(A+15C)+4*B*b*a^3)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//3*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(a^2+-1*b^2)^-1*(-16*C*a^3+-6*b^3*(A+B+-1C)+2*a*b^2*(A+3B+9C)+4*b*a^2*(B+-3C))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2)*sec(c+d*x), x) == :(-1//3*b^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*(-2*a*(B*b+-1*C*a)+2*A*b^2)*tan(c+d*x)+1//3*b^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*(4*C*a^3+6*B*b^3+-4*a*b^2*(2A+3C)+2*B*b*a^2)*tan(c+d*x)+b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(-3b+3a)^-1*(4*C*a^3+6*B*b^3+-12*C*a*b^2+-8*A*a*b^2+2*B*b*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//3*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(a^2+-1*b^2)^-1*(-2*b^2*(A+3B+3C)+4*C*a^2+2*a*b*(B+3A+3C))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate(sec(c+d*x)^5//2*(a+b*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//7*d^-1*sec(c+d*x)^7//2*(2*B*b+2*C*a)*sin(c+d*x)+1//15*d^-1*sec(c+d*x)^(1/2)*(14*C*b+18*A*b+18*B*a)*sin(c+d*x)+1//21*d^-1*sec(c+d*x)^3//2*(10*B*b+10*C*a+14*A*a)*sin(c+d*x)+1//45*d^-1*sec(c+d*x)^5//2*(14*C*b+18*A*b+18*B*a)*sin(c+d*x)+-1//15*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(14*C*b+18*A*b+18*B*a)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(10*B*b+10*C*a+14*A*a)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//9*C*b*d^-1*sec(c+d*x)^9//2*sin(c+d*x))
@test integrate(sec(c+d*x)^3//2*(a+b*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//5*d^-1*sec(c+d*x)^(1/2)*(6*B*b+6*C*a+10*A*a)*sin(c+d*x)+1//5*d^-1*sec(c+d*x)^5//2*(2*B*b+2*C*a)*sin(c+d*x)+1//21*d^-1*sec(c+d*x)^3//2*(10*C*b+14*A*b+14*B*a)*sin(c+d*x)+-1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(6*B*b+6*C*a+10*A*a)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(10*C*b+14*A*b+14*B*a)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//7*C*b*d^-1*sec(c+d*x)^7//2*sin(c+d*x))
@test integrate(sec(c+d*x)^(1/2)*(a+b*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//3*d^-1*sec(c+d*x)^3//2*(2*B*b+2*C*a)*sin(c+d*x)+1//5*d^-1*sec(c+d*x)^(1/2)*(6*C*b+10*A*b+10*B*a)*sin(c+d*x)+-1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(6*C*b+10*A*b+10*B*a)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*B*b+2*a*(C+3A))*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*C*b*d^-1*sec(c+d*x)^5//2*sin(c+d*x))
@test integrate(sec(c+d*x)^-1//2*(a+b*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(d^-1*sec(c+d*x)^(1/2)*(2*B*b+2*C*a)*sin(c+d*x)+-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-2*a*(A+-1C)+2*B*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*C*b+6*A*b+6*B*a)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*C*b*d^-1*sec(c+d*x)^3//2*sin(c+d*x))
@test integrate(sec(c+d*x)^-3//2*(a+b*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-2*C*b+2*A*b+2*B*a)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*C*b*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+1//3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*a*(A+3C)+6*B*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*A*a*d^-1*sec(c+d*x)^-1//2*sin(c+d*x))
@test integrate(sec(c+d*x)^-5//2*(a+b*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//3*d^-1*sec(c+d*x)^-1//2*(2*A*b+2*B*a)*sin(c+d*x)+1//3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*A*b+2*B*a+6*C*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(6*A*a+10*B*b+10*C*a)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//5*A*a*d^-1*sec(c+d*x)^-3//2*sin(c+d*x))
@test integrate(sec(c+d*x)^-7//2*(a+b*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//5*d^-1*sec(c+d*x)^-3//2*(2*A*b+2*B*a)*sin(c+d*x)+1//21*d^-1*sec(c+d*x)^-1//2*(10*A*a+14*B*b+14*C*a)*sin(c+d*x)+1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(6*A*b+6*B*a+10*C*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(10*A*a+14*B*b+14*C*a)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//7*A*a*d^-1*sec(c+d*x)^-5//2*sin(c+d*x))
@test integrate(sec(c+d*x)^-9//2*(a+b*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//7*d^-1*sec(c+d*x)^-5//2*(2*A*b+2*B*a)*sin(c+d*x)+1//21*d^-1*sec(c+d*x)^-1//2*(10*A*b+10*B*a+14*C*b)*sin(c+d*x)+1//45*d^-1*sec(c+d*x)^-3//2*(14*A*a+18*B*b+18*C*a)*sin(c+d*x)+1//15*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(14*A*a+18*B*b+18*C*a)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(10*A*b+10*B*a+14*C*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//9*A*a*d^-1*sec(c+d*x)^-7//2*sin(c+d*x))
@test integrate(sec(c+d*x)^-11//2*(a+b*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//9*d^-1*sec(c+d*x)^-7//2*(2*A*b+2*B*a)*sin(c+d*x)+1//45*d^-1*sec(c+d*x)^-3//2*(14*A*b+14*B*a+18*C*b)*sin(c+d*x)+1//77*d^-1*sec(c+d*x)^-5//2*(18*A*a+22*B*b+22*C*a)*sin(c+d*x)+1//231*d^-1*sec(c+d*x)^-1//2*(90*A*a+110*B*b+110*C*a)*sin(c+d*x)+1//15*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(14*A*b+14*B*a+18*C*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//231*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(90*A*a+110*B*b+110*C*a)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//11*A*a*d^-1*sec(c+d*x)^-9//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//15*d^-1*sec(c+d*x)^(1/2)*(2*b^2*(7C+9A)+6*a^2*(3C+5A)+36*B*a*b)*sin(c+d*x)+1//21*d^-1*sec(c+d*x)^3//2*(10*B*b^2+14*B*a^2+20*C*a*b+28*A*a*b)*sin(c+d*x)+1//45*d^-1*sec(c+d*x)^5//2*(8*C*a^2+14*C*b^2+18*A*b^2+36*B*a*b)*sin(c+d*x)+-1//15*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*b^2*(7C+9A)+6*a^2*(3C+5A)+36*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(10*B*b^2+14*B*a^2+20*C*a*b+28*A*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//9*C*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^5//2*sin(c+d*x)+2//63*b*d^-1*sec(c+d*x)^7//2*(4*C*a+9*B*b)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//5*d^-1*sec(c+d*x)^(1/2)*(6*B*b^2+10*B*a^2+12*C*a*b+20*A*a*b)*sin(c+d*x)+1//21*d^-1*sec(c+d*x)^3//2*(8*C*a^2+10*C*b^2+14*A*b^2+28*B*a*b)*sin(c+d*x)+-1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(6*B*b^2+10*B*a^2+12*C*a*b+20*A*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*b^2*(5C+7A)+14*a^2*(C+3A)+28*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//7*C*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^3//2*sin(c+d*x)+2//35*b*d^-1*sec(c+d*x)^5//2*(4*C*a+7*B*b)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//5*d^-1*sec(c+d*x)^(1/2)*(6*C*b^2+8*C*a^2+10*A*b^2+20*B*a*b)*sin(c+d*x)+-1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-10*a^2*(A+-1C)+2*b^2*(3C+5A)+20*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*B*b^2+6*B*a^2+4*a*b*(C+3A))*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*C*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^(1/2)*sin(c+d*x)+2//15*b*d^-1*sec(c+d*x)^3//2*(4*C*a+5*B*b)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-2*B*b^2+2*B*a^2+4*a*b*(A+-1C))*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-2//3*b^2*d^-1*sec(c+d*x)^3//2*(A+-1C)*sin(c+d*x)+1//3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*a^2*(A+3C)+2*b^2*(C+3A)+12*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*A*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^-1//2*sin(c+d*x)+2//3*b*d^-1*sec(c+d*x)^(1/2)*(-2*a*(A+-3C)+3*B*b)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-2//5*b^2*d^-1*sec(c+d*x)^(1/2)*(A+-5C)*sin(c+d*x)+1//3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*B*a^2+6*B*b^2+4*a*b*(A+3C))*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*a^2*(3A+5C)+10*b^2*(A+-1C)+20*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//5*A*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^-3//2*sin(c+d*x)+2//15*a*d^-1*sec(c+d*x)^-1//2*(4*A*b+5*B*a)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^-7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//21*d^-1*sec(c+d*x)^-1//2*(2*a^2*(5A+7C)+8*A*b^2+28*B*a*b)*sin(c+d*x)+1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(6*B*a^2+10*B*b^2+12*A*a*b+20*C*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*a^2*(5A+7C)+14*b^2*(A+3C)+28*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//7*A*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^-5//2*sin(c+d*x)+2//35*a*d^-1*sec(c+d*x)^-3//2*(4*A*b+7*B*a)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^-9//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//21*d^-1*sec(c+d*x)^-1//2*(10*B*a^2+14*B*b^2+20*A*a*b+28*C*a*b)*sin(c+d*x)+1//45*d^-1*sec(c+d*x)^-3//2*(2*a^2*(7A+9C)+8*A*b^2+36*B*a*b)*sin(c+d*x)+1//15*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*a^2*(7A+9C)+6*b^2*(3A+5C)+36*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(10*B*a^2+14*B*b^2+20*A*a*b+28*C*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//9*A*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^-7//2*sin(c+d*x)+2//63*a*d^-1*sec(c+d*x)^-5//2*(4*A*b+9*B*a)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//15*d^-1*sec(c+d*x)^(1/2)*(2*b^3*(7C+9A)+30*B*a^3+18*b*a^2*(3C+5A)+54*B*a*b^2)*sin(c+d*x)+1//63*d^-1*sec(c+d*x)^3//2*(16*C*a^3+30*B*b^3+18*a*b^2*(5C+7A)+108*B*b*a^2)*sin(c+d*x)+-1//15*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*b^3*(7C+9A)+30*B*a^3+18*b*a^2*(3C+5A)+54*B*a*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^3//2*(4*C*a+6*B*b)*sin(c+d*x)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(10*B*b^3+14*a^3*(C+3A)+6*a*b^2*(5C+7A)+42*B*b*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//9*C*d^-1*(a+b*sec(c+d*x))^3*sec(c+d*x)^3//2*sin(c+d*x)+2//315*b*d^-1*sec(c+d*x)^5//2*(24*C*a^2+49*C*b^2+63*A*b^2+99*B*a*b)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//35*d^-1*sec(c+d*x)^(1/2)*(42*B*b^3+48*C*a^3+42*a*b^2*(3C+5A)+196*B*b*a^2)*sin(c+d*x)+-1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-10*a^3*(A+-1C)+6*B*b^3+6*a*b^2*(3C+5A)+30*B*b*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*b^3*(5C+7A)+42*B*a^3+42*B*a*b^2+42*b*a^2*(C+3A))*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//35*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^(1/2)*(12*C*a+14*B*b)*sin(c+d*x)+2//7*C*d^-1*(a+b*sec(c+d*x))^3*sec(c+d*x)^(1/2)*sin(c+d*x)+2//105*b*d^-1*sec(c+d*x)^3//2*(24*C*a^2+25*C*b^2+35*A*b^2+63*B*a*b)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-2//15*b^2*d^-1*sec(c+d*x)^3//2*(-9*C*a+-5*B*b+5*A*a)*sin(c+d*x)+1//3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*B*b^3+2*a^3*(A+3C)+6*a*b^2*(C+3A)+18*B*b*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-2*b^3*(3C+5A)+10*B*a^3+-30*B*a*b^2+30*b*a^2*(A+-1C))*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*A*d^-1*(a+b*sec(c+d*x))^3*sec(c+d*x)^-1//2*sin(c+d*x)+2//15*b*d^-1*sec(c+d*x)^(1/2)*(-1*a^2*(-42C+10A)+3*b^2*(3C+5A)+45*B*a*b)*sin(c+d*x)+-2//15*b*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^(1/2)*(-3C+5A)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-2//15*b*d^-1*sec(c+d*x)^(1/2)*(-15*B*b^2+10*B*a^2+3*a*b*(-15C+7A))*sin(c+d*x)+-2//15*b^2*d^-1*sec(c+d*x)^3//2*(-5*C*b+5*B*a+9*A*b)*sin(c+d*x)+1//3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*B*a^3+2*b^3*(C+3A)+6*b*a^2*(A+3C)+18*B*a*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-10*B*b^3+2*a^3*(3A+5C)+30*B*b*a^2+30*a*b^2*(A+-1C))*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//15*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^-1//2*(10*B*a+12*A*b)*sin(c+d*x)+2//5*A*d^-1*(a+b*sec(c+d*x))^3*sec(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^-7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-2//35*b^2*d^-1*sec(c+d*x)^(1/2)*(-35*C*b+7*B*a+11*A*b)*sin(c+d*x)+1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(6*B*a^3+10*b^3*(A+-1C)+6*b*a^2*(3A+5C)+30*B*a*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*a^3*(5A+7C)+42*B*b^3+42*B*b*a^2+42*a*b^2*(A+3C))*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//35*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^-3//2*(12*A*b+14*B*a)*sin(c+d*x)+2//7*A*d^-1*(a+b*sec(c+d*x))^3*sec(c+d*x)^-5//2*sin(c+d*x)+2//105*a*d^-1*sec(c+d*x)^-1//2*(5*a^2*(5A+7C)+24*A*b^2+63*B*a*b)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^-9//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//63*d^-1*sec(c+d*x)^-1//2*(16*A*b^3+30*B*a^3+18*b*a^2*(5A+7C)+108*B*a*b^2)*sin(c+d*x)+1//15*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*a^3*(7A+9C)+30*B*b^3+18*a*b^2*(3A+5C)+54*B*b*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^-5//2*(4*A*b+6*B*a)*sin(c+d*x)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(10*B*a^3+14*b^3*(A+3C)+6*b*a^2*(5A+7C)+42*B*a*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//9*A*d^-1*(a+b*sec(c+d*x))^3*sec(c+d*x)^-7//2*sin(c+d*x)+2//315*a*d^-1*sec(c+d*x)^-3//2*(7*a^2*(7A+9C)+24*A*b^2+99*B*a*b)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^-11//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//231*d^-1*sec(c+d*x)^-1//2*(10*a^3*(9A+11C)+154*B*b^3+66*a*b^2*(5A+7C)+330*B*b*a^2)*sin(c+d*x)+1//495*d^-1*sec(c+d*x)^-3//2*(48*A*b^3+154*B*a^3+66*b*a^2*(7A+9C)+484*B*a*b^2)*sin(c+d*x)+1//15*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(6*b^3*(3A+5C)+14*B*a^3+6*b*a^2*(7A+9C)+54*B*a*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//99*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^-7//2*(12*A*b+22*B*a)*sin(c+d*x)+1//231*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(10*a^3*(9A+11C)+154*B*b^3+66*a*b^2*(5A+7C)+330*B*b*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//11*A*d^-1*(a+b*sec(c+d*x))^3*sec(c+d*x)^-9//2*sin(c+d*x)+2//693*a*d^-1*sec(c+d*x)^-5//2*(9*a^2*(9A+11C)+24*A*b^2+143*B*a*b)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//15*d^-1*sec(c+d*x)^(1/2)*(14*B*b^4+30*B*a^4+8*a*b^3*(7C+9A)+24*b*a^3*(3C+5A)+108*B*a^2*b^2)*sin(c+d*x)+1//693*d^-1*sec(c+d*x)^3//2*(30*b^4*(9C+11A)+128*C*a^4+18*a^2*b^2*(101C+143A)+1320*B*a*b^3+1364*B*b*a^3)*sin(c+d*x)+-1//15*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(14*B*b^4+30*B*a^4+8*a*b^3*(7C+9A)+24*b*a^3*(3C+5A)+108*B*a^2*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//99*d^-1*(a+b*sec(c+d*x))^3*sec(c+d*x)^3//2*(16*C*a+22*B*b)*sin(c+d*x)+1//231*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^3//2*(32*C*a^2+54*C*b^2+66*A*b^2+110*B*a*b)*sin(c+d*x)+1//231*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(10*b^4*(9C+11A)+154*a^4*(C+3A)+132*a^2*b^2*(5C+7A)+440*B*a*b^3+616*B*b*a^3)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//11*C*d^-1*(a+b*sec(c+d*x))^4*sec(c+d*x)^3//2*sin(c+d*x)+2//3465*b*d^-1*sec(c+d*x)^5//2*(192*C*a^3+539*B*b^3+2*a*b^2*(673C+891A)+1353*B*b*a^2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//315*d^-1*sec(c+d*x)^(1/2)*(42*b^4*(7C+9A)+384*C*a^4+14*a^2*b^2*(155C+261A)+1512*B*a*b^3+2196*B*b*a^3)*sin(c+d*x)+-1//15*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-30*a^4*(A+-1C)+2*b^4*(7C+9A)+36*a^2*b^2*(3C+5A)+72*B*a*b^3+120*B*b*a^3)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(10*B*b^4+42*B*a^4+8*a*b^3*(5C+7A)+56*b*a^3*(C+3A)+84*B*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//63*d^-1*(a+b*sec(c+d*x))^3*sec(c+d*x)^(1/2)*(16*C*a+18*B*b)*sin(c+d*x)+1//315*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^(1/2)*(96*C*a^2+98*C*b^2+126*A*b^2+234*B*a*b)*sin(c+d*x)+2//9*C*d^-1*(a+b*sec(c+d*x))^4*sec(c+d*x)^(1/2)*sin(c+d*x)+2//315*b*d^-1*sec(c+d*x)^3//2*(64*C*a^3+75*B*b^3+2*a*b^2*(101C+147A)+261*B*b*a^2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-6*B*b^4+10*B*a^4+-60*B*a^2*b^2+-8*a*b^3*(3C+5A)+40*b*a^3*(A+-1C))*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*b^4*(5C+7A)+14*a^4*(A+3C)+56*B*a*b^3+84*a^2*b^2*(C+3A)+168*B*b*a^3)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*A*d^-1*(a+b*sec(c+d*x))^4*sec(c+d*x)^-1//2*sin(c+d*x)+2//105*b*d^-1*sec(c+d*x)^(1/2)*(-1*a^3*(-366C+70A)+63*B*b^3+84*a*b^2*(3C+5A)+609*B*b*a^2)*sin(c+d*x)+2//105*b^2*d^-1*sec(c+d*x)^3//2*(-1*a^2*(-87C+35A)+5*b^2*(5C+7A)+98*B*a*b)*sin(c+d*x)+-2//21*b*d^-1*(a+b*sec(c+d*x))^3*sec(c+d*x)^(1/2)*(-3C+7A)*sin(c+d*x)+-2//105*b*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^(1/2)*(-39*C*a+-21*B*b+35*A*a)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-2//15*b*d^-1*sec(c+d*x)^(1/2)*(-3*b^3*(3C+5A)+10*B*a^3+b*a^2*(-87C+31A)+-60*B*a*b^2)*sin(c+d*x)+-2//15*b^2*d^-1*sec(c+d*x)^3//2*(-5*B*b^2+5*B*a^2+14*a*b*(A+-1C))*sin(c+d*x)+1//3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*B*a^4+2*B*b^4+8*a*b^3*(C+3A)+8*b*a^3*(A+3C)+36*B*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-2*b^4*(3C+5A)+2*a^4*(3A+5C)+-40*B*a*b^3+40*B*b*a^3+60*a^2*b^2*(A+-1C))*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//15*d^-1*(a+b*sec(c+d*x))^3*sec(c+d*x)^-1//2*(10*B*a+16*A*b)*sin(c+d*x)+2//5*A*d^-1*(a+b*sec(c+d*x))^4*sec(c+d*x)^-3//2*sin(c+d*x)+-2//15*b*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^(1/2)*(-3*C*b+5*B*a+11*A*b)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*sec(c+d*x)^-7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-2//105*b*d^-1*sec(c+d*x)^(1/2)*(-105*B*b^3+10*a^3*(5A+7C)+12*a*b^2*(-35C+19A)+217*B*b*a^2)*sin(c+d*x)+-2//105*b^2*d^-1*sec(c+d*x)^3//2*(b^2*(-35C+87A)+5*a^2*(5A+7C)+98*B*a*b)*sin(c+d*x)+1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-10*B*b^4+6*B*a^4+8*b*a^3*(3A+5C)+40*a*b^3*(A+-1C)+60*B*a^2*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*a^4*(5A+7C)+14*b^4*(C+3A)+56*B*b*a^3+84*a^2*b^2*(A+3C)+168*B*a*b^3)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//35*d^-1*(a+b*sec(c+d*x))^3*sec(c+d*x)^-3//2*(14*B*a+16*A*b)*sin(c+d*x)+1//105*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^-1//2*(10*a^2*(5A+7C)+96*A*b^2+154*B*a*b)*sin(c+d*x)+2//7*A*d^-1*(a+b*sec(c+d*x))^4*sec(c+d*x)^-5//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*sec(c+d*x)^-9//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-2//315*b^2*d^-1*sec(c+d*x)^(1/2)*(3*b^2*(-105C+41A)+7*a^2*(7A+9C)+162*B*a*b)*sin(c+d*x)+1//15*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*a^4*(7A+9C)+30*b^4*(A+-1C)+36*a^2*b^2*(3A+5C)+72*B*b*a^3+120*B*a*b^3)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(10*B*a^4+42*B*b^4+8*b*a^3*(5A+7C)+56*a*b^3*(A+3C)+84*B*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//63*d^-1*(a+b*sec(c+d*x))^3*sec(c+d*x)^-5//2*(16*A*b+18*B*a)*sin(c+d*x)+1//315*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^-3//2*(14*a^2*(7A+9C)+96*A*b^2+234*B*a*b)*sin(c+d*x)+2//9*A*d^-1*(a+b*sec(c+d*x))^4*sec(c+d*x)^-7//2*sin(c+d*x)+2//315*a*d^-1*sec(c+d*x)^-1//2*(a^2*(202*A*b+294*C*b)+64*A*b^3+75*B*a^3+261*B*a*b^2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*sec(c+d*x)^-11//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//693*d^-1*sec(c+d*x)^-1//2*(30*a^4*(9A+11C)+128*A*b^4+18*a^2*b^2*(101A+143C)+1320*B*b*a^3+1364*B*a*b^3)*sin(c+d*x)+1//15*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(14*B*a^4+30*B*b^4+8*b*a^3*(7A+9C)+24*a*b^3*(3A+5C)+108*B*a^2*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//99*d^-1*(a+b*sec(c+d*x))^3*sec(c+d*x)^-7//2*(16*A*b+22*B*a)*sin(c+d*x)+1//231*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^-5//2*(6*a^2*(9A+11C)+32*A*b^2+110*B*a*b)*sin(c+d*x)+1//231*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(10*a^4*(9A+11C)+154*b^4*(A+3C)+132*a^2*b^2*(5A+7C)+440*B*b*a^3+616*B*a*b^3)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//11*A*d^-1*(a+b*sec(c+d*x))^4*sec(c+d*x)^-9//2*sin(c+d*x)+2//3465*a*d^-1*sec(c+d*x)^-3//2*(192*A*b^3+539*B*a^3+2*b*a^2*(673A+891C)+1353*B*a*b^2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*sec(c+d*x)^-13//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//231*d^-1*sec(c+d*x)^-1//2*(90*B*a^4+154*B*b^4+40*b*a^3*(9A+11C)+88*a*b^3*(5A+7C)+660*B*a^2*b^2)*sin(c+d*x)+1//6435*d^-1*sec(c+d*x)^-3//2*(154*a^4*(11A+13C)+384*A*b^4+22*a^2*b^2*(491A+637C)+6916*B*a*b^3+8008*B*b*a^3)*sin(c+d*x)+1//143*d^-1*(a+b*sec(c+d*x))^3*sec(c+d*x)^-9//2*(16*A*b+26*B*a)*sin(c+d*x)+1//195*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*a^4*(77A+91C)+78*b^4*(3A+5C)+156*a^2*b^2*(7A+9C)+728*B*b*a^3+936*B*a*b^3)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//231*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(90*B*a^4+154*B*b^4+40*b*a^3*(9A+11C)+88*a*b^3*(5A+7C)+660*B*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//1287*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^-7//2*(22*a^2*(11A+13C)+96*A*b^2+442*B*a*b)*sin(c+d*x)+2//13*A*d^-1*(a+b*sec(c+d*x))^4*sec(c+d*x)^-11//2*sin(c+d*x)+2//9009*a*d^-1*sec(c+d*x)^-5//2*(a^2*(2518*A*b+3146*C*b)+192*A*b^3+1053*B*a^3+2171*B*a*b^2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//5*A*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*sin(c+d*x)+1//15*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(2*A*b+10*B*a)*sin(c+d*x)+-1//15*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(-6*a^2*(3A+5C)+4*A*b^2+-10*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//15*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-2*a^2+2*b^2)*(-5*B*a+2*A*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//7*A*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*sin(c+d*x)+-1//105*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(-10*a^2*(5A+7C)+8*A*b^2+-14*B*a*b)*sin(c+d*x)+1//35*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*(2*A*b+14*B*a)*sin(c+d*x)+1//105*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(16*A*b^3+126*B*a^3+-28*B*a*b^2+2*b*a^2*(19A+35C))*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//105*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-2*b^2+2*a^2)*(8*A*b^2+25*A*a^2+35*C*a^2+-14*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-9//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//9*A*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-7//2*sin(c+d*x)+-1//315*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*(-14*a^2*(7A+9C)+12*A*b^2+-18*B*a*b)*sin(c+d*x)+1//63*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*(2*A*b+18*B*a)*sin(c+d*x)+1//315*a^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(16*A*b^3+150*B*a^3+-24*B*a*b^2+2*b*a^2*(13A+21C))*sin(c+d*x)+-1//315*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(-42*a^4*(7A+9C)+32*A*b^4+-114*B*b*a^3+-48*B*a*b^3+12*a^2*b^2*(4A+7C))*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//315*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-2*a^2+2*b^2)*(-75*B*a^3+16*A*b^3+-24*B*a*b^2+6*b*a^2*(6A+7C))*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^3//2*sec(c+d*x)^-7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//35*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*(6*A*b+14*B*a)*sin(c+d*x)+2//7*A*d^-1*(a+b*sec(c+d*x))^3//2*sec(c+d*x)^-5//2*sin(c+d*x)+1//105*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(6*A*b^2+10*a^2*(5A+7C)+84*B*a*b)*sin(c+d*x)+-1//105*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(-126*B*a^3+12*A*b^3+-42*B*a*b^2+-4*b*a^2*(41A+70C))*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//105*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-2*b^2+2*a^2)*(-6*A*b^2+25*A*a^2+35*C*a^2+21*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^3//2*sec(c+d*x)^-9//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//21*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*(2*A*b+6*B*a)*sin(c+d*x)+2//9*A*d^-1*(a+b*sec(c+d*x))^3//2*sec(c+d*x)^-7//2*sin(c+d*x)+-1//315*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(-150*B*a^3+8*A*b^3+-18*B*a*b^2+-4*b*a^2*(44A+63C))*sin(c+d*x)+1//315*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*(6*A*b^2+14*a^2*(7A+9C)+144*B*a*b)*sin(c+d*x)+1//315*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(16*A*b^4+42*a^4*(7A+9C)+-36*B*a*b^3+6*a^2*b^2*(11A+21C)+492*B*b*a^3)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//315*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-2*b^2+2*a^2)*(a^2*(39*A*b+63*C*b)+8*A*b^3+75*B*a^3+-18*B*a*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^5//2*sec(c+d*x)^-9//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//63*d^-1*(a+b*sec(c+d*x))^3//2*sec(c+d*x)^-5//2*(10*A*b+18*B*a)*sin(c+d*x)+1//315*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*(14*a^2*(7A+9C)+30*A*b^2+180*B*a*b)*sin(c+d*x)+2//9*A*d^-1*(a+b*sec(c+d*x))^5//2*sec(c+d*x)^-7//2*sin(c+d*x)+1//315*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(10*A*b^3+150*B*a^3+2*b*a^2*(163A+231C)+270*B*a*b^2)*sin(c+d*x)+-1//315*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(-42*a^4*(7A+9C)+20*A*b^4+-870*B*b*a^3+-90*B*a*b^3+-6*a^2*b^2*(93A+161C))*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//315*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-2*a^2+2*b^2)*(-75*B*a^3+10*A*b^3+-45*B*a*b^2+-6*b*a^2*(19A+28C))*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^5//2*sec(c+d*x)^-11//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//99*d^-1*(a+b*sec(c+d*x))^3//2*sec(c+d*x)^-7//2*(10*A*b+22*B*a)*sin(c+d*x)+1//231*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*(6*a^2*(9A+11C)+10*A*b^2+88*B*a*b)*sin(c+d*x)+2//11*A*d^-1*(a+b*sec(c+d*x))^5//2*sec(c+d*x)^-9//2*sin(c+d*x)+-1//3465*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(-150*a^4*(9A+11C)+40*A*b^4+-3586*B*b*a^3+-110*B*a*b^3+-10*a^2*b^2*(205A+297C))*sin(c+d*x)+1//3465*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*(30*A*b^3+1078*B*a^3+10*b*a^2*(229A+297C)+1650*B*a*b^2)*sin(c+d*x)+1//3465*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(80*A*b^5+3234*B*a^5+-220*B*a*b^4+30*b*a^4*(247A+319C)+30*a^2*b^3*(17A+33C)+6138*B*a^3*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3465*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-2*b^2+2*a^2)*(40*A*b^4+75*a^4*(9A+11C)+-110*B*a*b^3+15*a^2*b^2*(19A+33C)+1254*B*b*a^3)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//3*A*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*sin(c+d*x)+-1//3*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(-6*B*a+4*A*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(2*a^2*(A+3C)+4*A*b^2+-6*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-1//2*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//15*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(-10*B*a+8*A*b)*sin(c+d*x)+2//5*A*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*sin(c+d*x)+1//15*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-16*A*b^3+10*B*a^3+-2*b*a^2*(7A+15C)+20*B*a*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//15*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(6*a^2*(3A+5C)+16*A*b^2+-20*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-1//2*sec(c+d*x)^-7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//35*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*(-14*B*a+12*A*b)*sin(c+d*x)+1//105*a^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(10*a^2*(5A+7C)+48*A*b^2+-56*B*a*b)*sin(c+d*x)+2//7*A*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*sin(c+d*x)+-1//105*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(-126*B*a^3+2*a^2*(44*A*b+70*C*b)+96*A*b^3+-112*B*a*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//105*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(10*a^4*(5A+7C)+96*A*b^4+-112*B*a*b^3+-98*B*b*a^3+4*a^2*b^2*(16A+35C))*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-3//2*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*(-2*a*(B*b+-1*C*a)+2*A*b^2)*sin(c+d*x)+-1*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-2*B*a+4*A*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+-1*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*sec(c+d*x)^-1//2*(-2*a^2*(A+-1C)+4*A*b^2+-2*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-3//2*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^-1//2*(-2*a*(B*b+-1*C*a)+2*A*b^2)*sin(c+d*x)+-1//3*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*sec(c+d*x)^-1//2*(-2*a^2*(A+-3C)+8*A*b^2+-6*B*a*b)*sin(c+d*x)+1//3*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(2*a^2*(A+3C)+16*A*b^2+-12*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*sec(c+d*x)^-1//2*(-2*a^2*(-3*C*b+5*A*b)+6*B*a^3+16*A*b^3+-12*B*a*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-3//2*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^-3//2*(-2*a*(B*b+-1*C*a)+2*A*b^2)*sin(c+d*x)+-1//5*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*sec(c+d*x)^-3//2*(-2*a^2*(A+-5C)+12*A*b^2+-10*B*a*b)*sin(c+d*x)+-1//15*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-10*B*a^3+96*A*b^3+-80*B*a*b^2+12*b*a^2*(2A+5C))*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//15*a^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*sec(c+d*x)^-1//2*(-2*a^2*(-15*C*b+9*A*b)+10*B*a^3+48*A*b^3+-40*B*a*b^2)*sin(c+d*x)+-1//15*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*sec(c+d*x)^-1//2*(-6*a^4*(3A+5C)+96*A*b^4+-80*B*a*b^3+-12*a^2*b^2*(-5C+4A)+50*B*b*a^3)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//3*b^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*(-2*a*(B*b+-1*C*a)+2*A*b^2)*sin(c+d*x)+-1//3*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*(-2*a^2*(C+3A)+4*A*b^2+2*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+-1//3*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*sec(c+d*x)^-1//2*(4*A*b^3+6*B*a^3+-4*b*a^2*(2C+3A)+2*B*a*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3*a^-1*b^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*sec(c+d*x)^(1/2)*(2*A*b^4+2*C*a^4+-10*a^2*b^2*(A+C)+4*B*a*b^3+4*B*b*a^3)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//3*a^-2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*sec(c+d*x)^(1/2)*(-4*C*a^4+8*A*b^4+-4*a^2*b^2*(C+4A)+-2*B*a*b^3+10*B*b*a^3)*sin(c+d*x)+1//3*a^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*(-2*a*(B*b+-1*C*a)+2*A*b^2)*sin(c+d*x)+1//3*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*(6*B*a^3+16*A*b^3+-4*B*a*b^2+-2*b*a^2*(C+9A))*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*sec(c+d*x)^-1//2*(6*a^4*(A+-1C)+16*A*b^4+-4*B*a*b^3+-2*a^2*b^2*(C+15A)+12*B*b*a^3)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//3*a^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*sec(c+d*x)^-1//2*(-2*a*(B*b+-1*C*a)+2*A*b^2)*sin(c+d*x)+1//3*a^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*sec(c+d*x)^-1//2*(2*a^4*(A+-5C)+16*A*b^4+-8*B*a*b^3+-2*a^2*b^2*(-1C+13A)+16*B*b*a^3)*sin(c+d*x)+1//3*a^-2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*sec(c+d*x)^-1//2*(-12*A*b^4+8*C*a^4+-14*B*b*a^3+6*B*a*b^3+20*A*a^2*b^2)*sin(c+d*x)+-1//3*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*(-2*a^4*(A+3C)+32*A*b^4+-16*B*a*b^3+-4*a^2*b^2*(-1C+8A)+18*B*b*a^3)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+-1//3*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*sec(c+d*x)^-1//2*(-6*B*a^5+2*a^4*(-6*C*b+8*A*b)+32*A*b^5+-16*B*a*b^4+-4*a^2*b^3*(-1C+14A)+30*B*a^3*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//3*a^-2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*sec(c+d*x)^-3//2*(-12*C*a^4+16*A*b^4+-10*B*a*b^3+-4*a^2*b^2*(-1C+6A)+18*B*b*a^3)*sin(c+d*x)+-1//15*a^-4*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*sec(c+d*x)^-1//2*(-10*B*a^5+128*A*b^5+-80*B*a*b^4+-4*a^2*b^3*(-10C+49A)+4*b*a^4*(-20C+7A)+130*B*a^3*b^2)*sin(c+d*x)+1//3*a^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*sec(c+d*x)^-3//2*(-2*a*(B*b+-1*C*a)+2*A*b^2)*sin(c+d*x)+1//15*a^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*sec(c+d*x)^-3//2*(2*a^4*(-35C+3A)+96*A*b^4+-60*B*a*b^3+-2*a^2*b^2*(-15C+71A)+100*B*b*a^3)*sin(c+d*x)+1//15*a^-5*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*(10*B*a^5+256*A*b^5+-160*B*a*b^4+-8*a^2*b^3*(-10C+29A)+-2*b*a^4*(17A+45C)+160*B*a^3*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//15*a^-5*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*sec(c+d*x)^-1//2*(6*a^6*(3A+5C)+256*A*b^6+-160*B*a*b^5+-80*B*b*a^5+-8*a^2*b^4*(-10C+53A)+10*a^4*b^2*(-15C+11A)+280*B*a^3*b^3)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate(cos(c+d*x)^9//2*(A+C*sec(c+d*x)^2), x) == :(1//15*d^-1*(14A+18C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//45*d^-1*cos(c+d*x)^3//2*(14A+18C)*sin(c+d*x)+2//9*A*d^-1*cos(c+d*x)^7//2*sin(c+d*x))
@test integrate(cos(c+d*x)^7//2*(A+C*sec(c+d*x)^2), x) == :(1//21*d^-1*(10A+14C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*(10A+14C)*sin(c+d*x)+2//7*A*d^-1*cos(c+d*x)^5//2*sin(c+d*x))
@test integrate(cos(c+d*x)^5//2*(A+C*sec(c+d*x)^2), x) == :(1//5*d^-1*(6A+10C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//5*A*d^-1*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate(cos(c+d*x)^3//2*(A+C*sec(c+d*x)^2), x) == :(1//3*d^-1*(2A+6C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*A*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate(cos(c+d*x)^(1/2)*(A+C*sec(c+d*x)^2), x) == :(d^-1*(-2C+2A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*C*d^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate(cos(c+d*x)^-1//2*(A+C*sec(c+d*x)^2), x) == :(1//3*d^-1*(2C+6A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*C*d^-1*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate(cos(c+d*x)^-3//2*(A+C*sec(c+d*x)^2), x) == :(-1//5*d^-1*(6C+10A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*cos(c+d*x)^-1//2*(6C+10A)*sin(c+d*x)+2//5*C*d^-1*cos(c+d*x)^-5//2*sin(c+d*x))
@test integrate(cos(c+d*x)^-5//2*(A+C*sec(c+d*x)^2), x) == :(1//21*d^-1*(10C+14A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^-3//2*(10C+14A)*sin(c+d*x)+2//7*C*d^-1*cos(c+d*x)^-7//2*sin(c+d*x))
@test integrate(cos(c+d*x)^9//2*(A+C*sec(c+d*x)^2)*(a+a*sec(c+d*x)), x) == :(2//15*a*d^-1*(7A+9C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//21*a*d^-1*(5A+7C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//7*A*a*d^-1*cos(c+d*x)^5//2*sin(c+d*x)+2//9*A*a*d^-1*cos(c+d*x)^7//2*sin(c+d*x)+2//21*a*d^-1*cos(c+d*x)^(1/2)*(5A+7C)*sin(c+d*x)+2//45*a*d^-1*cos(c+d*x)^3//2*(7A+9C)*sin(c+d*x))
@test integrate(cos(c+d*x)^7//2*(A+C*sec(c+d*x)^2)*(a+a*sec(c+d*x)), x) == :(2//5*a*d^-1*(3A+5C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//21*a*d^-1*(5A+7C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*A*a*d^-1*cos(c+d*x)^3//2*sin(c+d*x)+2//7*A*a*d^-1*cos(c+d*x)^5//2*sin(c+d*x)+2//21*a*d^-1*cos(c+d*x)^(1/2)*(5A+7C)*sin(c+d*x))
@test integrate(cos(c+d*x)^5//2*(A+C*sec(c+d*x)^2)*(a+a*sec(c+d*x)), x) == :(2//3*a*d^-1*(A+3C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*a*d^-1*(3A+5C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*A*a*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+2//5*A*a*d^-1*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate(cos(c+d*x)^3//2*(A+C*sec(c+d*x)^2)*(a+a*sec(c+d*x)), x) == :(2*a*d^-1*(A+-1C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*(A+3C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*C*a*d^-1*cos(c+d*x)^-1//2*sin(c+d*x)+2//3*A*a*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate(cos(c+d*x)^(1/2)*(A+C*sec(c+d*x)^2)*(a+a*sec(c+d*x)), x) == :(2*a*d^-1*(A+-1C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*(C+3A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*C*a*d^-1*cos(c+d*x)^-1//2*sin(c+d*x)+2//3*C*a*d^-1*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate(cos(c+d*x)^-1//2*(A+C*sec(c+d*x)^2)*(a+a*sec(c+d*x)), x) == :(-2//5*a*d^-1*(3C+5A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*(C+3A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*C*a*d^-1*cos(c+d*x)^-3//2*sin(c+d*x)+2//5*C*a*d^-1*cos(c+d*x)^-5//2*sin(c+d*x)+2//5*a*d^-1*cos(c+d*x)^-1//2*(3C+5A)*sin(c+d*x))
@test integrate(cos(c+d*x)^-3//2*(A+C*sec(c+d*x)^2)*(a+a*sec(c+d*x)), x) == :(-2//5*a*d^-1*(3C+5A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//21*a*d^-1*(5C+7A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*C*a*d^-1*cos(c+d*x)^-5//2*sin(c+d*x)+2//5*a*d^-1*cos(c+d*x)^-1//2*(3C+5A)*sin(c+d*x)+2//7*C*a*d^-1*cos(c+d*x)^-7//2*sin(c+d*x)+2//21*a*d^-1*cos(c+d*x)^-3//2*(5C+7A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^11//2*(A+C*sec(c+d*x)^2), x) == :(4//15*a^2*d^-1*(7A+9C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+8//231*a^2*d^-1*(25A+33C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//11*A*d^-1*(a+a*cos(c+d*x))^2*cos(c+d*x)^5//2*sin(c+d*x)+2//693*a^2*d^-1*cos(c+d*x)^5//2*(89A+99C)*sin(c+d*x)+4//45*a^2*d^-1*cos(c+d*x)^3//2*(7A+9C)*sin(c+d*x)+8//99*A*d^-1*cos(c+d*x)^5//2*(a^2+a^2*cos(c+d*x))*sin(c+d*x)+8//231*a^2*d^-1*cos(c+d*x)^(1/2)*(25A+33C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^9//2*(A+C*sec(c+d*x)^2), x) == :(4//21*a^2*d^-1*(5A+7C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+16//15*a^2*d^-1*(2A+3C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//9*A*d^-1*(a+a*cos(c+d*x))^2*cos(c+d*x)^3//2*sin(c+d*x)+2//105*a^2*d^-1*cos(c+d*x)^3//2*(19A+21C)*sin(c+d*x)+4//21*a^2*d^-1*cos(c+d*x)^(1/2)*(5A+7C)*sin(c+d*x)+8//63*A*d^-1*cos(c+d*x)^3//2*(a^2+a^2*cos(c+d*x))*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^7//2*(A+C*sec(c+d*x)^2), x) == :(4//5*a^2*d^-1*(3A+5C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+8//21*a^2*d^-1*(3A+7C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//7*A*d^-1*(a+a*cos(c+d*x))^2*cos(c+d*x)^(1/2)*sin(c+d*x)+2//105*a^2*d^-1*cos(c+d*x)^(1/2)*(33A+35C)*sin(c+d*x)+8//35*A*d^-1*cos(c+d*x)^(1/2)*(a^2+a^2*cos(c+d*x))*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^5//2*(A+C*sec(c+d*x)^2), x) == :(4//3*a^2*d^-1*(A+3C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+16//5*A*a^2*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*C*d^-1*(a+a*cos(c+d*x))^2*cos(c+d*x)^-1//2*sin(c+d*x)+1//5*d^-1*cos(c+d*x)^(1/2)*(a^2+a^2*cos(c+d*x))*(-10C+2A)*sin(c+d*x)+2//15*a^2*d^-1*cos(c+d*x)^(1/2)*(-15C+7A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^3//2*(A+C*sec(c+d*x)^2), x) == :(4*a^2*d^-1*(A+-1C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+8//3*a^2*d^-1*(A+C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*C*d^-1*(a+a*cos(c+d*x))^2*cos(c+d*x)^-3//2*sin(c+d*x)+2//3*a^2*d^-1*cos(c+d*x)^(1/2)*(A+-5C)*sin(c+d*x)+8//3*C*d^-1*cos(c+d*x)^-1//2*(a^2+a^2*cos(c+d*x))*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^(1/2)*(A+C*sec(c+d*x)^2), x) == :(-16//5*C*a^2*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//3*a^2*d^-1*(C+3A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*C*d^-1*(a+a*cos(c+d*x))^2*cos(c+d*x)^-5//2*sin(c+d*x)+2//15*a^2*d^-1*cos(c+d*x)^-1//2*(15A+17C)*sin(c+d*x)+8//15*C*d^-1*cos(c+d*x)^-3//2*(a^2+a^2*cos(c+d*x))*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^-1//2*(A+C*sec(c+d*x)^2), x) == :(-4//5*a^2*d^-1*(3C+5A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+8//21*a^2*d^-1*(3C+7A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//7*C*d^-1*(a+a*cos(c+d*x))^2*cos(c+d*x)^-7//2*sin(c+d*x)+2//105*a^2*d^-1*cos(c+d*x)^-3//2*(33C+35A)*sin(c+d*x)+4//5*a^2*d^-1*cos(c+d*x)^-1//2*(3C+5A)*sin(c+d*x)+8//35*C*d^-1*cos(c+d*x)^-5//2*(a^2+a^2*cos(c+d*x))*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^-3//2*(A+C*sec(c+d*x)^2), x) == :(-16//15*a^2*d^-1*(2C+3A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^2*d^-1*(5C+7A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//9*C*d^-1*(a+a*cos(c+d*x))^2*cos(c+d*x)^-9//2*sin(c+d*x)+2//105*a^2*d^-1*cos(c+d*x)^-5//2*(19C+21A)*sin(c+d*x)+4//21*a^2*d^-1*cos(c+d*x)^-3//2*(5C+7A)*sin(c+d*x)+8//63*C*d^-1*cos(c+d*x)^-7//2*(a^2+a^2*cos(c+d*x))*sin(c+d*x)+16//15*a^2*d^-1*cos(c+d*x)^-1//2*(2C+3A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^13//2*(A+C*sec(c+d*x)^2), x) == :(4//195*a^3*d^-1*(175A+221C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//231*a^3*d^-1*(95A+121C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//1287*d^-1*cos(c+d*x)^5//2*(a^3+a^3*cos(c+d*x))*(286C+290A)*sin(c+d*x)+2//13*A*d^-1*(a+a*cos(c+d*x))^3*cos(c+d*x)^5//2*sin(c+d*x)+4//231*a^3*d^-1*cos(c+d*x)^(1/2)*(95A+121C)*sin(c+d*x)+4//585*a^3*d^-1*cos(c+d*x)^3//2*(175A+221C)*sin(c+d*x)+40//9009*a^3*d^-1*cos(c+d*x)^5//2*(118A+143C)*sin(c+d*x)+12//143*A*a^-1*d^-1*(a^2+a^2*cos(c+d*x))^2*cos(c+d*x)^5//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^11//2*(A+C*sec(c+d*x)^2), x) == :(4//5*a^3*d^-1*(5A+7C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//231*a^3*d^-1*(105A+143C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//231*d^-1*cos(c+d*x)^3//2*(a^3+a^3*cos(c+d*x))*(66C+70A)*sin(c+d*x)+2//11*A*d^-1*(a+a*cos(c+d*x))^3*cos(c+d*x)^3//2*sin(c+d*x)+4//231*a^3*d^-1*cos(c+d*x)^(1/2)*(105A+143C)*sin(c+d*x)+8//385*a^3*d^-1*cos(c+d*x)^3//2*(35A+44C)*sin(c+d*x)+4//33*A*a^-1*d^-1*(a^2+a^2*cos(c+d*x))^2*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^9//2*(A+C*sec(c+d*x)^2), x) == :(4//15*a^3*d^-1*(17A+27C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^3*d^-1*(11A+21C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//315*d^-1*cos(c+d*x)^(1/2)*(a^3+a^3*cos(c+d*x))*(126C+146A)*sin(c+d*x)+2//9*A*d^-1*(a+a*cos(c+d*x))^3*cos(c+d*x)^(1/2)*sin(c+d*x)+8//105*a^3*d^-1*cos(c+d*x)^(1/2)*(16A+21C)*sin(c+d*x)+4//21*A*a^-1*d^-1*(a^2+a^2*cos(c+d*x))^2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^7//2*(A+C*sec(c+d*x)^2), x) == :(4//5*a^3*d^-1*(5C+7A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^3*d^-1*(13A+35C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*C*d^-1*(a+a*cos(c+d*x))^3*cos(c+d*x)^-1//2*sin(c+d*x)+1//35*d^-1*cos(c+d*x)^(1/2)*(a^3+a^3*cos(c+d*x))*(-70C+22A)*sin(c+d*x)+4//105*a^3*d^-1*cos(c+d*x)^(1/2)*(-35C+41A)*sin(c+d*x)+1//7*a^-1*d^-1*(a^2+a^2*cos(c+d*x))^2*cos(c+d*x)^(1/2)*(-14C+2A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^5//2*(A+C*sec(c+d*x)^2), x) == :(4//3*a^3*d^-1*(3A+5C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+4//5*a^3*d^-1*(-5C+9A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//15*d^-1*cos(c+d*x)^(1/2)*(a^3+a^3*cos(c+d*x))*(-70C+6A)*sin(c+d*x)+2//3*C*d^-1*(a+a*cos(c+d*x))^3*cos(c+d*x)^-3//2*sin(c+d*x)+8//15*a^3*d^-1*cos(c+d*x)^(1/2)*(-10C+3A)*sin(c+d*x)+4*C*a^-1*d^-1*(a^2+a^2*cos(c+d*x))^2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^3//2*(A+C*sec(c+d*x)^2), x) == :(4//3*a^3*d^-1*(3C+5A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+4//5*a^3*d^-1*(-9C+5A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-4//15*a^3*d^-1*cos(c+d*x)^(1/2)*(5A+21C)*sin(c+d*x)+1//5*d^-1*cos(c+d*x)^-1//2*(a^3+a^3*cos(c+d*x))*(10A+22C)*sin(c+d*x)+2//5*C*d^-1*(a+a*cos(c+d*x))^3*cos(c+d*x)^-5//2*sin(c+d*x)+4//5*C*a^-1*d^-1*(a^2+a^2*cos(c+d*x))^2*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^(1/2)*(A+C*sec(c+d*x)^2), x) == :(-4//5*a^3*d^-1*(5A+7C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^3*d^-1*(13C+35A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//15*d^-1*cos(c+d*x)^-3//2*(a^3+a^3*cos(c+d*x))*(10A+14C)*sin(c+d*x)+2//7*C*d^-1*(a+a*cos(c+d*x))^3*cos(c+d*x)^-7//2*sin(c+d*x)+8//105*a^3*d^-1*cos(c+d*x)^-1//2*(53C+70A)*sin(c+d*x)+12//35*C*a^-1*d^-1*(a^2+a^2*cos(c+d*x))^2*cos(c+d*x)^-5//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^-1//2*(A+C*sec(c+d*x)^2), x) == :(-4//15*a^3*d^-1*(17C+27A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^3*d^-1*(11C+21A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//315*d^-1*cos(c+d*x)^-5//2*(a^3+a^3*cos(c+d*x))*(126A+146C)*sin(c+d*x)+2//9*C*d^-1*(a+a*cos(c+d*x))^3*cos(c+d*x)^-9//2*sin(c+d*x)+4//15*a^3*d^-1*cos(c+d*x)^-1//2*(17C+27A)*sin(c+d*x)+8//105*a^3*d^-1*cos(c+d*x)^-3//2*(16C+21A)*sin(c+d*x)+4//21*C*a^-1*d^-1*(a^2+a^2*cos(c+d*x))^2*cos(c+d*x)^-7//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^-3//2*(A+C*sec(c+d*x)^2), x) == :(-4//5*a^3*d^-1*(5C+7A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//231*a^3*d^-1*(105C+143A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//231*d^-1*cos(c+d*x)^-7//2*(a^3+a^3*cos(c+d*x))*(66A+70C)*sin(c+d*x)+2//11*C*d^-1*(a+a*cos(c+d*x))^3*cos(c+d*x)^-11//2*sin(c+d*x)+4//5*a^3*d^-1*cos(c+d*x)^-1//2*(5C+7A)*sin(c+d*x)+4//231*a^3*d^-1*cos(c+d*x)^-3//2*(105C+143A)*sin(c+d*x)+8//385*a^3*d^-1*cos(c+d*x)^-5//2*(35C+44A)*sin(c+d*x)+4//33*C*a^-1*d^-1*(a^2+a^2*cos(c+d*x))^2*cos(c+d*x)^-9//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^7//2*(A+C*sec(c+d*x)^2), x) == :(-1//5*a^-1*d^-1*(15C+21A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*a^-1*d^-1*(35C+45A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1*d^-1*(a+a*cos(c+d*x))^-1*cos(c+d*x)^7//2*(A+C)*sin(c+d*x)+-1//5*a^-1*d^-1*cos(c+d*x)^3//2*(5C+7A)*sin(c+d*x)+1//7*a^-1*d^-1*cos(c+d*x)^5//2*(7C+9A)*sin(c+d*x)+1//21*a^-1*d^-1*cos(c+d*x)^(1/2)*(35C+45A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^5//2*(A+C*sec(c+d*x)^2), x) == :(-1//3*a^-1*d^-1*(3C+5A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*a^-1*d^-1*(15C+21A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1*d^-1*(a+a*cos(c+d*x))^-1*cos(c+d*x)^5//2*(A+C)*sin(c+d*x)+-1//3*a^-1*d^-1*cos(c+d*x)^(1/2)*(3C+5A)*sin(c+d*x)+1//5*a^-1*d^-1*cos(c+d*x)^3//2*(5C+7A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^3//2*(A+C*sec(c+d*x)^2), x) == :(-1*a^-1*d^-1*(C+3A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-1*d^-1*(3C+5A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1*d^-1*(a+a*cos(c+d*x))^-1*cos(c+d*x)^3//2*(A+C)*sin(c+d*x)+1//3*a^-1*d^-1*cos(c+d*x)^(1/2)*(3C+5A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^(1/2)*(A+C*sec(c+d*x)^2), x) == :(a^-1*d^-1*(C+3A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1*a^-1*d^-1*(A+-1C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1*d^-1*(a+a*cos(c+d*x))^-1*cos(c+d*x)^(1/2)*(A+C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^-1//2*(A+C*sec(c+d*x)^2), x) == :(a^-1*d^-1*(A+-1C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1*a^-1*d^-1*(A+3C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+a^-1*d^-1*cos(c+d*x)^-1//2*(A+3C)*sin(c+d*x)+-1*d^-1*(a+a*cos(c+d*x))^-1*cos(c+d*x)^-1//2*(A+C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^-3//2*(A+C*sec(c+d*x)^2), x) == :(a^-1*d^-1*(A+3C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-1*d^-1*(3A+5C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1*a^-1*d^-1*cos(c+d*x)^-1//2*(A+3C)*sin(c+d*x)+-1*d^-1*(a+a*cos(c+d*x))^-1*cos(c+d*x)^-3//2*(A+C)*sin(c+d*x)+1//3*a^-1*d^-1*cos(c+d*x)^-3//2*(3A+5C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^-5//2*(A+C*sec(c+d*x)^2), x) == :(-1//3*a^-1*d^-1*(3A+5C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//5*a^-1*d^-1*(15A+21C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1*d^-1*(a+a*cos(c+d*x))^-1*cos(c+d*x)^-5//2*(A+C)*sin(c+d*x)+-1//3*a^-1*d^-1*cos(c+d*x)^-3//2*(3A+5C)*sin(c+d*x)+1//5*a^-1*d^-1*cos(c+d*x)^-5//2*(5A+7C)*sin(c+d*x)+1//5*a^-1*d^-1*cos(c+d*x)^-1//2*(15A+21C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^5//2*(A+C*sec(c+d*x)^2), x) == :(-1//3*a^-2*d^-1*(5C+15A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*a^-2*d^-1*(20C+56A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*(5C+15A)*sin(c+d*x)+-1//3*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^7//2*(A+C)*sin(c+d*x)+1//15*a^-2*d^-1*cos(c+d*x)^3//2*(20C+56A)*sin(c+d*x)+-1*a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^5//2*(C+3A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^3//2*(A+C*sec(c+d*x)^2), x) == :(-1*a^-2*d^-1*(C+7A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-2*d^-1*(2C+10A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//3*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^5//2*(A+C)*sin(c+d*x)+1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*(2C+10A)*sin(c+d*x)+-1//3*a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^3//2*(C+7A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^(1/2)*(A+C*sec(c+d*x)^2), x) == :(4*A*a^-2*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//3*a^-2*d^-1*(-1C+5A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//3*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^3//2*(A+C)*sin(c+d*x)+-1//3*a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^(1/2)*(-1C+5A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^-1//2*(A+C*sec(c+d*x)^2), x) == :(-1*a^-2*d^-1*(A+-1C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-2*d^-1*(2A+2C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//3*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^(1/2)*(A+C)*sin(c+d*x)+a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^(1/2)*(A+-1C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^-3//2*(A+C*sec(c+d*x)^2), x) == :(-4*C*a^-2*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-2*d^-1*(A+-5C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+4*C*a^-2*d^-1*cos(c+d*x)^-1//2*sin(c+d*x)+-1//3*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^-1//2*(A+C)*sin(c+d*x)+1//3*a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^-1//2*(A+-5C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^-5//2*(A+C*sec(c+d*x)^2), x) == :(a^-2*d^-1*(A+7C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-2*d^-1*(2A+10C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1*a^-2*d^-1*cos(c+d*x)^-1//2*(A+7C)*sin(c+d*x)+-1//3*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^-3//2*(A+C)*sin(c+d*x)+1//3*a^-2*d^-1*cos(c+d*x)^-3//2*(2A+10C)*sin(c+d*x)+-1//3*a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^-3//2*(A+7C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^5//2*(A+C*sec(c+d*x)^2), x) == :(-1//6*a^-3*d^-1*(13C+63A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//10*a^-3*d^-1*(49C+231A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^9//2*(A+C)*sin(c+d*x)+-1//6*a^-3*d^-1*cos(c+d*x)^(1/2)*(13C+63A)*sin(c+d*x)+-1//10*d^-1*(a^3+a^3*cos(c+d*x))^-1*cos(c+d*x)^5//2*(13C+63A)*sin(c+d*x)+1//30*a^-3*d^-1*cos(c+d*x)^3//2*(49C+231A)*sin(c+d*x)+-1//15*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^7//2*(2C+12A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^3//2*(A+C*sec(c+d*x)^2), x) == :((1/2)*a^-3*d^-1*(C+11A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//10*a^-3*d^-1*(9C+119A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+(1/2)*a^-3*d^-1*cos(c+d*x)^(1/2)*(C+11A)*sin(c+d*x)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^7//2*(A+C)*sin(c+d*x)+-1//30*d^-1*(a^3+a^3*cos(c+d*x))^-1*cos(c+d*x)^3//2*(9C+119A)*sin(c+d*x)+-2//3*A*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^5//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^(1/2)*(A+C*sec(c+d*x)^2), x) == :(-1//6*a^-3*d^-1*(-1C+13A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//10*a^-3*d^-1*(-1C+49A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^5//2*(A+C)*sin(c+d*x)+-1//6*d^-1*(a^3+a^3*cos(c+d*x))^-1*cos(c+d*x)^(1/2)*(-1C+13A)*sin(c+d*x)+-1//15*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^3//2*(-2C+8A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^-1//2*(A+C*sec(c+d*x)^2), x) == :(-1//10*a^-3*d^-1*(-1C+9A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//6*a^-3*d^-1*(C+3A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^3//2*(A+C)*sin(c+d*x)+1//10*d^-1*(a^3+a^3*cos(c+d*x))^-1*cos(c+d*x)^(1/2)*(-1C+9A)*sin(c+d*x)+-1//15*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^(1/2)*(-4C+6A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^-3//2*(A+C*sec(c+d*x)^2), x) == :(-1//10*a^-3*d^-1*(A+-9C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//6*a^-3*d^-1*(A+3C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^(1/2)*(A+C)*sin(c+d*x)+1//10*d^-1*(a^3+a^3*cos(c+d*x))^-1*cos(c+d*x)^(1/2)*(A+-9C)*sin(c+d*x)+1//15*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^(1/2)*(-6C+4A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^-5//2*(A+C*sec(c+d*x)^2), x) == :(1//6*a^-3*d^-1*(A+-13C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//10*a^-3*d^-1*(A+-49C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^-1//2*(A+C)*sin(c+d*x)+-1//10*a^-3*d^-1*cos(c+d*x)^-1//2*(A+-49C)*sin(c+d*x)+1//6*d^-1*(a^3+a^3*cos(c+d*x))^-1*cos(c+d*x)^-1//2*(A+-13C)*sin(c+d*x)+1//15*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^-1//2*(-8C+2A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^-7//2*(A+C*sec(c+d*x)^2), x) == :((1/2)*a^-3*d^-1*(A+11C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//10*a^-3*d^-1*(9A+119C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+(1/2)*a^-3*d^-1*cos(c+d*x)^-3//2*(A+11C)*sin(c+d*x)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^-3//2*(A+C)*sin(c+d*x)+-1//10*a^-3*d^-1*cos(c+d*x)^-1//2*(9A+119C)*sin(c+d*x)+-1//30*d^-1*(a^3+a^3*cos(c+d*x))^-1*cos(c+d*x)^-3//2*(9A+119C)*sin(c+d*x)+-2//3*C*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^9//2*(A+C*sec(c+d*x)^2), x) == :(2//9*A*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^7//2*sin(c+d*x)+2//63*A*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^5//2*sin(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(16A+21C)*sin(c+d*x)+8//315*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(16A+21C)*sin(c+d*x)+16//315*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(16A+21C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^7//2*(A+C*sec(c+d*x)^2), x) == :(2//7*A*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*sin(c+d*x)+2//35*A*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(24A+35C)*sin(c+d*x)+4//105*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(24A+35C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*(A+C*sec(c+d*x)^2), x) == :(2//5*A*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*sin(c+d*x)+2//15*A*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x)+2//15*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(7A+15C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*(A+C*sec(c+d*x)^2), x) == :(2//3*A*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x)+2*C*a^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//3*A*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(A+C*sec(c+d*x)^2), x) == :(C*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-1//2*sin(c+d*x)+C*a^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-1C+2A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-1//2*(A+C*sec(c+d*x)^2), x) == :((1/2)*C*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-3//2*sin(c+d*x)+1//4*C*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+1//4*a^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3C+8A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-3//2*(A+C*sec(c+d*x)^2), x) == :(1//3*C*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-5//2*sin(c+d*x)+1//8*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(5C+8A)*sin(c+d*x)+1//8*a^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5C+8A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//12*C*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-5//2*(A+C*sec(c+d*x)^2), x) == :(1//4*C*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-7//2*sin(c+d*x)+1//24*C*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-7//2*sin(c+d*x)+1//64*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(35C+48A)*sin(c+d*x)+1//64*a^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(35C+48A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//96*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*(35C+48A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^11//2*(A+C*sec(c+d*x)^2), x) == :(2//11*A*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^9//2*sin(c+d*x)+2//33*A*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^7//2*sin(c+d*x)+2//231*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^5//2*(28A+33C)*sin(c+d*x)+2//385*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(112A+143C)*sin(c+d*x)+8//1155*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(112A+143C)*sin(c+d*x)+16//1155*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(112A+143C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^9//2*(A+C*sec(c+d*x)^2), x) == :(2//9*A*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^7//2*sin(c+d*x)+2//21*A*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*sin(c+d*x)+2//315*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(136A+189C)*sin(c+d*x)+2//315*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(52A+63C)*sin(c+d*x)+4//315*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(136A+189C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^7//2*(A+C*sec(c+d*x)^2), x) == :(2//7*A*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^5//2*sin(c+d*x)+6//35*A*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^3//2*sin(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(19A+35C)*sin(c+d*x)+8//105*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(19A+35C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^5//2*(A+C*sec(c+d*x)^2), x) == :(2//5*A*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^3//2*sin(c+d*x)+2*C*a^3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//5*A*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x)+2//5*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(4A+5C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^3//2*(A+C*sec(c+d*x)^2), x) == :(2//3*A*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^(1/2)*sin(c+d*x)+3*C*a^3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//3*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-1//2*(-3C+2A)*sin(c+d*x)+1//3*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-3C+8A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^(1/2)*(A+C*sec(c+d*x)^2), x) == :((1/2)*C*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^-1//2*sin(c+d*x)+1//4*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-5C+8A)*sin(c+d*x)+1//4*a^3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(7C+8A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+3//4*C*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^-1//2*(A+C*sec(c+d*x)^2), x) == :(1//3*C*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^-3//2*sin(c+d*x)+1//4*C*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-3//2*sin(c+d*x)+1//8*a^3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(11C+24A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//24*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(19C+24A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^-3//2*(A+C*sec(c+d*x)^2), x) == :(1//4*C*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^-5//2*sin(c+d*x)+1//8*C*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-5//2*sin(c+d*x)+1//32*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*(13C+16A)*sin(c+d*x)+1//64*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(75C+112A)*sin(c+d*x)+1//64*a^3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(75C+112A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^-5//2*(A+C*sec(c+d*x)^2), x) == :(1//5*C*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^-7//2*sin(c+d*x)+1//128*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(133C+176A)*sin(c+d*x)+1//128*a^3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(133C+176A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//192*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*(133C+176A)*sin(c+d*x)+1//240*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-7//2*(67C+80A)*sin(c+d*x)+3//40*C*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-7//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^13//2*(A+C*sec(c+d*x)^2), x) == :(2//13*A*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^11//2*sin(c+d*x)+2//1287*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^7//2*(136A+143C)*sin(c+d*x)+2//9009*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^5//2*(2224A+2717C)*sin(c+d*x)+2//15015*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(8368A+10439C)*sin(c+d*x)+8//45045*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(8368A+10439C)*sin(c+d*x)+10//143*A*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^9//2*sin(c+d*x)+16//45045*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(8368A+10439C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^11//2*(A+C*sec(c+d*x)^2), x) == :(2//11*A*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^9//2*sin(c+d*x)+2//231*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*(32A+33C)*sin(c+d*x)+2//693*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(568A+759C)*sin(c+d*x)+2//693*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(232A+297C)*sin(c+d*x)+4//693*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(568A+759C)*sin(c+d*x)+10//99*A*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^7//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^9//2*(A+C*sec(c+d*x)^2), x) == :(2//9*A*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^7//2*sin(c+d*x)+10//63*A*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^5//2*sin(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^3//2*(13A+21C)*sin(c+d*x)+16//315*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(13A+21C)*sin(c+d*x)+64//315*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(13A+21C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^7//2*(A+C*sec(c+d*x)^2), x) == :(2//7*A*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^5//2*sin(c+d*x)+2*C*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//7*A*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^3//2*sin(c+d*x)+2//21*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(7C+8A)*sin(c+d*x)+2//21*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(32A+49C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^5//2*(A+C*sec(c+d*x)^2), x) == :(2//5*A*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^3//2*sin(c+d*x)+5*C*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//15*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-1//2*(-15C+16A)*sin(c+d*x)+1//15*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(15C+64A)*sin(c+d*x)+2//3*A*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^3//2*(A+C*sec(c+d*x)^2), x) == :(2//3*A*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^(1/2)*sin(c+d*x)+-1//6*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^-1//2*(-3C+4A)*sin(c+d*x)+-1//12*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-1//2*(-21C+8A)*sin(c+d*x)+1//4*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(8A+19C)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//12*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-27C+56A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^(1/2)*(A+C*sec(c+d*x)^2), x) == :(1//3*C*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^-1//2*sin(c+d*x)+1//24*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-1//2*(24A+31C)*sin(c+d*x)+1//24*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-49C+24A)*sin(c+d*x)+5//8*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5C+8A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+5//12*C*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^-1//2*(A+C*sec(c+d*x)^2), x) == :(1//4*C*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^-3//2*sin(c+d*x)+1//32*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-3//2*(16A+17C)*sin(c+d*x)+1//64*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(163C+304A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//192*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(299C+432A)*sin(c+d*x)+5//24*C*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^-3//2*(A+C*sec(c+d*x)^2), x) == :(1//5*C*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^-5//2*sin(c+d*x)+1//8*C*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^-5//2*sin(c+d*x)+1//128*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(283C+400A)*sin(c+d*x)+1//128*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(283C+400A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//240*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-5//2*(79C+80A)*sin(c+d*x)+1//960*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*(787C+1040A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^-5//2*(A+C*sec(c+d*x)^2), x) == :(1//6*C*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^-7//2*sin(c+d*x)+1//12*C*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^-7//2*sin(c+d*x)+1//96*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-7//2*(23C+24A)*sin(c+d*x)+1//192*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-7//2*(109C+136A)*sin(c+d*x)+1//512*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(1015C+1304A)*sin(c+d*x)+1//512*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(1015C+1304A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//768*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*(1015C+1304A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^7//2*(A+C*sec(c+d*x)^2), x) == :(-2//35*A*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x)+-1//105*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(70C+86A)*sin(c+d*x)+1//105*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(62A+70C)*sin(c+d*x)+2//7*A*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^5//2*sin(c+d*x)+2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+C)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^5//2*(A+C*sec(c+d*x)^2), x) == :(-2//15*A*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)+1//15*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(26A+30C)*sin(c+d*x)+2//5*A*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+C)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(A+C*sec(c+d*x)^2), x) == :(-2//3*A*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+2//3*A*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)+2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+C)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(A+C*sec(c+d*x)^2), x) == :(2*A*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+2*C*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1*2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+C)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(A+C*sec(c+d*x)^2), x) == :(C*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+-1*C*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+C)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(A+C*sec(c+d*x)^2), x) == :((1/2)*C*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x)+-1//4*C*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+1//4*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(7C+8A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1*2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+C)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*(A+C*sec(c+d*x)^2), x) == :(-1//12*C*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x)+1//3*C*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-7//2*sin(c+d*x)+1//8*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(7C+8A)*sin(c+d*x)+-1//8*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(8A+9C)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+C)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^5//2*(A+C*sec(c+d*x)^2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^3//2*(A+C)*sin(c+d*x)+-1//10*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(5C+13A)*sin(c+d*x)+1//10*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(25C+49A)*sin(c+d*x)+1//10*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(5C+9A)*sin(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(7C+15A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^3//2*(A+C*sec(c+d*x)^2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^(1/2)*(A+C)*sin(c+d*x)+-1//6*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(3C+19A)*sin(c+d*x)+1//6*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(3C+7A)*sin(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3C+11A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^(1/2)*(A+C*sec(c+d*x)^2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-1//2*(A+C)*sin(c+d*x)+(1/2)*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(C+5A)*sin(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-1C+7A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-1//2*(A+C*sec(c+d*x)^2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-3//2*(A+C)*sin(c+d*x)+2*C*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-5C+3A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-3//2*(A+C*sec(c+d*x)^2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-5//2*(A+C)*sin(c+d*x)+(1/2)*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(A+3C)*sin(c+d*x)+-3*C*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+9C)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-5//2*(A+C*sec(c+d*x)^2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-7//2*(A+C)*sin(c+d*x)+(1/2)*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*(A+2C)*sin(c+d*x)+-1//4*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(2A+7C)*sin(c+d*x)+1//4*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(8A+19C)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5A+13C)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^5//2*(A+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^3//2*(A+C)*sin(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^3//2*(5C+21A)*sin(c+d*x)+-1//240*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(195C+787A)*sin(c+d*x)+1//80*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(45C+157A)*sin(c+d*x)+1//240*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(735C+2671A)*sin(c+d*x)+-1//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(75C+283A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^3//2*(A+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^(1/2)*(A+C)*sin(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^(1/2)*(C+17A)*sin(c+d*x)+-1//48*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(27C+299A)*sin(c+d*x)+1//48*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(15C+95A)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(19C+163A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^(1/2)*(A+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-1//2*(A+C)*sin(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-1//2*(-3C+13A)*sin(c+d*x)+1//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(C+49A)*sin(c+d*x)+-1//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-5C+75A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-1//2*(A+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-3//2*(A+C)*sin(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-3//2*(-7C+9A)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3C+19A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-3//2*(A+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-5//2*(A+C)*sin(c+d*x)+2*C*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-3//2*(-11C+5A)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-43C+5A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-5//2*(A+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-7//2*(A+C)*sin(c+d*x)+-5*C*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-5//2*(A+-15C)*sin(c+d*x)+1//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(3A+35C)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3A+115C)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate(cos(c+d*x)^9//2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(6//5*C*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+10//21*B*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*C*d^-1*cos(c+d*x)^3//2*sin(c+d*x)+2//7*B*d^-1*cos(c+d*x)^5//2*sin(c+d*x)+10//21*B*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate(cos(c+d*x)^7//2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//3*C*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+6//5*B*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*C*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+2//5*B*d^-1*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate(cos(c+d*x)^5//2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2*C*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*B*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*B*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate(cos(c+d*x)^3//2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2*B*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*C*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(cos(c+d*x)^(1/2)*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-2*C*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*B*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*C*d^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate(cos(c+d*x)^-1//2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-2*B*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*C*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*B*d^-1*cos(c+d*x)^-1//2*sin(c+d*x)+2//3*C*d^-1*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate(cos(c+d*x)^-3//2*(B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-6//5*C*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*B*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*B*d^-1*cos(c+d*x)^-3//2*sin(c+d*x)+2//5*C*d^-1*cos(c+d*x)^-5//2*sin(c+d*x)+6//5*C*d^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate(cos(c+d*x)^7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//21*d^-1*(10A+14C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+6//5*B*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*(10A+14C)*sin(c+d*x)+2//5*B*d^-1*cos(c+d*x)^3//2*sin(c+d*x)+2//7*A*d^-1*cos(c+d*x)^5//2*sin(c+d*x))
@test integrate(cos(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//5*d^-1*(6A+10C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*B*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*B*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+2//5*A*d^-1*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate(cos(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2*B*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*(2A+6C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*A*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate(cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(d^-1*(-2C+2A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*B*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*C*d^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate(cos(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-2*B*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*(2C+6A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*B*d^-1*cos(c+d*x)^-1//2*sin(c+d*x)+2//3*C*d^-1*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate(cos(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//5*d^-1*(-10A+-6C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*B*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*cos(c+d*x)^-1//2*(6C+10A)*sin(c+d*x)+2//3*B*d^-1*cos(c+d*x)^-3//2*sin(c+d*x)+2//5*C*d^-1*cos(c+d*x)^-5//2*sin(c+d*x))
@test integrate(cos(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-6//5*B*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*(10C+14A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^-3//2*(10C+14A)*sin(c+d*x)+2//5*B*d^-1*cos(c+d*x)^-5//2*sin(c+d*x)+2//7*C*d^-1*cos(c+d*x)^-7//2*sin(c+d*x)+6//5*B*d^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate(cos(c+d*x)^9//2*(a+a*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//15*a*d^-1*(7A+9B+9C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//21*a*d^-1*(5A+5B+7C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//7*a*d^-1*cos(c+d*x)^5//2*(A+B)*sin(c+d*x)+2//9*A*a*d^-1*cos(c+d*x)^7//2*sin(c+d*x)+2//21*a*d^-1*cos(c+d*x)^(1/2)*(5A+5B+7C)*sin(c+d*x)+2//45*a*d^-1*cos(c+d*x)^3//2*(7A+9B+9C)*sin(c+d*x))
@test integrate(cos(c+d*x)^7//2*(a+a*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//5*a*d^-1*(3A+3B+5C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//21*a*d^-1*(5A+7B+7C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*a*d^-1*cos(c+d*x)^3//2*(A+B)*sin(c+d*x)+2//7*A*a*d^-1*cos(c+d*x)^5//2*sin(c+d*x)+2//21*a*d^-1*cos(c+d*x)^(1/2)*(5A+7B+7C)*sin(c+d*x))
@test integrate(cos(c+d*x)^5//2*(a+a*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//3*a*d^-1*(A+B+3C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*a*d^-1*(3A+5B+5C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*cos(c+d*x)^(1/2)*(A+B)*sin(c+d*x)+2//5*A*a*d^-1*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate(cos(c+d*x)^3//2*(a+a*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2*a*d^-1*(A+B+-1C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*(A+3B+3C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*C*a*d^-1*cos(c+d*x)^-1//2*sin(c+d*x)+2//3*A*a*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate(cos(c+d*x)^(1/2)*(a+a*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2*a*d^-1*(A+-1B+-1C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*(C+3A+3B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*a*d^-1*cos(c+d*x)^-1//2*(B+C)*sin(c+d*x)+2//3*C*a*d^-1*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate(cos(c+d*x)^-1//2*(a+a*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-2//5*a*d^-1*(3C+5A+5B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*(B+C+3A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*cos(c+d*x)^-3//2*(B+C)*sin(c+d*x)+2//5*C*a*d^-1*cos(c+d*x)^-5//2*sin(c+d*x)+2//5*a*d^-1*cos(c+d*x)^-1//2*(3C+5A+5B)*sin(c+d*x))
@test integrate(cos(c+d*x)^-3//2*(a+a*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-2//5*a*d^-1*(3B+3C+5A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//21*a*d^-1*(5C+7A+7B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*a*d^-1*cos(c+d*x)^-5//2*(B+C)*sin(c+d*x)+2//5*a*d^-1*cos(c+d*x)^-1//2*(3B+3C+5A)*sin(c+d*x)+2//7*C*a*d^-1*cos(c+d*x)^-7//2*sin(c+d*x)+2//21*a*d^-1*cos(c+d*x)^-3//2*(5C+7A+7B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^11//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(4//15*a^2*d^-1*(7A+8B+9C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//231*a^2*d^-1*(50A+55B+66C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//99*d^-1*cos(c+d*x)^5//2*(a^2+a^2*cos(c+d*x))*(8A+22B)*sin(c+d*x)+2//11*A*d^-1*(a+a*cos(c+d*x))^2*cos(c+d*x)^5//2*sin(c+d*x)+2//693*a^2*d^-1*cos(c+d*x)^5//2*(89A+99C+121B)*sin(c+d*x)+4//45*a^2*d^-1*cos(c+d*x)^3//2*(7A+8B+9C)*sin(c+d*x)+4//231*a^2*d^-1*cos(c+d*x)^(1/2)*(50A+55B+66C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^9//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(4//15*a^2*d^-1*(8A+9B+12C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^2*d^-1*(5A+6B+7C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//63*d^-1*cos(c+d*x)^3//2*(a^2+a^2*cos(c+d*x))*(8A+18B)*sin(c+d*x)+2//9*A*d^-1*(a+a*cos(c+d*x))^2*cos(c+d*x)^3//2*sin(c+d*x)+2//105*a^2*d^-1*cos(c+d*x)^3//2*(19A+21C+27B)*sin(c+d*x)+4//21*a^2*d^-1*cos(c+d*x)^(1/2)*(5A+6B+7C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(4//5*a^2*d^-1*(3A+4B+5C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^2*d^-1*(6A+7B+14C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//35*d^-1*cos(c+d*x)^(1/2)*(a^2+a^2*cos(c+d*x))*(8A+14B)*sin(c+d*x)+2//7*A*d^-1*(a+a*cos(c+d*x))^2*cos(c+d*x)^(1/2)*sin(c+d*x)+2//105*a^2*d^-1*cos(c+d*x)^(1/2)*(33A+35C+49B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(4//3*a^2*d^-1*(A+2B+3C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+4//5*a^2*d^-1*(4A+5B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*C*d^-1*(a+a*cos(c+d*x))^2*cos(c+d*x)^-1//2*sin(c+d*x)+1//5*d^-1*cos(c+d*x)^(1/2)*(a^2+a^2*cos(c+d*x))*(-10C+2A)*sin(c+d*x)+2//15*a^2*d^-1*cos(c+d*x)^(1/2)*(-15C+5B+7A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(4*a^2*d^-1*(A+-1C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//3*a^2*d^-1*(2A+2C+3B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*cos(c+d*x)^-1//2*(a^2+a^2*cos(c+d*x))*(6B+8C)*sin(c+d*x)+2//3*C*d^-1*(a+a*cos(c+d*x))^2*cos(c+d*x)^-3//2*sin(c+d*x)+2//3*a^2*d^-1*cos(c+d*x)^(1/2)*(A+-5C+-3B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-4//5*a^2*d^-1*(4C+5B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//3*a^2*d^-1*(C+2B+3A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//15*d^-1*cos(c+d*x)^-3//2*(a^2+a^2*cos(c+d*x))*(8C+10B)*sin(c+d*x)+2//5*C*d^-1*(a+a*cos(c+d*x))^2*cos(c+d*x)^-5//2*sin(c+d*x)+2//15*a^2*d^-1*cos(c+d*x)^-1//2*(15A+17C+25B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-4//5*a^2*d^-1*(3C+4B+5A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^2*d^-1*(6C+7B+14A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//35*d^-1*cos(c+d*x)^-5//2*(a^2+a^2*cos(c+d*x))*(8C+14B)*sin(c+d*x)+2//7*C*d^-1*(a+a*cos(c+d*x))^2*cos(c+d*x)^-7//2*sin(c+d*x)+2//105*a^2*d^-1*cos(c+d*x)^-3//2*(33C+35A+49B)*sin(c+d*x)+4//5*a^2*d^-1*cos(c+d*x)^-1//2*(3C+4B+5A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-4//15*a^2*d^-1*(8C+9B+12A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^2*d^-1*(5C+6B+7A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//63*d^-1*cos(c+d*x)^-7//2*(a^2+a^2*cos(c+d*x))*(8C+18B)*sin(c+d*x)+2//9*C*d^-1*(a+a*cos(c+d*x))^2*cos(c+d*x)^-9//2*sin(c+d*x)+2//105*a^2*d^-1*cos(c+d*x)^-5//2*(19C+21A+27B)*sin(c+d*x)+4//15*a^2*d^-1*cos(c+d*x)^-1//2*(8C+9B+12A)*sin(c+d*x)+4//21*a^2*d^-1*cos(c+d*x)^-3//2*(5C+6B+7A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^11//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(4//15*a^3*d^-1*(15A+17B+21C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//231*a^3*d^-1*(105A+121B+143C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//693*d^-1*cos(c+d*x)^3//2*(a^3+a^3*cos(c+d*x))*(198C+210A+286B)*sin(c+d*x)+2//11*A*d^-1*(a+a*cos(c+d*x))^3*cos(c+d*x)^3//2*sin(c+d*x)+4//231*a^3*d^-1*cos(c+d*x)^(1/2)*(105A+121B+143C)*sin(c+d*x)+4//1155*a^3*d^-1*cos(c+d*x)^3//2*(210A+253B+264C)*sin(c+d*x)+1//99*a^-1*d^-1*(a^2+a^2*cos(c+d*x))^2*cos(c+d*x)^3//2*(12A+22B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^9//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(4//15*a^3*d^-1*(17A+21B+27C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^3*d^-1*(11A+13B+21C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//315*d^-1*cos(c+d*x)^(1/2)*(a^3+a^3*cos(c+d*x))*(126C+146A+198B)*sin(c+d*x)+2//9*A*d^-1*(a+a*cos(c+d*x))^3*cos(c+d*x)^(1/2)*sin(c+d*x)+4//105*a^3*d^-1*cos(c+d*x)^(1/2)*(32A+41B+42C)*sin(c+d*x)+1//21*a^-1*d^-1*(a^2+a^2*cos(c+d*x))^2*cos(c+d*x)^(1/2)*(4A+6B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(4//5*a^3*d^-1*(5C+7A+9B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^3*d^-1*(13A+21B+35C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*C*d^-1*(a+a*cos(c+d*x))^3*cos(c+d*x)^-1//2*sin(c+d*x)+1//35*d^-1*cos(c+d*x)^(1/2)*(a^3+a^3*cos(c+d*x))*(-70C+14B+22A)*sin(c+d*x)+4//105*a^3*d^-1*cos(c+d*x)^(1/2)*(-35C+41A+42B)*sin(c+d*x)+1//7*a^-1*d^-1*(a^2+a^2*cos(c+d*x))^2*cos(c+d*x)^(1/2)*(-14C+2A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(4//3*a^3*d^-1*(3A+5B+5C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+4//5*a^3*d^-1*(-5C+5B+9A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//15*d^-1*cos(c+d*x)^(1/2)*(a^3+a^3*cos(c+d*x))*(-70C+-30B+6A)*sin(c+d*x)+2//3*C*d^-1*(a+a*cos(c+d*x))^3*cos(c+d*x)^-3//2*sin(c+d*x)+4//15*a^3*d^-1*cos(c+d*x)^(1/2)*(-20C+-5B+6A)*sin(c+d*x)+a^-1*d^-1*(a^2+a^2*cos(c+d*x))^2*cos(c+d*x)^-1//2*(2B+4C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(4//3*a^3*d^-1*(3C+5A+5B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+4//5*a^3*d^-1*(-9C+-5B+5A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-4//15*a^3*d^-1*cos(c+d*x)^(1/2)*(5A+20B+21C)*sin(c+d*x)+1//15*d^-1*cos(c+d*x)^-1//2*(a^3+a^3*cos(c+d*x))*(30A+66C+70B)*sin(c+d*x)+2//5*C*d^-1*(a+a*cos(c+d*x))^3*cos(c+d*x)^-5//2*sin(c+d*x)+1//15*a^-1*d^-1*(a^2+a^2*cos(c+d*x))^2*cos(c+d*x)^-3//2*(10B+12C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-4//5*a^3*d^-1*(5A+7C+9B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^3*d^-1*(13C+21B+35A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//15*d^-1*cos(c+d*x)^-3//2*(a^3+a^3*cos(c+d*x))*(10A+14C+18B)*sin(c+d*x)+2//7*C*d^-1*(a+a*cos(c+d*x))^3*cos(c+d*x)^-7//2*sin(c+d*x)+4//105*a^3*d^-1*cos(c+d*x)^-1//2*(106C+140A+147B)*sin(c+d*x)+1//35*a^-1*d^-1*(a^2+a^2*cos(c+d*x))^2*cos(c+d*x)^-5//2*(12C+14B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-4//15*a^3*d^-1*(17C+21B+27A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^3*d^-1*(11C+13B+21A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//315*d^-1*cos(c+d*x)^-5//2*(a^3+a^3*cos(c+d*x))*(126A+146C+198B)*sin(c+d*x)+2//9*C*d^-1*(a+a*cos(c+d*x))^3*cos(c+d*x)^-9//2*sin(c+d*x)+4//15*a^3*d^-1*cos(c+d*x)^-1//2*(17C+21B+27A)*sin(c+d*x)+4//105*a^3*d^-1*cos(c+d*x)^-3//2*(32C+41B+42A)*sin(c+d*x)+1//21*a^-1*d^-1*(a^2+a^2*cos(c+d*x))^2*cos(c+d*x)^-7//2*(4C+6B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^13//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(8//195*a^4*d^-1*(185A+208B+247C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+8//231*a^4*d^-1*(100A+113B+132C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//99*d^-1*(a^2+a^2*cos(c+d*x))^2*cos(c+d*x)^3//2*(22C+26A+34B)*sin(c+d*x)+1//9009*d^-1*cos(c+d*x)^3//2*(a^4+a^4*cos(c+d*x))*(5420A+6292C+6448B)*sin(c+d*x)+2//13*A*d^-1*(a+a*cos(c+d*x))^4*cos(c+d*x)^3//2*sin(c+d*x)+4//15015*a^4*d^-1*cos(c+d*x)^3//2*(5255A+6019B+6721C)*sin(c+d*x)+8//231*a^4*d^-1*cos(c+d*x)^(1/2)*(100A+113B+132C)*sin(c+d*x)+2//143*a*d^-1*(a+a*cos(c+d*x))^3*cos(c+d*x)^3//2*(8A+13B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^11//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(8//15*a^4*d^-1*(16A+19B+24C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+8//231*a^4*d^-1*(113A+132B+187C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//231*d^-1*(a^2+a^2*cos(c+d*x))^2*cos(c+d*x)^(1/2)*(66C+86A+110B)*sin(c+d*x)+1//3465*d^-1*cos(c+d*x)^(1/2)*(a^4+a^4*cos(c+d*x))*(3076A+3564C+3784B)*sin(c+d*x)+2//11*A*d^-1*(a+a*cos(c+d*x))^4*cos(c+d*x)^(1/2)*sin(c+d*x)+4//1155*a^4*d^-1*cos(c+d*x)^(1/2)*(667A+803B+913C)*sin(c+d*x)+2//99*a*d^-1*(a+a*cos(c+d*x))^3*cos(c+d*x)^(1/2)*(8A+11B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^9//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(8//15*a^4*d^-1*(19A+21C+24B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+8//21*a^4*d^-1*(12A+17B+28C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*C*d^-1*(a+a*cos(c+d*x))^4*cos(c+d*x)^-1//2*sin(c+d*x)+1//21*d^-1*(a^2+a^2*cos(c+d*x))^2*cos(c+d*x)^(1/2)*(-42C+6B+10A)*sin(c+d*x)+1//315*d^-1*cos(c+d*x)^(1/2)*(a^4+a^4*cos(c+d*x))*(-504C+324B+344A)*sin(c+d*x)+4//105*a^4*d^-1*cos(c+d*x)^(1/2)*(7C+73A+83B)*sin(c+d*x)+2//9*a*d^-1*(a+a*cos(c+d*x))^3*cos(c+d*x)^(1/2)*(A+-9C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(8//5*a^4*d^-1*(7B+8A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+8//21*a^4*d^-1*(17A+28B+35C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//7*d^-1*(a^2+a^2*cos(c+d*x))^2*cos(c+d*x)^(1/2)*(-42C+-14B+2A)*sin(c+d*x)+1//105*d^-1*cos(c+d*x)^(1/2)*(a^4+a^4*cos(c+d*x))*(-700C+-168B+108A)*sin(c+d*x)+2//3*C*d^-1*(a+a*cos(c+d*x))^4*cos(c+d*x)^-3//2*sin(c+d*x)+4//105*a^4*d^-1*cos(c+d*x)^(1/2)*(-175C+7B+83A)*sin(c+d*x)+2//3*a*d^-1*(a+a*cos(c+d*x))^3*cos(c+d*x)^-1//2*(3B+8C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(8//3*a^4*d^-1*(4A+4C+5B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+56//5*a^4*d^-1*(A+-1C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//15*d^-1*cos(c+d*x)^(1/2)*(a^4+a^4*cos(c+d*x))*(24A+100B+136C)*sin(c+d*x)+1//5*d^-1*(a^2+a^2*cos(c+d*x))^2*cos(c+d*x)^-1//2*(10A+30B+38C)*sin(c+d*x)+2//5*C*d^-1*(a+a*cos(c+d*x))^4*cos(c+d*x)^-5//2*sin(c+d*x)+4//15*a^4*d^-1*cos(c+d*x)^(1/2)*(A+-41C+-25B)*sin(c+d*x)+2//15*a*d^-1*(a+a*cos(c+d*x))^3*cos(c+d*x)^-3//2*(5B+8C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-8//5*a^4*d^-1*(7B+8C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+8//21*a^4*d^-1*(17C+28B+35A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-4//105*a^4*d^-1*cos(c+d*x)^(1/2)*(175A+253C+287B)*sin(c+d*x)+1//105*d^-1*(a^2+a^2*cos(c+d*x))^2*cos(c+d*x)^-3//2*(70A+146C+154B)*sin(c+d*x)+1//105*d^-1*cos(c+d*x)^-1//2*(a^4+a^4*cos(c+d*x))*(700A+788C+952B)*sin(c+d*x)+2//7*C*d^-1*(a+a*cos(c+d*x))^4*cos(c+d*x)^-7//2*sin(c+d*x)+2//35*a*d^-1*(a+a*cos(c+d*x))^3*cos(c+d*x)^-5//2*(7B+8C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-8//15*a^4*d^-1*(19C+21A+24B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+8//21*a^4*d^-1*(12C+17B+28A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//45*d^-1*cos(c+d*x)^-3//2*(a^4+a^4*cos(c+d*x))*(76C+84A+96B)*sin(c+d*x)+1//315*d^-1*(a^2+a^2*cos(c+d*x))^2*cos(c+d*x)^-5//2*(126A+194C+234B)*sin(c+d*x)+2//9*C*d^-1*(a+a*cos(c+d*x))^4*cos(c+d*x)^-9//2*sin(c+d*x)+4//105*a^4*d^-1*cos(c+d*x)^-1//2*(193C+253B+287A)*sin(c+d*x)+2//63*a*d^-1*(a+a*cos(c+d*x))^3*cos(c+d*x)^-7//2*(8C+9B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-8//15*a^4*d^-1*(16C+19B+24A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+8//231*a^4*d^-1*(113C+132B+187A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//231*d^-1*(a^2+a^2*cos(c+d*x))^2*cos(c+d*x)^-7//2*(66A+86C+110B)*sin(c+d*x)+1//3465*d^-1*cos(c+d*x)^-5//2*(a^4+a^4*cos(c+d*x))*(3076C+3564A+3784B)*sin(c+d*x)+2//11*C*d^-1*(a+a*cos(c+d*x))^4*cos(c+d*x)^-11//2*sin(c+d*x)+4//1155*a^4*d^-1*cos(c+d*x)^-3//2*(667C+803B+913A)*sin(c+d*x)+8//15*a^4*d^-1*cos(c+d*x)^-1//2*(16C+19B+24A)*sin(c+d*x)+2//99*a*d^-1*(a+a*cos(c+d*x))^3*cos(c+d*x)^-9//2*(8C+11B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//5*a^-1*d^-1*(-21A+-15C+21B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*a^-1*d^-1*(-35B+35C+45A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1*d^-1*(a+a*cos(c+d*x))^-1*cos(c+d*x)^7//2*(A+C+-1B)*sin(c+d*x)+-1//5*a^-1*d^-1*cos(c+d*x)^3//2*(-7B+5C+7A)*sin(c+d*x)+1//7*a^-1*d^-1*cos(c+d*x)^5//2*(-7B+7C+9A)*sin(c+d*x)+1//21*a^-1*d^-1*cos(c+d*x)^(1/2)*(-35B+35C+45A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//3*a^-1*d^-1*(-5B+3C+5A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*a^-1*d^-1*(-15B+15C+21A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1*d^-1*(a+a*cos(c+d*x))^-1*cos(c+d*x)^5//2*(A+C+-1B)*sin(c+d*x)+-1//3*a^-1*d^-1*cos(c+d*x)^(1/2)*(-5B+3C+5A)*sin(c+d*x)+1//5*a^-1*d^-1*cos(c+d*x)^3//2*(-5B+5C+7A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1*a^-1*d^-1*(C+-3B+3A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-1*d^-1*(-3B+3C+5A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1*d^-1*(a+a*cos(c+d*x))^-1*cos(c+d*x)^3//2*(A+C+-1B)*sin(c+d*x)+1//3*a^-1*d^-1*cos(c+d*x)^(1/2)*(-3B+3C+5A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^-1*d^-1*(C+-1B+3A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1*a^-1*d^-1*(A+-1B+-1C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1*d^-1*(a+a*cos(c+d*x))^-1*cos(c+d*x)^(1/2)*(A+C+-1B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^-1*d^-1*(A+B+-1C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1*a^-1*d^-1*(A+-1B+3C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+a^-1*d^-1*cos(c+d*x)^-1//2*(A+-1B+3C)*sin(c+d*x)+-1*d^-1*(a+a*cos(c+d*x))^-1*cos(c+d*x)^-1//2*(A+C+-1B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^-1*d^-1*(A+-3B+3C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-1*d^-1*(-3B+3A+5C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1*a^-1*d^-1*cos(c+d*x)^-1//2*(A+-3B+3C)*sin(c+d*x)+-1*d^-1*(a+a*cos(c+d*x))^-1*cos(c+d*x)^-3//2*(A+C+-1B)*sin(c+d*x)+1//3*a^-1*d^-1*cos(c+d*x)^-3//2*(-3B+3A+5C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//3*a^-1*d^-1*(-5B+3A+5C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*a^-1*d^-1*(-21C+-15A+15B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1*d^-1*(a+a*cos(c+d*x))^-1*cos(c+d*x)^-5//2*(A+C+-1B)*sin(c+d*x)+-1//3*a^-1*d^-1*cos(c+d*x)^-3//2*(-5B+3A+5C)*sin(c+d*x)+1//5*a^-1*d^-1*cos(c+d*x)^-5//2*(-5B+5A+7C)*sin(c+d*x)+1//5*a^-1*d^-1*cos(c+d*x)^-1//2*(-15B+15A+21C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//5*a^-2*d^-1*(-77A+-35C+56B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*a^-2*d^-1*(-105B+70C+150A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//3*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^9//2*(A+C+-1B)*sin(c+d*x)+-1//15*a^-2*d^-1*cos(c+d*x)^3//2*(-56B+35C+77A)*sin(c+d*x)+1//7*a^-2*d^-1*cos(c+d*x)^5//2*(-21B+14C+30A)*sin(c+d*x)+1//21*a^-2*d^-1*cos(c+d*x)^(1/2)*(-105B+70C+150A)*sin(c+d*x)+-1//3*a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^7//2*(-8B+5C+11A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//3*a^-2*d^-1*(-10B+5C+15A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*a^-2*d^-1*(-35B+20C+56A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*(-10B+5C+15A)*sin(c+d*x)+-1//3*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^7//2*(A+C+-1B)*sin(c+d*x)+1//15*a^-2*d^-1*cos(c+d*x)^3//2*(-35B+20C+56A)*sin(c+d*x)+-1*a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^5//2*(C+-2B+3A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1*a^-2*d^-1*(C+-4B+7A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-2*d^-1*(-5B+2C+10A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//3*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^5//2*(A+C+-1B)*sin(c+d*x)+1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*(-5B+2C+10A)*sin(c+d*x)+-1//3*a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^3//2*(C+-4B+7A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^-2*d^-1*(-1B+4A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//3*a^-2*d^-1*(-1C+-2B+5A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//3*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^3//2*(A+C+-1B)*sin(c+d*x)+-1//3*a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^(1/2)*(-1C+-2B+5A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1*a^-2*d^-1*(A+-1C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-2*d^-1*(B+2A+2C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//3*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^(1/2)*(A+C+-1B)*sin(c+d*x)+a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^(1/2)*(A+-1C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^-2*d^-1*(B+-4C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-2*d^-1*(A+-5C+2B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1*a^-2*d^-1*cos(c+d*x)^-1//2*(B+-4C)*sin(c+d*x)+-1//3*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^-1//2*(A+C+-1B)*sin(c+d*x)+1//3*a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^-1//2*(A+-5C+2B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^-2*d^-1*(A+-4B+7C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-2*d^-1*(-5B+2A+10C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1*a^-2*d^-1*cos(c+d*x)^-1//2*(A+-4B+7C)*sin(c+d*x)+-1//3*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^-3//2*(A+C+-1B)*sin(c+d*x)+1//3*a^-2*d^-1*cos(c+d*x)^-3//2*(-5B+2A+10C)*sin(c+d*x)+-1//3*a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^-3//2*(A+-4B+7C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^-7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//3*a^-2*d^-1*(-10B+5A+15C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//5*a^-2*d^-1*(-35B+20A+56C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//3*a^-2*d^-1*cos(c+d*x)^-3//2*(-10B+5A+15C)*sin(c+d*x)+-1//3*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^-5//2*(A+C+-1B)*sin(c+d*x)+1//5*a^-2*d^-1*cos(c+d*x)^-1//2*(-35B+20A+56C)*sin(c+d*x)+1//15*a^-2*d^-1*cos(c+d*x)^-5//2*(-35B+20A+56C)*sin(c+d*x)+-1*a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^-5//2*(A+-2B+3C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//6*a^-3*d^-1*(-33B+13C+63A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//10*a^-3*d^-1*(-119B+49C+231A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^9//2*(A+C+-1B)*sin(c+d*x)+-1//6*a^-3*d^-1*cos(c+d*x)^(1/2)*(-33B+13C+63A)*sin(c+d*x)+-1//10*d^-1*(a^3+a^3*cos(c+d*x))^-1*cos(c+d*x)^5//2*(-33B+13C+63A)*sin(c+d*x)+1//30*a^-3*d^-1*cos(c+d*x)^3//2*(-119B+49C+231A)*sin(c+d*x)+-1//15*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^7//2*(-7B+2C+12A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//10*a^-3*d^-1*(-49B+9C+119A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//6*a^-3*d^-1*(-13B+3C+33A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^7//2*(A+C+-1B)*sin(c+d*x)+-1//30*d^-1*(a^3+a^3*cos(c+d*x))^-1*cos(c+d*x)^3//2*(-49B+9C+119A)*sin(c+d*x)+1//6*a^-3*d^-1*cos(c+d*x)^(1/2)*(-13B+3C+33A)*sin(c+d*x)+-1//3*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^5//2*(-1B+2A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//6*a^-3*d^-1*(-1C+-3B+13A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//10*a^-3*d^-1*(-1C+-9B+49A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^5//2*(A+C+-1B)*sin(c+d*x)+-1//6*d^-1*(a^3+a^3*cos(c+d*x))^-1*cos(c+d*x)^(1/2)*(-1C+-3B+13A)*sin(c+d*x)+-1//15*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^3//2*(-3B+-2C+8A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//10*a^-3*d^-1*(B+-1C+9A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//6*a^-3*d^-1*(B+C+3A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^3//2*(A+C+-1B)*sin(c+d*x)+1//10*d^-1*(a^3+a^3*cos(c+d*x))^-1*cos(c+d*x)^(1/2)*(B+-1C+9A)*sin(c+d*x)+-1//15*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^(1/2)*(-1B+-4C+6A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//10*a^-3*d^-1*(A+-1B+-9C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//6*a^-3*d^-1*(A+B+3C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^(1/2)*(A+C+-1B)*sin(c+d*x)+1//10*d^-1*(a^3+a^3*cos(c+d*x))^-1*cos(c+d*x)^(1/2)*(A+-1B+-9C)*sin(c+d*x)+1//15*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^(1/2)*(B+-6C+4A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//6*a^-3*d^-1*(A+-13C+3B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//10*a^-3*d^-1*(A+-49C+9B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^-1//2*(A+C+-1B)*sin(c+d*x)+-1//10*a^-3*d^-1*cos(c+d*x)^-1//2*(A+-49C+9B)*sin(c+d*x)+1//6*d^-1*(a^3+a^3*cos(c+d*x))^-1*cos(c+d*x)^-1//2*(A+-13C+3B)*sin(c+d*x)+1//15*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^-1//2*(-8C+2A+3B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^-7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//6*a^-3*d^-1*(-13B+3A+33C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//10*a^-3*d^-1*(-49B+9A+119C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^-3//2*(A+C+-1B)*sin(c+d*x)+-1//10*a^-3*d^-1*cos(c+d*x)^-1//2*(-49B+9A+119C)*sin(c+d*x)+-1//30*d^-1*(a^3+a^3*cos(c+d*x))^-1*cos(c+d*x)^-3//2*(-49B+9A+119C)*sin(c+d*x)+1//6*a^-3*d^-1*cos(c+d*x)^-3//2*(-13B+3A+33C)*sin(c+d*x)+1//3*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^-3//2*(B+-2C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*cos(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//10*a^-4*d^-1*(-57B+8C+176A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//42*a^-4*d^-1*(-108B+17C+339A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//7*d^-1*(a+a*cos(c+d*x))^-4*cos(c+d*x)^9//2*(A+C+-1B)*sin(c+d*x)+1//42*a^-4*d^-1*cos(c+d*x)^(1/2)*(-108B+17C+339A)*sin(c+d*x)+-1//30*a^-4*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^3//2*(-57B+8C+176A)*sin(c+d*x)+-1//35*a^-1*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^7//2*(-1C+-6B+13A)*sin(c+d*x)+-1//42*a^-4*d^-1*(1+cos(c+d*x))^-2*cos(c+d*x)^5//2*(C+-15B+43A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//42*a^-4*d^-1*(-17B+-4C+108A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//10*a^-4*d^-1*(-1C+-8B+57A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//7*d^-1*(a+a*cos(c+d*x))^-4*cos(c+d*x)^7//2*(A+C+-1B)*sin(c+d*x)+-1//35*a^-1*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^5//2*(-4B+-3C+11A)*sin(c+d*x)+-1//42*a^-4*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^(1/2)*(-17B+-4C+108A)*sin(c+d*x)+-1//210*a^-4*d^-1*(1+cos(c+d*x))^-2*cos(c+d*x)^3//2*(-29B+-13C+141A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//10*a^-4*d^-1*(B+8A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//42*a^-4*d^-1*(3C+4B+17A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//7*d^-1*(a+a*cos(c+d*x))^-4*cos(c+d*x)^5//2*(A+C+-1B)*sin(c+d*x)+-1//35*a^-1*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^3//2*(-5C+-2B+9A)*sin(c+d*x)+-1//210*a^-4*d^-1*(1+cos(c+d*x))^-2*cos(c+d*x)^(1/2)*(B+-15C+83A)*sin(c+d*x)+1//10*a^-4*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^(1/2)*(B+8A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*cos(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//10*a^-4*d^-1*(A+-1C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//42*a^-4*d^-1*(3B+4A+4C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//7*d^-1*(a+a*cos(c+d*x))^-4*cos(c+d*x)^3//2*(A+C+-1B)*sin(c+d*x)+-1//5*a^-1*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^(1/2)*(A+-1C)*sin(c+d*x)+1//10*a^-4*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^(1/2)*(A+-1C)*sin(c+d*x)+1//210*a^-4*d^-1*(1+cos(c+d*x))^-2*cos(c+d*x)^(1/2)*(-1C+15B+41A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*cos(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//10*a^-4*d^-1*(B+8C)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//42*a^-4*d^-1*(3A+4B+17C)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//7*d^-1*(a+a*cos(c+d*x))^-4*cos(c+d*x)^(1/2)*(A+C+-1B)*sin(c+d*x)+-1//10*a^-4*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^(1/2)*(B+8C)*sin(c+d*x)+1//35*a^-1*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^(1/2)*(-9C+2B+5A)*sin(c+d*x)+1//210*a^-4*d^-1*(1+cos(c+d*x))^-2*cos(c+d*x)^(1/2)*(-1B+-83C+15A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*cos(c+d*x)^-7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//10*a^-4*d^-1*(A+-57C+8B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//42*a^-4*d^-1*(-108C+4A+17B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//7*d^-1*(a+a*cos(c+d*x))^-4*cos(c+d*x)^-1//2*(A+C+-1B)*sin(c+d*x)+-1//10*a^-4*d^-1*cos(c+d*x)^-1//2*(A+-57C+8B)*sin(c+d*x)+1//35*a^-1*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^-1//2*(-11C+3A+4B)*sin(c+d*x)+1//42*a^-4*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^-1//2*(-108C+4A+17B)*sin(c+d*x)+1//210*a^-4*d^-1*(1+cos(c+d*x))^-2*cos(c+d*x)^-1//2*(-141C+13A+29B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^9//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//9*A*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^7//2*sin(c+d*x)+2//63*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^5//2*(A+9B)*sin(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(16A+18B+21C)*sin(c+d*x)+8//315*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(16A+18B+21C)*sin(c+d*x)+16//315*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(16A+18B+21C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//7*A*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*sin(c+d*x)+2//35*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(A+7B)*sin(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(24A+28B+35C)*sin(c+d*x)+4//105*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(24A+28B+35C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//15*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(2A+10B)*sin(c+d*x)+2//5*A*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*sin(c+d*x)+2//15*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(5B+7A+15C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//3*A*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x)+2*C*a^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//3*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(A+3B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(C*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-1//2*sin(c+d*x)+a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-1C+2A)*sin(c+d*x)+a^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(C+2B)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*C*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-3//2*sin(c+d*x)+1//4*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(C+4B)*sin(c+d*x)+1//4*a^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3C+4B+8A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//3*C*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-5//2*sin(c+d*x)+1//8*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(5C+6B+8A)*sin(c+d*x)+1//8*a^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5C+6B+8A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//12*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*(C+6B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//4*C*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-7//2*sin(c+d*x)+1//24*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-7//2*(C+8B)*sin(c+d*x)+1//64*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(35C+40B+48A)*sin(c+d*x)+1//64*a^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(35C+40B+48A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//96*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*(35C+40B+48A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^11//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//11*A*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^9//2*sin(c+d*x)+2//99*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^7//2*(3A+11B)*sin(c+d*x)+2//693*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^5//2*(84A+99C+110B)*sin(c+d*x)+2//1155*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(336A+374B+429C)*sin(c+d*x)+8//3465*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(336A+374B+429C)*sin(c+d*x)+16//3465*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(336A+374B+429C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^9//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//9*A*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^7//2*sin(c+d*x)+2//21*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*(A+3B)*sin(c+d*x)+2//315*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(136A+156B+189C)*sin(c+d*x)+2//315*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(52A+63C+72B)*sin(c+d*x)+4//315*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(136A+156B+189C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//35*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^3//2*(6A+14B)*sin(c+d*x)+2//7*A*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^5//2*sin(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(19A+21B+35C)*sin(c+d*x)+8//105*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(19A+21B+35C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//5*A*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^3//2*sin(c+d*x)+2*C*a^3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//15*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(3A+5B)*sin(c+d*x)+2//15*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(12A+15C+20B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//3*A*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^(1/2)*sin(c+d*x)+a^3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2B+3C)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//3*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-1//2*(-3C+2A)*sin(c+d*x)+1//3*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-3C+6B+8A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*C*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^-1//2*sin(c+d*x)+1//4*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-1//2*(3C+4B)*sin(c+d*x)+1//4*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-5C+-4B+8A)*sin(c+d*x)+1//4*a^3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(7C+8A+12B)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//3*C*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^-3//2*sin(c+d*x)+1//4*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-3//2*(C+2B)*sin(c+d*x)+1//8*a^3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(11C+14B+24A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//24*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(19C+24A+30B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//4*C*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^-5//2*sin(c+d*x)+1//24*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-5//2*(3C+8B)*sin(c+d*x)+1//64*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(75C+88B+112A)*sin(c+d*x)+1//64*a^3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(75C+88B+112A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//96*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*(39C+48A+56B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//5*C*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^-7//2*sin(c+d*x)+1//40*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-7//2*(3C+10B)*sin(c+d*x)+1//128*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(133C+150B+176A)*sin(c+d*x)+1//128*a^3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(133C+150B+176A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//192*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*(133C+150B+176A)*sin(c+d*x)+1//240*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-7//2*(67C+80A+90B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^13//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//13*A*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^11//2*sin(c+d*x)+2//143*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^9//2*(5A+13B)*sin(c+d*x)+2//1287*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^7//2*(136A+143C+182B)*sin(c+d*x)+2//9009*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^5//2*(2224A+2522B+2717C)*sin(c+d*x)+2//15015*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(8368A+9230B+10439C)*sin(c+d*x)+8//45045*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(8368A+9230B+10439C)*sin(c+d*x)+16//45045*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(8368A+9230B+10439C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^11//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//11*A*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^9//2*sin(c+d*x)+2//99*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^7//2*(5A+11B)*sin(c+d*x)+2//231*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*(32A+33C+44B)*sin(c+d*x)+2//3465*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(2840A+3212B+3795C)*sin(c+d*x)+2//3465*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(1160A+1364B+1485C)*sin(c+d*x)+4//3465*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(2840A+3212B+3795C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^9//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//63*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^5//2*(10A+18B)*sin(c+d*x)+2//9*A*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^7//2*sin(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^3//2*(13A+15B+21C)*sin(c+d*x)+16//315*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(13A+15B+21C)*sin(c+d*x)+64//315*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(13A+15B+21C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//7*A*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^5//2*sin(c+d*x)+2*C*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//35*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^3//2*(5A+7B)*sin(c+d*x)+2//105*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(35C+40A+56B)*sin(c+d*x)+2//105*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(160A+224B+245C)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//5*A*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^3//2*sin(c+d*x)+a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2B+5C)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//15*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-1//2*(-15C+10B+16A)*sin(c+d*x)+1//15*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(15C+64A+70B)*sin(c+d*x)+2//3*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^(1/2)*(A+B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//3*A*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^(1/2)*sin(c+d*x)+-1//6*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^-1//2*(-3C+4A)*sin(c+d*x)+-1//12*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-1//2*(-21C+-12B+8A)*sin(c+d*x)+1//4*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(8A+19C+20B)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//12*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-27C+12B+56A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//3*C*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^-1//2*sin(c+d*x)+1//8*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(25C+38B+40A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//12*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^-1//2*(5C+6B)*sin(c+d*x)+1//24*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-1//2*(24A+31C+42B)*sin(c+d*x)+1//24*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-54B+-49C+24A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//4*C*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^-3//2*sin(c+d*x)+1//24*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^-3//2*(5C+8B)*sin(c+d*x)+1//32*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-3//2*(16A+17C+24B)*sin(c+d*x)+1//64*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(163C+200B+304A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//192*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(299C+392B+432A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//5*C*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^-5//2*sin(c+d*x)+1//8*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^-5//2*(C+2B)*sin(c+d*x)+1//128*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(283C+326B+400A)*sin(c+d*x)+1//128*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(283C+326B+400A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//240*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-5//2*(79C+80A+110B)*sin(c+d*x)+1//960*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*(787C+950B+1040A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//6*C*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^-7//2*sin(c+d*x)+1//60*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^-7//2*(5C+12B)*sin(c+d*x)+1//480*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-7//2*(115C+120A+156B)*sin(c+d*x)+1//512*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(1015C+1132B+1304A)*sin(c+d*x)+1//512*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(1015C+1132B+1304A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//768*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*(1015C+1132B+1304A)*sin(c+d*x)+1//960*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-7//2*(545C+628B+680A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//35*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(-14B+2A)*sin(c+d*x)+-1//105*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-182B+70C+86A)*sin(c+d*x)+1//105*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(-14B+62A+70C)*sin(c+d*x)+2//7*A*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^5//2*sin(c+d*x)+2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+C+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//15*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(-10B+2A)*sin(c+d*x)+1//15*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-10B+26A+30C)*sin(c+d*x)+2//5*A*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+C+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-6B+2A)*sin(c+d*x)+2//3*A*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)+2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+C+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2*A*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+2*C*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1*2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+C+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(C*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-1C+2B)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+C+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :((1/2)*C*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x)+1//4*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(-1C+4B)*sin(c+d*x)+1//4*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-4B+7C+8A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1*2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+C+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//3*C*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-7//2*sin(c+d*x)+1//8*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(-2B+7C+8A)*sin(c+d*x)+1//12*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*(-1C+6B)*sin(c+d*x)+-1//8*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-14B+8A+9C)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+C+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(A*a+(A*b+B*a)*sec(c+d*x)+B*b*sec(c+d*x)^2), x) == :(2*A*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+2*B*b*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1*2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1B)*(a+-1b)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^3//2*(A+C+-1B)*sin(c+d*x)+-1//30*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(-35B+15C+39A)*sin(c+d*x)+1//10*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(-5B+5C+9A)*sin(c+d*x)+1//30*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-95B+75C+147A)*sin(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-11B+7C+15A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^(1/2)*(A+C+-1B)*sin(c+d*x)+-1//6*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-15B+3C+19A)*sin(c+d*x)+1//6*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(-3B+3C+7A)*sin(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-7B+3C+11A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-1//2*(A+C+-1B)*sin(c+d*x)+(1/2)*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(C+-1B+5A)*sin(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-1C+-3B+7A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-3//2*(A+C+-1B)*sin(c+d*x)+2*C*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(B+-5C+3A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-5//2*(A+C+-1B)*sin(c+d*x)+a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-3C+2B)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(A+-1B+3C)*sin(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-5B+9C)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-7//2*(A+C+-1B)*sin(c+d*x)+(1/2)*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*(A+-1B+2C)*sin(c+d*x)+-1//4*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(-6B+2A+7C)*sin(c+d*x)+1//4*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-12B+8A+19C)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-9B+5A+13C)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^3//2*(A+C+-1B)*sin(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^3//2*(-13B+5C+21A)*sin(c+d*x)+-1//240*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(-475B+195C+787A)*sin(c+d*x)+1//80*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(-85B+45C+157A)*sin(c+d*x)+1//240*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-1495B+735C+2671A)*sin(c+d*x)+-1//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-163B+75C+283A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^(1/2)*(A+C+-1B)*sin(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^(1/2)*(C+-9B+17A)*sin(c+d*x)+-1//48*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-147B+27C+299A)*sin(c+d*x)+1//48*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(-39B+15C+95A)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-75B+19C+163A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-1//2*(A+C+-1B)*sin(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-1//2*(-5B+-3C+13A)*sin(c+d*x)+1//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(C+-9B+49A)*sin(c+d*x)+-1//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-19B+-5C+75A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-3//2*(A+C+-1B)*sin(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-3//2*(-1B+-7C+9A)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3C+5B+19A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-5//2*(A+C+-1B)*sin(c+d*x)+2*C*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-3//2*(-11C+3B+5A)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-43C+3B+5A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-7//2*(A+C+-1B)*sin(c+d*x)+a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-5C+2B)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-5//2*(A+-15C+7B)*sin(c+d*x)+1//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(-11B+3A+35C)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-43B+3A+115C)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate(cos(c+d*x)^9//2*(a+b*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//15*d^-1*(14*A*a+18*B*b+18*C*a)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*(10*A*b+10*B*a+14*C*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//7*d^-1*cos(c+d*x)^5//2*(2*A*b+2*B*a)*sin(c+d*x)+1//21*d^-1*cos(c+d*x)^(1/2)*(10*A*b+10*B*a+14*C*b)*sin(c+d*x)+1//45*d^-1*cos(c+d*x)^3//2*(14*A*a+18*B*b+18*C*a)*sin(c+d*x)+2//9*A*a*d^-1*cos(c+d*x)^7//2*sin(c+d*x))
@test integrate(cos(c+d*x)^7//2*(a+b*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//5*d^-1*(6*A*b+6*B*a+10*C*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*(10*A*a+14*B*b+14*C*a)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*cos(c+d*x)^3//2*(2*A*b+2*B*a)*sin(c+d*x)+1//21*d^-1*cos(c+d*x)^(1/2)*(10*A*a+14*B*b+14*C*a)*sin(c+d*x)+2//7*A*a*d^-1*cos(c+d*x)^5//2*sin(c+d*x))
@test integrate(cos(c+d*x)^5//2*(a+b*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//3*d^-1*(2*A*b+2*B*a+6*C*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*(6*A*a+10*B*b+10*C*a)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*cos(c+d*x)^(1/2)*(2*A*b+2*B*a)*sin(c+d*x)+2//5*A*a*d^-1*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate(cos(c+d*x)^3//2*(a+b*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(d^-1*(-2*C*b+2*A*b+2*B*a)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*(2*a*(A+3C)+6*B*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*C*b*d^-1*cos(c+d*x)^-1//2*sin(c+d*x)+2//3*A*a*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate(cos(c+d*x)^(1/2)*(a+b*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1*d^-1*(-2*a*(A+-1C)+2*B*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*(2*C*b+6*A*b+6*B*a)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+d^-1*cos(c+d*x)^-1//2*(2*B*b+2*C*a)*sin(c+d*x)+2//3*C*b*d^-1*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate(cos(c+d*x)^-1//2*(a+b*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//5*d^-1*(6*C*b+10*A*b+10*B*a)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*(2*B*b+2*a*(C+3A))*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*cos(c+d*x)^-3//2*(2*B*b+2*C*a)*sin(c+d*x)+1//5*d^-1*cos(c+d*x)^-1//2*(6*C*b+10*A*b+10*B*a)*sin(c+d*x)+2//5*C*b*d^-1*cos(c+d*x)^-5//2*sin(c+d*x))
@test integrate(cos(c+d*x)^-3//2*(a+b*sec(c+d*x))*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//5*d^-1*(6*B*b+6*C*a+10*A*a)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*(10*C*b+14*A*b+14*B*a)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*cos(c+d*x)^-5//2*(2*B*b+2*C*a)*sin(c+d*x)+1//5*d^-1*cos(c+d*x)^-1//2*(6*B*b+6*C*a+10*A*a)*sin(c+d*x)+1//21*d^-1*cos(c+d*x)^-3//2*(10*C*b+14*A*b+14*B*a)*sin(c+d*x)+2//7*C*b*d^-1*cos(c+d*x)^-7//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^9//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//15*d^-1*(2*a^2*(7A+9C)+6*b^2*(3A+5C)+36*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*(10*B*a^2+14*B*b^2+20*A*a*b+28*C*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*(10*B*a^2+14*B*b^2+20*A*a*b+28*C*a*b)*sin(c+d*x)+1//45*d^-1*cos(c+d*x)^3//2*(2*a^2*(7A+9C)+8*A*b^2+36*B*a*b)*sin(c+d*x)+2//9*A*d^-1*(b+a*cos(c+d*x))^2*cos(c+d*x)^3//2*sin(c+d*x)+2//63*a*d^-1*cos(c+d*x)^5//2*(4*A*b+9*B*a)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//5*d^-1*(6*B*a^2+10*B*b^2+12*A*a*b+20*C*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*(2*a^2*(5A+7C)+14*b^2*(A+3C)+28*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*(2*a^2*(5A+7C)+8*A*b^2+28*B*a*b)*sin(c+d*x)+2//7*A*d^-1*(b+a*cos(c+d*x))^2*cos(c+d*x)^(1/2)*sin(c+d*x)+2//35*a*d^-1*cos(c+d*x)^3//2*(4*A*b+7*B*a)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//3*d^-1*(2*B*a^2+6*B*b^2+4*a*b*(A+3C))*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*(2*a^2*(3A+5C)+10*b^2*(A+-1C)+20*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*C*d^-1*(b+a*cos(c+d*x))^2*cos(c+d*x)^-1//2*sin(c+d*x)+2//3*a*d^-1*cos(c+d*x)^(1/2)*(B*a+-6*C*b+2*A*b)*sin(c+d*x)+2//5*a^2*d^-1*cos(c+d*x)^3//2*(A+-5C)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(d^-1*(-2*B*b^2+2*B*a^2+4*a*b*(A+-1C))*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*(2*a^2*(A+3C)+2*b^2*(C+3A)+12*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*C*d^-1*(b+a*cos(c+d*x))^2*cos(c+d*x)^-3//2*sin(c+d*x)+2//3*b*d^-1*cos(c+d*x)^-1//2*(3*B*b+4*C*a)*sin(c+d*x)+2//3*a^2*d^-1*cos(c+d*x)^(1/2)*(A+-1C)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//5*d^-1*(-10*a^2*(A+-1C)+2*b^2*(3C+5A)+20*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*(2*B*b^2+6*B*a^2+4*a*b*(C+3A))*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*cos(c+d*x)^-1//2*(6*C*b^2+8*C*a^2+10*A*b^2+20*B*a*b)*sin(c+d*x)+2//5*C*d^-1*(b+a*cos(c+d*x))^2*cos(c+d*x)^-5//2*sin(c+d*x)+2//15*b*d^-1*cos(c+d*x)^-3//2*(4*C*a+5*B*b)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//5*d^-1*(6*B*b^2+10*B*a^2+12*C*a*b+20*A*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*(2*b^2*(5C+7A)+14*a^2*(C+3A)+28*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*cos(c+d*x)^-1//2*(6*B*b^2+10*B*a^2+12*C*a*b+20*A*a*b)*sin(c+d*x)+1//21*d^-1*cos(c+d*x)^-3//2*(8*C*a^2+10*C*b^2+14*A*b^2+28*B*a*b)*sin(c+d*x)+2//7*C*d^-1*(b+a*cos(c+d*x))^2*cos(c+d*x)^-7//2*sin(c+d*x)+2//35*b*d^-1*cos(c+d*x)^-5//2*(4*C*a+7*B*b)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^11//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//15*d^-1*(6*b^3*(3A+5C)+14*B*a^3+6*b*a^2*(7A+9C)+54*B*a*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//231*d^-1*(10*a^3*(9A+11C)+154*B*b^3+66*a*b^2*(5A+7C)+330*B*b*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//231*d^-1*cos(c+d*x)^(1/2)*(10*a^3*(9A+11C)+154*B*b^3+66*a*b^2*(5A+7C)+330*B*b*a^2)*sin(c+d*x)+1//495*d^-1*cos(c+d*x)^3//2*(48*A*b^3+154*B*a^3+66*b*a^2*(7A+9C)+484*B*a*b^2)*sin(c+d*x)+1//99*d^-1*(b+a*cos(c+d*x))^2*cos(c+d*x)^3//2*(12*A*b+22*B*a)*sin(c+d*x)+2//11*A*d^-1*(b+a*cos(c+d*x))^3*cos(c+d*x)^3//2*sin(c+d*x)+2//693*a*d^-1*cos(c+d*x)^5//2*(9*a^2*(9A+11C)+24*A*b^2+143*B*a*b)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^9//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//15*d^-1*(2*a^3*(7A+9C)+30*B*b^3+18*a*b^2*(3A+5C)+54*B*b*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*(10*B*a^3+14*b^3*(A+3C)+6*b*a^2*(5A+7C)+42*B*a*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//63*d^-1*cos(c+d*x)^(1/2)*(16*A*b^3+30*B*a^3+18*b*a^2*(5A+7C)+108*B*a*b^2)*sin(c+d*x)+1//21*d^-1*(b+a*cos(c+d*x))^2*cos(c+d*x)^(1/2)*(4*A*b+6*B*a)*sin(c+d*x)+2//9*A*d^-1*(b+a*cos(c+d*x))^3*cos(c+d*x)^(1/2)*sin(c+d*x)+2//315*a*d^-1*cos(c+d*x)^3//2*(7*a^2*(7A+9C)+24*A*b^2+99*B*a*b)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//5*d^-1*(6*B*a^3+10*b^3*(A+-1C)+6*b*a^2*(3A+5C)+30*B*a*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*(2*a^3*(5A+7C)+42*B*b^3+42*B*b*a^2+42*a*b^2*(A+3C))*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*C*d^-1*(b+a*cos(c+d*x))^3*cos(c+d*x)^-1//2*sin(c+d*x)+2//21*a*d^-1*cos(c+d*x)^(1/2)*(a^2*(5A+7C)+6*b^2*(-7C+3A)+21*B*a*b)*sin(c+d*x)+2//35*a^2*d^-1*cos(c+d*x)^3//2*(-35*C*b+7*B*a+11*A*b)*sin(c+d*x)+2//7*a*d^-1*(b+a*cos(c+d*x))^2*cos(c+d*x)^(1/2)*(A+-7C)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//3*d^-1*(2*B*a^3+2*b^3*(C+3A)+6*b*a^2*(A+3C)+18*B*a*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*(-10*B*b^3+2*a^3*(3A+5C)+30*B*b*a^2+30*a*b^2*(A+-1C))*Elliptic.E((1/2)*c+(1/2)*d*x,2)+d^-1*(b+a*cos(c+d*x))^2*cos(c+d*x)^-1//2*(2*B*b+4*C*a)*sin(c+d*x)+2//3*C*d^-1*(b+a*cos(c+d*x))^3*cos(c+d*x)^-3//2*sin(c+d*x)+2//3*a*d^-1*cos(c+d*x)^(1/2)*(B*a^2+-6*B*b^2+3*a*b*(A+-5C))*sin(c+d*x)+2//15*a^2*d^-1*cos(c+d*x)^3//2*(-35*C*a+-15*B*b+3*A*a)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//3*d^-1*(2*B*b^3+2*a^3*(A+3C)+6*a*b^2*(C+3A)+18*B*b*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*(-2*b^3*(3C+5A)+10*B*a^3+-30*B*a*b^2+30*b*a^2*(A+-1C))*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//15*d^-1*(b+a*cos(c+d*x))^2*cos(c+d*x)^-3//2*(10*B*b+12*C*a)*sin(c+d*x)+2//5*C*d^-1*(b+a*cos(c+d*x))^3*cos(c+d*x)^-5//2*sin(c+d*x)+2//15*b*d^-1*cos(c+d*x)^-1//2*(9*C*b^2+15*A*b^2+24*C*a^2+35*B*a*b)*sin(c+d*x)+2//15*a^2*d^-1*cos(c+d*x)^(1/2)*(-9*C*a+-5*B*b+5*A*a)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//5*d^-1*(-10*a^3*(A+-1C)+6*B*b^3+6*a*b^2*(3C+5A)+30*B*b*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*(2*b^3*(5C+7A)+42*B*a^3+42*B*a*b^2+42*b*a^2*(C+3A))*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//35*d^-1*cos(c+d*x)^-1//2*(42*B*b^3+48*C*a^3+42*a*b^2*(3C+5A)+196*B*b*a^2)*sin(c+d*x)+1//35*d^-1*(b+a*cos(c+d*x))^2*cos(c+d*x)^-5//2*(12*C*a+14*B*b)*sin(c+d*x)+2//7*C*d^-1*(b+a*cos(c+d*x))^3*cos(c+d*x)^-7//2*sin(c+d*x)+2//105*b*d^-1*cos(c+d*x)^-3//2*(24*C*a^2+25*C*b^2+35*A*b^2+63*B*a*b)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//15*d^-1*(2*b^3*(7C+9A)+30*B*a^3+18*b*a^2*(3C+5A)+54*B*a*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*(10*B*b^3+14*a^3*(C+3A)+6*a*b^2*(5C+7A)+42*B*b*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//15*d^-1*cos(c+d*x)^-1//2*(2*b^3*(7C+9A)+30*B*a^3+18*b*a^2*(3C+5A)+54*B*a*b^2)*sin(c+d*x)+1//63*d^-1*cos(c+d*x)^-3//2*(16*C*a^3+30*B*b^3+18*a*b^2*(5C+7A)+108*B*b*a^2)*sin(c+d*x)+1//21*d^-1*(b+a*cos(c+d*x))^2*cos(c+d*x)^-7//2*(4*C*a+6*B*b)*sin(c+d*x)+2//9*C*d^-1*(b+a*cos(c+d*x))^3*cos(c+d*x)^-9//2*sin(c+d*x)+2//315*b*d^-1*cos(c+d*x)^-5//2*(24*C*a^2+49*C*b^2+63*A*b^2+99*B*a*b)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^11//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//15*d^-1*(14*B*a^4+30*B*b^4+8*b*a^3*(7A+9C)+24*a*b^3*(3A+5C)+108*B*a^2*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//231*d^-1*(10*a^4*(9A+11C)+154*b^4*(A+3C)+132*a^2*b^2*(5A+7C)+440*B*b*a^3+616*B*a*b^3)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//693*d^-1*cos(c+d*x)^(1/2)*(30*a^4*(9A+11C)+128*A*b^4+18*a^2*b^2*(101A+143C)+1320*B*b*a^3+1364*B*a*b^3)*sin(c+d*x)+1//99*d^-1*(b+a*cos(c+d*x))^3*cos(c+d*x)^(1/2)*(16*A*b+22*B*a)*sin(c+d*x)+1//231*d^-1*(b+a*cos(c+d*x))^2*cos(c+d*x)^(1/2)*(6*a^2*(9A+11C)+32*A*b^2+110*B*a*b)*sin(c+d*x)+2//11*A*d^-1*(b+a*cos(c+d*x))^4*cos(c+d*x)^(1/2)*sin(c+d*x)+2//3465*a*d^-1*cos(c+d*x)^3//2*(192*A*b^3+539*B*a^3+2*b*a^2*(673A+891C)+1353*B*a*b^2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^9//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//15*d^-1*(2*a^4*(7A+9C)+30*b^4*(A+-1C)+36*a^2*b^2*(3A+5C)+72*B*b*a^3+120*B*a*b^3)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*(10*B*a^4+42*B*b^4+8*b*a^3*(5A+7C)+56*a*b^3*(A+3C)+84*B*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*C*d^-1*(b+a*cos(c+d*x))^4*cos(c+d*x)^-1//2*sin(c+d*x)+2//63*a*d^-1*cos(c+d*x)^(1/2)*(2*b^3*(-63C+31A)+15*B*a^3+12*b*a^2*(5A+7C)+117*B*a*b^2)*sin(c+d*x)+2//315*a^2*d^-1*cos(c+d*x)^3//2*(3*b^2*(-105C+41A)+7*a^2*(7A+9C)+162*B*a*b)*sin(c+d*x)+2//9*a*d^-1*(b+a*cos(c+d*x))^3*cos(c+d*x)^(1/2)*(A+-9C)*sin(c+d*x)+2//21*a*d^-1*(b+a*cos(c+d*x))^2*cos(c+d*x)^(1/2)*(-21*C*b+3*B*a+5*A*b)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//5*d^-1*(-10*B*b^4+6*B*a^4+8*b*a^3*(3A+5C)+40*a*b^3*(A+-1C)+60*B*a^2*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*(2*a^4*(5A+7C)+14*b^4*(C+3A)+56*B*b*a^3+84*a^2*b^2*(A+3C)+168*B*a*b^3)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*(b+a*cos(c+d*x))^3*cos(c+d*x)^-1//2*(6*B*b+16*C*a)*sin(c+d*x)+2//3*C*d^-1*(b+a*cos(c+d*x))^4*cos(c+d*x)^-3//2*sin(c+d*x)+2//21*a*d^-1*cos(c+d*x)^(1/2)*(a^3*(5A+7C)+-42*B*b^3+3*a*b^2*(-49C+13A)+28*B*b*a^2)*sin(c+d*x)+2//105*a^2*d^-1*cos(c+d*x)^3//2*(-105*B*b^2+21*B*a^2+-350*C*a*b+54*A*a*b)*sin(c+d*x)+2//7*a*d^-1*(b+a*cos(c+d*x))^2*cos(c+d*x)^(1/2)*(A*a+-21*C*a+-7*B*b)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//3*d^-1*(2*B*a^4+2*B*b^4+8*a*b^3*(C+3A)+8*b*a^3*(A+3C)+36*B*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*(-2*b^4*(3C+5A)+2*a^4*(3A+5C)+-40*B*a*b^3+40*B*b*a^3+60*a^2*b^2*(A+-1C))*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-2//15*a^2*d^-1*cos(c+d*x)^3//2*(-1*a^2*(-59C+3A)+3*b^2*(3C+5A)+50*B*a*b)*sin(c+d*x)+1//5*d^-1*(b+a*cos(c+d*x))^2*cos(c+d*x)^-1//2*(6*C*b^2+10*A*b^2+32*C*a^2+30*B*a*b)*sin(c+d*x)+1//15*d^-1*(b+a*cos(c+d*x))^3*cos(c+d*x)^-3//2*(10*B*b+16*C*a)*sin(c+d*x)+2//5*C*d^-1*(b+a*cos(c+d*x))^4*cos(c+d*x)^-5//2*sin(c+d*x)+2//15*a*d^-1*cos(c+d*x)^(1/2)*(-6*b^3*(3C+5A)+5*B*a^3+-105*B*a*b^2+4*b*a^2*(-33C+5A))*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//5*d^-1*(-6*B*b^4+10*B*a^4+-60*B*a^2*b^2+-8*a*b^3*(3C+5A)+40*b*a^3*(A+-1C))*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*(2*b^4*(5C+7A)+14*a^4*(A+3C)+56*B*a*b^3+84*a^2*b^2*(C+3A)+168*B*b*a^3)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-2//105*a^2*d^-1*cos(c+d*x)^(1/2)*(-1*a^2*(-87C+35A)+5*b^2*(5C+7A)+98*B*a*b)*sin(c+d*x)+1//35*d^-1*(b+a*cos(c+d*x))^3*cos(c+d*x)^-5//2*(14*B*b+16*C*a)*sin(c+d*x)+1//105*d^-1*(b+a*cos(c+d*x))^2*cos(c+d*x)^-3//2*(50*C*b^2+70*A*b^2+96*C*a^2+154*B*a*b)*sin(c+d*x)+2//7*C*d^-1*(b+a*cos(c+d*x))^4*cos(c+d*x)^-7//2*sin(c+d*x)+2//105*b*d^-1*cos(c+d*x)^-1//2*(63*B*b^3+192*C*a^3+2*a*b^2*(101C+175A)+413*B*b*a^2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//15*d^-1*(-30*a^4*(A+-1C)+2*b^4*(7C+9A)+36*a^2*b^2*(3C+5A)+72*B*a*b^3+120*B*b*a^3)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*(10*B*b^4+42*B*a^4+8*a*b^3*(5C+7A)+56*b*a^3*(C+3A)+84*B*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//315*d^-1*cos(c+d*x)^-1//2*(42*b^4*(7C+9A)+384*C*a^4+14*a^2*b^2*(155C+261A)+1512*B*a*b^3+2196*B*b*a^3)*sin(c+d*x)+1//63*d^-1*(b+a*cos(c+d*x))^3*cos(c+d*x)^-7//2*(16*C*a+18*B*b)*sin(c+d*x)+1//315*d^-1*(b+a*cos(c+d*x))^2*cos(c+d*x)^-5//2*(96*C*a^2+98*C*b^2+126*A*b^2+234*B*a*b)*sin(c+d*x)+2//9*C*d^-1*(b+a*cos(c+d*x))^4*cos(c+d*x)^-9//2*sin(c+d*x)+2//315*b*d^-1*cos(c+d*x)^-3//2*(64*C*a^3+75*B*b^3+2*a*b^2*(101C+147A)+261*B*b*a^2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^9//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//9*A*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^7//2*sin(c+d*x)+-1//315*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*(-14*a^2*(7A+9C)+12*A*b^2+-18*B*a*b)*sin(c+d*x)+1//63*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*(2*A*b+18*B*a)*sin(c+d*x)+1//315*a^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(16*A*b^3+150*B*a^3+-24*B*a*b^2+2*b*a^2*(13A+21C))*sin(c+d*x)+-1//315*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(-42*a^4*(7A+9C)+32*A*b^4+-114*B*b*a^3+-48*B*a*b^3+12*a^2*b^2*(4A+7C))*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//315*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-2*a^2+2*b^2)*(-75*B*a^3+16*A*b^3+-24*B*a*b^2+6*b*a^2*(6A+7C))*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//7*A*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*sin(c+d*x)+-1//105*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(-10*a^2*(5A+7C)+8*A*b^2+-14*B*a*b)*sin(c+d*x)+1//35*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*(2*A*b+14*B*a)*sin(c+d*x)+1//105*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(16*A*b^3+126*B*a^3+-28*B*a*b^2+2*b*a^2*(19A+35C))*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//105*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-2*b^2+2*a^2)*(8*A*b^2+25*A*a^2+35*C*a^2+-14*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//5*A*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*sin(c+d*x)+1//15*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(2*A*b+10*B*a)*sin(c+d*x)+-1//15*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(-6*a^2*(3A+5C)+4*A*b^2+-10*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//15*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-2*a^2+2*b^2)*(-5*B*a+2*A*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^3//2*cos(c+d*x)^9//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//21*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*(2*A*b+6*B*a)*sin(c+d*x)+2//9*A*d^-1*(a+b*sec(c+d*x))^3//2*cos(c+d*x)^7//2*sin(c+d*x)+-1//315*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(-150*B*a^3+8*A*b^3+-18*B*a*b^2+-4*b*a^2*(44A+63C))*sin(c+d*x)+1//315*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*(6*A*b^2+14*a^2*(7A+9C)+144*B*a*b)*sin(c+d*x)+1//315*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(16*A*b^4+42*a^4*(7A+9C)+-36*B*a*b^3+6*a^2*b^2*(11A+21C)+492*B*b*a^3)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//315*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-2*b^2+2*a^2)*(a^2*(39*A*b+63*C*b)+8*A*b^3+75*B*a^3+-18*B*a*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^3//2*cos(c+d*x)^7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//35*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*(6*A*b+14*B*a)*sin(c+d*x)+2//7*A*d^-1*(a+b*sec(c+d*x))^3//2*cos(c+d*x)^5//2*sin(c+d*x)+1//105*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(6*A*b^2+10*a^2*(5A+7C)+84*B*a*b)*sin(c+d*x)+-1//105*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(-126*B*a^3+12*A*b^3+-42*B*a*b^2+-4*b*a^2*(41A+70C))*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//105*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-2*b^2+2*a^2)*(-6*A*b^2+25*A*a^2+35*C*a^2+21*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^5//2*cos(c+d*x)^11//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//99*d^-1*(a+b*sec(c+d*x))^3//2*cos(c+d*x)^7//2*(10*A*b+22*B*a)*sin(c+d*x)+1//231*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*(6*a^2*(9A+11C)+10*A*b^2+88*B*a*b)*sin(c+d*x)+2//11*A*d^-1*(a+b*sec(c+d*x))^5//2*cos(c+d*x)^9//2*sin(c+d*x)+-1//3465*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(-150*a^4*(9A+11C)+40*A*b^4+-3586*B*b*a^3+-110*B*a*b^3+-10*a^2*b^2*(205A+297C))*sin(c+d*x)+1//3465*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*(30*A*b^3+1078*B*a^3+10*b*a^2*(229A+297C)+1650*B*a*b^2)*sin(c+d*x)+1//3465*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(80*A*b^5+3234*B*a^5+-220*B*a*b^4+30*b*a^4*(247A+319C)+30*a^2*b^3*(17A+33C)+6138*B*a^3*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3465*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-2*b^2+2*a^2)*(40*A*b^4+75*a^4*(9A+11C)+-110*B*a*b^3+15*a^2*b^2*(19A+33C)+1254*B*b*a^3)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^5//2*cos(c+d*x)^9//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//63*d^-1*(a+b*sec(c+d*x))^3//2*cos(c+d*x)^5//2*(10*A*b+18*B*a)*sin(c+d*x)+1//315*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*(14*a^2*(7A+9C)+30*A*b^2+180*B*a*b)*sin(c+d*x)+2//9*A*d^-1*(a+b*sec(c+d*x))^5//2*cos(c+d*x)^7//2*sin(c+d*x)+1//315*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(10*A*b^3+150*B*a^3+2*b*a^2*(163A+231C)+270*B*a*b^2)*sin(c+d*x)+-1//315*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(-42*a^4*(7A+9C)+20*A*b^4+-870*B*b*a^3+-90*B*a*b^3+-6*a^2*b^2*(93A+161C))*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//315*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-2*a^2+2*b^2)*(-75*B*a^3+10*A*b^3+-45*B*a*b^2+-6*b*a^2*(19A+28C))*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-1//2*cos(c+d*x)^7//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//35*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*(-14*B*a+12*A*b)*sin(c+d*x)+1//105*a^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(10*a^2*(5A+7C)+48*A*b^2+-56*B*a*b)*sin(c+d*x)+2//7*A*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*sin(c+d*x)+-1//105*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(-126*B*a^3+2*a^2*(44*A*b+70*C*b)+96*A*b^3+-112*B*a*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//105*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(10*a^4*(5A+7C)+96*A*b^4+-112*B*a*b^3+-98*B*b*a^3+4*a^2*b^2*(16A+35C))*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-1//2*cos(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//15*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(-10*B*a+8*A*b)*sin(c+d*x)+2//5*A*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*sin(c+d*x)+1//15*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-16*A*b^3+10*B*a^3+-2*b*a^2*(7A+15C)+20*B*a*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//15*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(6*a^2*(3A+5C)+16*A*b^2+-20*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(2//3*A*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x)+-1//3*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(-6*B*a+4*A*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(2*a^2*(A+3C)+4*A*b^2+-6*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-3//2*cos(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^3//2*(-2*a*(B*b+-1*C*a)+2*A*b^2)*sin(c+d*x)+-1//5*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*cos(c+d*x)^3//2*(-2*a^2*(A+-5C)+12*A*b^2+-10*B*a*b)*sin(c+d*x)+-1//15*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-10*B*a^3+96*A*b^3+-80*B*a*b^2+12*b*a^2*(2A+5C))*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//15*a^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*cos(c+d*x)^(1/2)*(-2*a^2*(-15*C*b+9*A*b)+10*B*a^3+48*A*b^3+-40*B*a*b^2)*sin(c+d*x)+-1//15*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*cos(c+d*x)^(1/2)*(-6*a^4*(3A+5C)+96*A*b^4+-80*B*a*b^3+-12*a^2*b^2*(-5C+4A)+50*B*b*a^3)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-3//2*cos(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^(1/2)*(-2*a*(B*b+-1*C*a)+2*A*b^2)*sin(c+d*x)+-1//3*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*cos(c+d*x)^(1/2)*(-2*a^2*(A+-3C)+8*A*b^2+-6*B*a*b)*sin(c+d*x)+1//3*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(2*a^2*(A+3C)+16*A*b^2+-12*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*cos(c+d*x)^(1/2)*(-2*a^2*(-3*C*b+5*A*b)+6*B*a^3+16*A*b^3+-12*B*a*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-3//2*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(a^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*(-2*a*(B*b+-1*C*a)+2*A*b^2)*sin(c+d*x)+-1*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-2*B*a+4*A*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+-1*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*cos(c+d*x)^(1/2)*(-2*a^2*(A+-1C)+4*A*b^2+-2*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-5//2*cos(c+d*x)^5//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//3*a^-2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*cos(c+d*x)^3//2*(-12*C*a^4+16*A*b^4+-10*B*a*b^3+-4*a^2*b^2*(-1C+6A)+18*B*b*a^3)*sin(c+d*x)+-1//15*a^-4*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*cos(c+d*x)^(1/2)*(-10*B*a^5+128*A*b^5+-80*B*a*b^4+-4*a^2*b^3*(-10C+49A)+4*b*a^4*(-20C+7A)+130*B*a^3*b^2)*sin(c+d*x)+1//3*a^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*cos(c+d*x)^3//2*(-2*a*(B*b+-1*C*a)+2*A*b^2)*sin(c+d*x)+1//15*a^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*cos(c+d*x)^3//2*(2*a^4*(-35C+3A)+96*A*b^4+-60*B*a*b^3+-2*a^2*b^2*(-15C+71A)+100*B*b*a^3)*sin(c+d*x)+1//15*a^-5*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*(10*B*a^5+256*A*b^5+-160*B*a*b^4+-8*a^2*b^3*(-10C+29A)+-2*b*a^4*(17A+45C)+160*B*a^3*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//15*a^-5*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*cos(c+d*x)^(1/2)*(6*a^6*(3A+5C)+256*A*b^6+-160*B*a*b^5+-80*B*b*a^5+-8*a^2*b^4*(-10C+53A)+10*a^4*b^2*(-15C+11A)+280*B*a^3*b^3)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-5//2*cos(c+d*x)^3//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(1//3*a^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*cos(c+d*x)^(1/2)*(-2*a*(B*b+-1*C*a)+2*A*b^2)*sin(c+d*x)+1//3*a^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*cos(c+d*x)^(1/2)*(2*a^4*(A+-5C)+16*A*b^4+-8*B*a*b^3+-2*a^2*b^2*(-1C+13A)+16*B*b*a^3)*sin(c+d*x)+1//3*a^-2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*cos(c+d*x)^(1/2)*(-12*A*b^4+8*C*a^4+-14*B*b*a^3+6*B*a*b^3+20*A*a^2*b^2)*sin(c+d*x)+-1//3*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*(-2*a^4*(A+3C)+32*A*b^4+-16*B*a*b^3+-4*a^2*b^2*(-1C+8A)+18*B*b*a^3)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+-1//3*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*cos(c+d*x)^(1/2)*(-6*B*a^5+2*a^4*(-6*C*b+8*A*b)+32*A*b^5+-16*B*a*b^4+-4*a^2*b^3*(-1C+14A)+30*B*a^3*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-5//2*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//3*a^-2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*cos(c+d*x)^-1//2*(-4*C*a^4+8*A*b^4+-4*a^2*b^2*(C+4A)+-2*B*a*b^3+10*B*b*a^3)*sin(c+d*x)+1//3*a^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*(-2*a*(B*b+-1*C*a)+2*A*b^2)*sin(c+d*x)+1//3*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*(6*B*a^3+16*A*b^3+-4*B*a*b^2+-2*b*a^2*(C+9A))*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*cos(c+d*x)^(1/2)*(6*a^4*(A+-1C)+16*A*b^4+-4*B*a*b^3+-2*a^2*b^2*(C+15A)+12*B*b*a^3)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-5//2*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)+C*sec(c+d*x)^2), x) == :(-1//3*b^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*(-2*a*(B*b+-1*C*a)+2*A*b^2)*sin(c+d*x)+-1//3*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*(-2*a^2*(C+3A)+4*A*b^2+2*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+-1//3*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*cos(c+d*x)^(1/2)*(4*A*b^3+6*B*a^3+-4*b*a^2*(2C+3A)+2*B*a*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3*a^-1*b^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*cos(c+d*x)^-1//2*(2*A*b^4+2*C*a^4+-10*a^2*b^2*(A+C)+4*B*a*b^3+4*B*b*a^3)*sin(c+d*x))

max_stars_repo_path: test/4 Trig functions/4.5 Secant/4.5.4.2 (a+b sec)^m (d sec)^n (A+B sec+C sec^2).jl