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

@test integrate(sin(e+f*x)^7*(a+b*sec(e+f*x)^2), x) == :(b*f^-1*sec(e+f*x)+f^-1*cos(e+f*x)^3*(a+-1b)+-1*f^-1*(a+-3b)*cos(e+f*x)+-1//5*f^-1*cos(e+f*x)^5*(-1b+3a)+1//7*a*f^-1*cos(e+f*x)^7)
@test integrate(sin(e+f*x)^5*(a+b*sec(e+f*x)^2), x) == :(b*f^-1*sec(e+f*x)+-1*f^-1*(a+-2b)*cos(e+f*x)+-1//5*a*f^-1*cos(e+f*x)^5+1//3*f^-1*cos(e+f*x)^3*(-1b+2a))
@test integrate(sin(e+f*x)^3*(a+b*sec(e+f*x)^2), x) == :(b*f^-1*sec(e+f*x)+-1*f^-1*(a+-1b)*cos(e+f*x)+1//3*a*f^-1*cos(e+f*x)^3)
@test integrate((a+b*sec(e+f*x)^2)*sin(e+f*x), x) == :(b*f^-1*sec(e+f*x)+-1*a*f^-1*cos(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)*csc(e+f*x), x) == :(b*f^-1*sec(e+f*x)+-1*f^-1*(a+b)*arctanh(cos(e+f*x)))
@test integrate(csc(e+f*x)^3*(a+b*sec(e+f*x)^2), x) == :(b*f^-1*sec(e+f*x)+-1//2*f^-1*(a+3b)*arctanh(cos(e+f*x))+-1//2*f^-1*(a+b)*cot(e+f*x)*csc(e+f*x))
@test integrate(csc(e+f*x)^5*(a+b*sec(e+f*x)^2), x) == :(b*f^-1*sec(e+f*x)+1//8*f^-1*(-15b+-3a)*arctanh(cos(e+f*x))+-1//4*f^-1*csc(e+f*x)^3*(a+b)*cot(e+f*x)+-1//8*f^-1*(3a+7b)*cot(e+f*x)*csc(e+f*x))
@test integrate(sin(e+f*x)^6*(a+b*sec(e+f*x)^2), x) == :(1//16*x*(-30b+5a)+b*f^-1*tan(e+f*x)+-1//6*a*f^-1*cos(e+f*x)^5*sin(e+f*x)+-1//16*f^-1*(-18b+11a)*cos(e+f*x)*sin(e+f*x)+1//24*f^-1*cos(e+f*x)^3*(-6b+13a)*sin(e+f*x))
@test integrate(sin(e+f*x)^4*(a+b*sec(e+f*x)^2), x) == :(1//8*x*(-12b+3a)+b*f^-1*tan(e+f*x)+-1//8*f^-1*(-4b+5a)*cos(e+f*x)*sin(e+f*x)+1//4*a*f^-1*cos(e+f*x)^3*sin(e+f*x))
@test integrate(sin(e+f*x)^2*(a+b*sec(e+f*x)^2), x) == :((1/2)*x*(a+-2b)+b*f^-1*tan(e+f*x)+-1//2*a*f^-1*cos(e+f*x)*sin(e+f*x))
@test integrate(a+b*sec(e+f*x)^2, x) == :(a*x+b*f^-1*tan(e+f*x))
@test integrate(csc(e+f*x)^2*(a+b*sec(e+f*x)^2), x) == :(b*f^-1*tan(e+f*x)+-1*f^-1*(a+b)*cot(e+f*x))
@test integrate(csc(e+f*x)^4*(a+b*sec(e+f*x)^2), x) == :(b*f^-1*tan(e+f*x)+-1*f^-1*(a+2b)*cot(e+f*x)+-1//3*f^-1*cot(e+f*x)^3*(a+b))
@test integrate(csc(e+f*x)^6*(a+b*sec(e+f*x)^2), x) == :(b*f^-1*tan(e+f*x)+-1*f^-1*(a+3b)*cot(e+f*x)+-1//3*f^-1*cot(e+f*x)^3*(2a+3b)+-1//5*f^-1*cot(e+f*x)^5*(a+b))
@test integrate((a+b*sec(e+f*x)^2)^2*sin(e+f*x)^5, x) == :(-1*f^-1*(a^2+b^2+-4*a*b)*cos(e+f*x)+-1//5*a^2*f^-1*cos(e+f*x)^5+1//3*b^2*f^-1*sec(e+f*x)^3+b*f^-1*(-2b+2a)*sec(e+f*x)+2//3*a*f^-1*cos(e+f*x)^3*(a+-1b))
@test integrate((a+b*sec(e+f*x)^2)^2*sin(e+f*x)^3, x) == :(1//3*a^2*f^-1*cos(e+f*x)^3+1//3*b^2*f^-1*sec(e+f*x)^3+b*f^-1*(-1b+2a)*sec(e+f*x)+-1*a*f^-1*(a+-2b)*cos(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^2*sin(e+f*x), x) == :(-1*a^2*f^-1*cos(e+f*x)+1//3*b^2*f^-1*sec(e+f*x)^3+2*a*b*f^-1*sec(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^2*csc(e+f*x), x) == :(-1*f^-1*(a+b)^2*arctanh(cos(e+f*x))+1//3*b^2*f^-1*sec(e+f*x)^3+b*f^-1*(b+2a)*sec(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^2*csc(e+f*x)^3, x) == :(-1//2*f^-1*(a+b)*(a+5b)*arctanh(cos(e+f*x))+-1//6*f^-1*(3*a^2+5*b^2+6*a*b)*cot(e+f*x)*csc(e+f*x)+1//3*b*f^-1*(5b+6a)*sec(e+f*x)+1//3*b^2*f^-1*csc(e+f*x)^2*sec(e+f*x)^3)
@test integrate((a+b*sec(e+f*x)^2)^2*csc(e+f*x)^5, x) == :(-1//8*f^-1*(3*a^2+35*b^2+30*a*b)*arctanh(cos(e+f*x))+-1//12*f^-1*csc(e+f*x)^3*(3*a^2+7*b^2+6*a*b)*cot(e+f*x)+-1//24*f^-1*(3a+7b)^2*cot(e+f*x)*csc(e+f*x)+1//3*b*f^-1*(6a+7b)*sec(e+f*x)+1//3*b^2*f^-1*csc(e+f*x)^4*sec(e+f*x)^3)
@test integrate((a+b*sec(e+f*x)^2)^2*sin(e+f*x)^6, x) == :(1//16*x*(5*a^2+40*b^2+-60*a*b)+-1//6*f^-1*(a^2+12*b^2+-12*a*b)*tan(e+f*x)+1//3*b^2*f^-1*tan(e+f*x)^3+-1//16*f^-1*(3*a^2+8*b^2+-36*a*b)*cos(e+f*x)*sin(e+f*x)+1//6*a^2*f^-1*sin(e+f*x)^6*tan(e+f*x)+1//24*a*f^-1*cos(e+f*x)^3*(a+-12b)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^2*sin(e+f*x)^4, x) == :(1//8*x*(3*a^2+8*b^2+-24*a*b)+-1//4*f^-1*(a^2+4*b^2+-8*a*b)*tan(e+f*x)+1//3*b^2*f^-1*tan(e+f*x)^3+1//4*a^2*f^-1*sin(e+f*x)^4*tan(e+f*x)+-1//8*a*f^-1*(a+-8b)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^2*sin(e+f*x)^2, x) == :((1/2)*a*x*(a+-4b)+1//3*b^2*f^-1*tan(e+f*x)^3+(1/2)*a^2*f^-1*sin(e+f*x)^2*tan(e+f*x)+-1//2*a*f^-1*(a+-4b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^2, x) == :(x*a^2+1//3*b^2*f^-1*tan(e+f*x)^3+b*f^-1*(b+2a)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^2*csc(e+f*x)^2, x) == :(-1*f^-1*(a+b)^2*cot(e+f*x)+1//3*b^2*f^-1*tan(e+f*x)^3+2*b*f^-1*(a+b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^2*csc(e+f*x)^4, x) == :(-1//3*f^-1*(a+b)^2*cot(e+f*x)^3+1//3*b^2*f^-1*tan(e+f*x)^3+b*f^-1*(2a+3b)*tan(e+f*x)+-1*f^-1*(a+b)*(a+3b)*cot(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^2*csc(e+f*x)^6, x) == :(-1*f^-1*(a^2+6*b^2+6*a*b)*cot(e+f*x)+-1//5*f^-1*(a+b)^2*cot(e+f*x)^5+1//3*b^2*f^-1*tan(e+f*x)^3+2*b*f^-1*(a+2b)*tan(e+f*x)+-1//3*f^-1*cot(e+f*x)^3*(a+2b)*(2a+2b))
@test integrate((a+b*sec(e+f*x)^2)^-1*sin(e+f*x)^5, x) == :(-1//5*a^-1*f^-1*cos(e+f*x)^5+-1*a^-3*f^-1*(a+b)^2*cos(e+f*x)+1//3*a^-2*f^-1*cos(e+f*x)^3*(b+2a)+a^-7//2*b^(1/2)*f^-1*(a+b)^2*arctan(a^(1/2)*b^-1//2*cos(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1*sin(e+f*x)^3, x) == :(1//3*a^-1*f^-1*cos(e+f*x)^3+-1*a^-2*f^-1*(a+b)*cos(e+f*x)+a^-5//2*b^(1/2)*f^-1*(a+b)*arctan(a^(1/2)*b^-1//2*cos(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1*sin(e+f*x), x) == :(-1*a^-1*f^-1*cos(e+f*x)+a^-3//2*b^(1/2)*f^-1*arctan(a^(1/2)*b^-1//2*cos(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1*csc(e+f*x), x) == :(-1*f^-1*(a+b)^-1*arctanh(cos(e+f*x))+a^-1//2*b^(1/2)*f^-1*(a+b)^-1*arctan(a^(1/2)*b^-1//2*cos(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1*csc(e+f*x)^3, x) == :(-1*f^-1*(2a+2b)^-1*cot(e+f*x)*csc(e+f*x)+-1//2*f^-1*(a+b)^-2*(a+-1b)*arctanh(cos(e+f*x))+a^(1/2)*b^(1/2)*f^-1*(a+b)^-2*arctan(a^(1/2)*b^-1//2*cos(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1*csc(e+f*x)^5, x) == :(-1*f^-1*(4a+4b)^-1*csc(e+f*x)^3*cot(e+f*x)+-1//8*f^-1*(a+b)^-3*(-1*b^2+3*a^2+-6*a*b)*arctanh(cos(e+f*x))+a^3//2*b^(1/2)*f^-1*(a+b)^-3*arctan(a^(1/2)*b^-1//2*cos(e+f*x))+-1//8*f^-1*(a+b)^-2*(-1b+3a)*cot(e+f*x)*csc(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-1*sin(e+f*x)^6, x) == :(1//16*x*a^-4*(5*a^3+16*b^3+30*b*a^2+40*a*b^2)+1//6*a^-1*f^-1*cos(e+f*x)^3*sin(e+f*x)^3+-1*a^-4*b^(1/2)*f^-1*(a+b)^5//2*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+-1//16*a^-3*f^-1*(8*b^2+11*a^2+18*a*b)*cos(e+f*x)*sin(e+f*x)+1//8*a^-2*f^-1*cos(e+f*x)^3*(2b+3a)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-1*sin(e+f*x)^4, x) == :(1//8*x*a^-3*(3*a^2+8*b^2+12*a*b)+1//4*a^-1*f^-1*cos(e+f*x)^3*sin(e+f*x)+-1*a^-3*b^(1/2)*f^-1*(a+b)^3//2*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+-1//8*a^-2*f^-1*(4b+5a)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-1*sin(e+f*x)^2, x) == :((1/2)*x*a^-2*(a+2b)+-1//2*a^-1*f^-1*cos(e+f*x)*sin(e+f*x)+-1*a^-2*b^(1/2)*f^-1*(a+b)^(1/2)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1, x) == :(x*a^-1+a^-1*b^(1/2)*f^-1*(a+b)^-1//2*arctan(b^-1//2*(a+b)^(1/2)*cot(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1*csc(e+f*x)^2, x) == :(-1*f^-1*(a+b)^-1*cot(e+f*x)+-1*b^(1/2)*f^-1*(a+b)^-3//2*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1*csc(e+f*x)^4, x) == :(-1*f^-1*(3a+3b)^-1*cot(e+f*x)^3+-1*a*f^-1*(a+b)^-2*cot(e+f*x)+-1*a*b^(1/2)*f^-1*(a+b)^-5//2*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1*csc(e+f*x)^6, x) == :(-1*f^-1*(5a+5b)^-1*cot(e+f*x)^5+-1*a^2*f^-1*(a+b)^-3*cot(e+f*x)+-1//3*f^-1*(a+b)^-2*cot(e+f*x)^3*(b+2a)+-1*a^2*b^(1/2)*f^-1*(a+b)^-7//2*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-2*sin(e+f*x)^5, x) == :(-1//5*a^-2*f^-1*cos(e+f*x)^5+-1//2*a^-4*f^-1*(a+b)*(3a+7b)*cos(e+f*x)+(1/2)*a^-9//2*b^(1/2)*f^-1*(a+b)*(3a+7b)*arctan(a^(1/2)*b^-1//2*cos(e+f*x))+-1//2*a^-2*b^-1*f^-1*(a+b)^2*(b+a*cos(e+f*x)^2)^-1*cos(e+f*x)^5+1//6*a^-3*b^-1*f^-1*cos(e+f*x)^3*(a+b)*(3a+7b))
@test integrate((a+b*sec(e+f*x)^2)^-2*sin(e+f*x)^3, x) == :(1//3*a^-2*f^-1*cos(e+f*x)^3+-1*a^-3*f^-1*(a+2b)*cos(e+f*x)+(1/2)*a^-7//2*b^(1/2)*f^-1*(3a+5b)*arctan(a^(1/2)*b^-1//2*cos(e+f*x))+-1//2*b*a^-3*f^-1*(b+a*cos(e+f*x)^2)^-1*(a+b)*cos(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-2*sin(e+f*x), x) == :(-3//2*a^-2*f^-1*cos(e+f*x)+(1/2)*a^-1*f^-1*(b+a*cos(e+f*x)^2)^-1*cos(e+f*x)^3+3//2*a^-5//2*b^(1/2)*f^-1*arctan(a^(1/2)*b^-1//2*cos(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-2*csc(e+f*x), x) == :(-1*f^-1*(a+b)^-2*arctanh(cos(e+f*x))+(1/2)*a^-3//2*b^(1/2)*f^-1*(a+b)^-2*(b+3a)*arctan(a^(1/2)*b^-1//2*cos(e+f*x))+-1//2*b*a^-1*f^-1*(a+b)^-1*(b+a*cos(e+f*x)^2)^-1*cos(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-2*csc(e+f*x)^3, x) == :(-1//2*f^-1*(a+b)^-3*(a+-3b)*arctanh(cos(e+f*x))+(1/2)*f^-1*(a+b)^-2*(b+a*cos(e+f*x)^2)^-1*(a+-1b)*cos(e+f*x)+-1*f^-1*(b+a*cos(e+f*x)^2)^-1*(2a+2b)^-1*cot(e+f*x)*csc(e+f*x)+(1/2)*a^-1//2*b^(1/2)*f^-1*(a+b)^-3*(-1b+3a)*arctan(a^(1/2)*b^-1//2*cos(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-2*csc(e+f*x)^5, x) == :(-1//8*f^-1*(a+b)^-4*(3*a^2+3*b^2+-18*a*b)*arctanh(cos(e+f*x))+-1*f^-1*(b+a*cos(e+f*x)^2)^-1*(4a+4b)^-1*csc(e+f*x)^3*cot(e+f*x)+-1//8*f^-1*(a+b)^-2*(b+a*cos(e+f*x)^2)^-1*(a+-5b)*cot(e+f*x)*csc(e+f*x)+3//2*a^(1/2)*b^(1/2)*f^-1*(a+b)^-4*(a+-1b)*arctan(a^(1/2)*b^-1//2*cos(e+f*x))+3//8*a*f^-1*(a+b)^-3*(b+a*cos(e+f*x)^2)^-1*(a+-3b)*cos(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-2*sin(e+f*x)^6, x) == :(1//16*x*a^-5*(5*a^3+64*b^3+60*b*a^2+120*a*b^2)+1//6*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-1*cos(e+f*x)^3*sin(e+f*x)^3+-1//2*a^-5*b^(1/2)*f^-1*(a+b)^3//2*(3a+8b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+-1//16*b*a^-4*f^-1*(a+b+b*tan(e+f*x)^2)^-1*(19*a^2+32*b^2+52*a*b)*tan(e+f*x)+-1//48*a^-3*f^-1*(a+b+b*tan(e+f*x)^2)^-1*(33*a^2+48*b^2+82*a*b)*cos(e+f*x)*sin(e+f*x)+1//24*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^-1*cos(e+f*x)^3*(8b+9a)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-2*sin(e+f*x)^4, x) == :(1//8*x*a^-4*(3*a^2+24*b^2+24*a*b)+1//4*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-1*cos(e+f*x)^3*sin(e+f*x)+-3//2*a^-4*b^(1/2)*f^-1*(a+b)^(1/2)*(a+2b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+-3//8*b*a^-3*f^-1*(a+b+b*tan(e+f*x)^2)^-1*(3a+4b)*tan(e+f*x)+-1//8*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^-1*(5a+6b)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-2*sin(e+f*x)^2, x) == :((1/2)*x*a^-3*(a+4b)+-1*b*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^-1*tan(e+f*x)+-1//2*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-1*cos(e+f*x)*sin(e+f*x)+-1//2*a^-3*b^(1/2)*f^-1*(a+b)^-1//2*(3a+4b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-2, x) == :(x*a^-2+-1//2*b*a^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1*tan(e+f*x)+-1//2*a^-2*b^(1/2)*f^-1*(a+b)^-3//2*(2b+3a)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-2*csc(e+f*x)^2, x) == :(-3//2*f^-1*(a+b)^-2*cot(e+f*x)+f^-1*(2a+2b)^-1*(a+b+b*tan(e+f*x)^2)^-1*cot(e+f*x)+-3//2*b^(1/2)*f^-1*(a+b)^-5//2*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-2*csc(e+f*x)^4, x) == :(-1//3*f^-1*(a+b)^-2*cot(e+f*x)^3+-1*f^-1*(a+b)^-3*(a+-1b)*cot(e+f*x)+-1//2*b^(1/2)*f^-1*(a+b)^-7//2*(-2b+3a)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+-1//2*a*b*f^-1*(a+b)^-3*(a+b+b*tan(e+f*x)^2)^-1*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-2*csc(e+f*x)^6, x) == :(-1*f^-1*(5a+5b)^-1*(a+b+b*tan(e+f*x)^2)^-1*cot(e+f*x)^5+-1//5*f^-1*(a+b)^-4*(-1*b^2+5*a^2+-10*a*b)*cot(e+f*x)+-1//15*f^-1*(a+b)^-3*cot(e+f*x)^3*(3b+10a)+-1//2*a*b^(1/2)*f^-1*(a+b)^-9//2*(-4b+3a)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+-1//10*b*f^-1*(a+b)^-4*(a+b+b*tan(e+f*x)^2)^-1*(2*b^2+5*a^2)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3*sin(e+f*x)^5, x) == :(-1//5*a^-3*f^-1*cos(e+f*x)^5+-1//2*a^-5*f^-1*(3*a^2+13*b^2+14*a*b)*cos(e+f*x)+1//8*a^-11//2*b^(1/2)*f^-1*(15*a^2+63*b^2+70*a*b)*arctan(a^(1/2)*b^-1//2*cos(e+f*x))+-1//4*a^-2*b^-1*f^-1*(a+b)^2*(b+a*cos(e+f*x)^2)^-2*cos(e+f*x)^7+1//12*a^-4*b^-1*f^-1*cos(e+f*x)^3*(a+3b)*(3a+5b)+-1//8*b*a^-5*f^-1*(b+a*cos(e+f*x)^2)^-1*(a+b)*(3a+11b)*cos(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3*sin(e+f*x)^3, x) == :(1//3*a^-3*f^-1*cos(e+f*x)^3+-1*a^-4*f^-1*(a+3b)*cos(e+f*x)+5//8*a^-9//2*b^(1/2)*f^-1*(3a+7b)*arctan(a^(1/2)*b^-1//2*cos(e+f*x))+-1//8*b*a^-4*f^-1*(b+a*cos(e+f*x)^2)^-1*(9a+13b)*cos(e+f*x)+1//4*a^-4*b^2*f^-1*(b+a*cos(e+f*x)^2)^-2*(a+b)*cos(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3*sin(e+f*x), x) == :(-15//8*a^-3*f^-1*cos(e+f*x)+1//4*a^-1*f^-1*(b+a*cos(e+f*x)^2)^-2*cos(e+f*x)^5+5//8*a^-2*f^-1*(b+a*cos(e+f*x)^2)^-1*cos(e+f*x)^3+15//8*a^-7//2*b^(1/2)*f^-1*arctan(a^(1/2)*b^-1//2*cos(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-3*csc(e+f*x), x) == :(-1*f^-1*(a+b)^-3*arctanh(cos(e+f*x))+-1//4*b*a^-1*f^-1*(a+b)^-1*(b+a*cos(e+f*x)^2)^-2*cos(e+f*x)^3+1//8*a^-5//2*b^(1/2)*f^-1*(a+b)^-3*(3*b^2+15*a^2+10*a*b)*arctan(a^(1/2)*b^-1//2*cos(e+f*x))+-1//8*b*a^-2*f^-1*(a+b)^-2*(b+a*cos(e+f*x)^2)^-1*(3b+7a)*cos(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3*csc(e+f*x)^3, x) == :(-1//2*f^-1*(a+b)^-4*(a+-5b)*arctanh(cos(e+f*x))+-1*f^-1*(b+a*cos(e+f*x)^2)^-2*(2a+2b)^-1*cot(e+f*x)^2*cos(e+f*x)+1//8*a^-1*f^-1*(a+b)^-3*(b+a*cos(e+f*x)^2)^-1*(-1*b^2+4*a^2+-9*a*b)*cos(e+f*x)+1//8*a^-3//2*b^(1/2)*f^-1*(a+b)^-4*(-1*b^2+15*a^2+-10*a*b)*arctan(a^(1/2)*b^-1//2*cos(e+f*x))+-1//4*b*a^-1*f^-1*(a+b)^-2*(b+a*cos(e+f*x)^2)^-2*(-1b+2a)*cos(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3*csc(e+f*x)^5, x) == :(-1//8*f^-1*(a+b)^-5*(3*a^2+15*b^2+-30*a*b)*arctanh(cos(e+f*x))+-1*f^-1*(b+a*cos(e+f*x)^2)^-2*(4a+4b)^-1*cot(e+f*x)^3*csc(e+f*x)+1//8*f^-1*(a+b)^-4*(b+a*cos(e+f*x)^2)^-1*(3*a^2+3*b^2+-18*a*b)*cos(e+f*x)+1//8*f^-1*(a+b)^-3*(b+a*cos(e+f*x)^2)^-2*(a^2+2*b^2+-9*a*b)*cos(e+f*x)+-1//8*f^-1*(a+b)^-2*(b+a*cos(e+f*x)^2)^-2*(a+-7b)*cot(e+f*x)*csc(e+f*x)+3//8*a^-1//2*b^(1/2)*f^-1*(a+b)^-5*(b^2+5*a^2+-10*a*b)*arctan(a^(1/2)*b^-1//2*cos(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-3*sin(e+f*x)^6, x) == :(1//16*x*a^-6*(5a+10b)*(a^2+16*b^2+16*a*b)+1//6*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-2*cos(e+f*x)^3*sin(e+f*x)^3+-5//16*b*a^-5*f^-1*(a+b+b*tan(e+f*x)^2)^-1*(5*a^2+16*b^2+20*a*b)*tan(e+f*x)+-5//48*b*a^-4*f^-1*(a+b+b*tan(e+f*x)^2)^-2*(9*a^2+24*b^2+32*a*b)*tan(e+f*x)+-1//48*a^-3*f^-1*(a+b+b*tan(e+f*x)^2)^-2*(33*a^2+80*b^2+110*a*b)*cos(e+f*x)*sin(e+f*x)+1//24*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^-2*cos(e+f*x)^3*(9a+10b)*sin(e+f*x)+-5//8*a^-6*b^(1/2)*f^-1*(a+b)^(1/2)*(a+4b)*(3a+4b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-3*sin(e+f*x)^4, x) == :(1//8*x*a^-5*(3*a^2+48*b^2+36*a*b)+1//4*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-2*cos(e+f*x)^3*sin(e+f*x)+-3//2*b*a^-4*f^-1*(a+b+b*tan(e+f*x)^2)^-1*(a+2b)*tan(e+f*x)+-3//8*a^-5*b^(1/2)*f^-1*(a+b)^-1//2*(5*a^2+16*b^2+20*a*b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+-1//8*b*a^-3*f^-1*(a+b+b*tan(e+f*x)^2)^-2*(7a+12b)*tan(e+f*x)+-1//8*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^-2*(5a+8b)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3*sin(e+f*x)^2, x) == :((1/2)*x*a^-4*(a+6b)+-3//4*b*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^-2*tan(e+f*x)+-1//2*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-2*cos(e+f*x)*sin(e+f*x)+-1//8*a^-4*b^(1/2)*f^-1*(a+b)^-3//2*(15*a^2+24*b^2+40*a*b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+-1//8*b*a^-3*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1*(11a+12b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3, x) == :(x*a^-3+-1//4*b*a^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-2*tan(e+f*x)+-1//8*a^-3*b^(1/2)*f^-1*(a+b)^-5//2*(8*b^2+15*a^2+20*a*b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+-1//8*b*a^-2*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1*(4b+7a)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3*csc(e+f*x)^2, x) == :(-15//8*f^-1*(a+b)^-3*cot(e+f*x)+f^-1*(4a+4b)^-1*(a+b+b*tan(e+f*x)^2)^-2*cot(e+f*x)+-15//8*b^(1/2)*f^-1*(a+b)^-7//2*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+5//8*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1*cot(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3*csc(e+f*x)^4, x) == :(-1//3*f^-1*(a+b)^-3*cot(e+f*x)^3+-1*f^-1*(a+b)^-4*(a+-2b)*cot(e+f*x)+1//8*b^(1/2)*f^-1*(a+b)^-9//2*(-15a+20b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+-1//4*a*b*f^-1*(a+b)^-3*(a+b+b*tan(e+f*x)^2)^-2*tan(e+f*x)+-1//8*b*f^-1*(a+b)^-4*(a+b+b*tan(e+f*x)^2)^-1*(-4b+7a)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3*csc(e+f*x)^6, x) == :(-1*f^-1*(5a+5b)^-1*(a+b+b*tan(e+f*x)^2)^-2*cot(e+f*x)^5+-1//5*f^-1*(a+b)^-5*(2*b^2+5*a^2+-20*a*b)*cot(e+f*x)+-1//15*f^-1*(a+b)^-4*cot(e+f*x)^3*(b+10a)+-1//8*b^(1/2)*f^-1*(a+b)^-11//2*(8*b^2+15*a^2+-40*a*b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+-1//20*b*f^-1*(a+b)^-4*(a+b+b*tan(e+f*x)^2)^-2*(4*b^2+5*a^2)*tan(e+f*x)+-1//40*b*f^-1*(a+b)^-5*(a+b+b*tan(e+f*x)^2)^-1*(24*b^2+35*a^2+-40*a*b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*sin(e+f*x)^5, x) == :(b^(1/2)*f^-1*arctanh(b^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*cos(e+f*x)+-1//5*a^-1*f^-1*(a+b*sec(e+f*x)^2)^3//2*cos(e+f*x)^5+1//15*a^-2*f^-1*(a+b*sec(e+f*x)^2)^3//2*cos(e+f*x)^3*(2b+10a))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*sin(e+f*x)^3, x) == :(b^(1/2)*f^-1*arctanh(b^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*cos(e+f*x)+1//3*a^-1*f^-1*(a+b*sec(e+f*x)^2)^3//2*cos(e+f*x)^3)
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*sin(e+f*x), x) == :(b^(1/2)*f^-1*arctanh(b^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*cos(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*csc(e+f*x), x) == :(b^(1/2)*f^-1*arctanh(b^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1*f^-1*(a+b)^(1/2)*arctanh((a+b)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*csc(e+f*x)^3, x) == :(b^(1/2)*f^-1*arctanh(b^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1//2*f^-1*(a+b)^-1//2*(a+2b)*arctanh((a+b)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1//2*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*cot(e+f*x)*csc(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*csc(e+f*x)^5, x) == :(b^(1/2)*f^-1*arctanh(b^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1//4*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*csc(e+f*x)^3*cot(e+f*x)+-1//8*f^-1*(a+b)^-3//2*(3*a^2+8*b^2+12*a*b)*arctanh((a+b)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(8a+8b)^-1*(3a+4b)*cot(e+f*x)*csc(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*sin(e+f*x)^6, x) == :(b^(1/2)*f^-1*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//6*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*sin(e+f*x)^5*cos(e+f*x)+1//16*a^-5//2*f^-1*(-1*b^3+5*a^3+-15*b*a^2+-5*a*b^2)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//24*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*sin(e+f*x)^3*(-1b+5a)*cos(e+f*x)+-1//16*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(a+-1b)*(b+5a)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*sin(e+f*x)^4, x) == :(b^(1/2)*f^-1*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//4*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*sin(e+f*x)^3*cos(e+f*x)+1//8*a^-3//2*f^-1*(-1*b^2+3*a^2+-6*a*b)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//8*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(-1b+3a)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*sin(e+f*x)^2, x) == :(b^(1/2)*f^-1*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+(1/2)*a^-1//2*f^-1*(a+-1b)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//2*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^(1/2), x) == :(a^(1/2)*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+b^(1/2)*f^-1*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*csc(e+f*x)^2, x) == :(b^(1/2)*f^-1*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*csc(e+f*x)^4, x) == :(b^(1/2)*f^-1*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)+-1*f^-1*(3a+3b)^-1*(a+b+b*tan(e+f*x)^2)^3//2*cot(e+f*x)^3)
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*csc(e+f*x)^6, x) == :(b^(1/2)*f^-1*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)+-1*f^-1*(5a+5b)^-1*(a+b+b*tan(e+f*x)^2)^3//2*cot(e+f*x)^5+-1//15*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^3//2*cot(e+f*x)^3*(8b+10a))
@test integrate((a+b*sec(e+f*x)^2)^3//2*sin(e+f*x)^5, x) == :((1/2)*b^(1/2)*f^-1*(-4b+3a)*arctanh(b^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1//5*a^-1*f^-1*(a+b*sec(e+f*x)^2)^5//2*cos(e+f*x)^5+2//3*a^-1*f^-1*(a+b*sec(e+f*x)^2)^5//2*cos(e+f*x)^3+-1//3*a^-1*f^-1*(a+b*sec(e+f*x)^2)^3//2*(-4b+3a)*cos(e+f*x)+(1/2)*b*a^-1*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(-4b+3a)*sec(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^3//2*sin(e+f*x)^3, x) == :((1/2)*b^(1/2)*f^-1*(-2b+3a)*arctanh(b^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+1//3*a^-1*f^-1*(a+b*sec(e+f*x)^2)^5//2*cos(e+f*x)^3+-1//3*a^-1*f^-1*(a+b*sec(e+f*x)^2)^3//2*(-2b+3a)*cos(e+f*x)+(1/2)*b*a^-1*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(-2b+3a)*sec(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^3//2*sin(e+f*x), x) == :(-1*f^-1*(a+b*sec(e+f*x)^2)^3//2*cos(e+f*x)+3//2*a*b^(1/2)*f^-1*arctanh(b^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+3//2*b*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*sec(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^3//2*csc(e+f*x), x) == :(-1*f^-1*(a+b)^3//2*arctanh((a+b)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+(1/2)*b*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*sec(e+f*x)+(1/2)*b^(1/2)*f^-1*(2b+3a)*arctanh(b^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^3//2*csc(e+f*x)^3, x) == :(b*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*sec(e+f*x)+(1/2)*b^(1/2)*f^-1*(3a+4b)*arctanh(b^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1//2*f^-1*(a+b)^(1/2)*(a+4b)*arctanh((a+b)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1//2*f^-1*(a+b*sec(e+f*x)^2)^3//2*cot(e+f*x)*csc(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^3//2*csc(e+f*x)^5, x) == :(-1//4*f^-1*(a+b*sec(e+f*x)^2)^3//2*csc(e+f*x)^3*cot(e+f*x)+-1//8*f^-1*(a+b)^-1//2*(3*a^2+24*b^2+24*a*b)*arctanh((a+b)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+1//8*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(3a+12b)*sec(e+f*x)+3//2*b^(1/2)*f^-1*(a+2b)*arctanh(b^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1//8*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*csc(e+f*x)^2*(3a+6b)*sec(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^3//2*sin(e+f*x)^6, x) == :((1/2)*b^(1/2)*f^-1*(-5b+3a)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//6*f^-1*(a+b+b*tan(e+f*x)^2)^3//2*sin(e+f*x)^5*cos(e+f*x)+1//16*a^-3//2*f^-1*(b^3+5*a^3+-45*b*a^2+15*a*b^2)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//16*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(b^2+5*a^2+-26*a*b)*tan(e+f*x)+1//24*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*sin(e+f*x)^4*(-3b+5a)*tan(e+f*x)+1//48*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*sin(e+f*x)^2*(3*b^2+5*a^2+-40*a*b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^3//2*sin(e+f*x)^4, x) == :((1/2)*b^(1/2)*f^-1*(-3b+3a)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//4*f^-1*(a+b+b*tan(e+f*x)^2)^3//2*sin(e+f*x)^3*cos(e+f*x)+-1//8*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(-9b+3a)*tan(e+f*x)+1//8*a^-1//2*f^-1*(3*a^2+3*b^2+-18*a*b)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//8*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*sin(e+f*x)^2*(-3b+3a)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^3//2*sin(e+f*x)^2, x) == :(b*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)+(1/2)*a^(1/2)*f^-1*(a+-3b)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+(1/2)*b^(1/2)*f^-1*(-1b+3a)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//2*f^-1*(a+b+b*tan(e+f*x)^2)^3//2*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^3//2, x) == :(a^3//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+(1/2)*b*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)+(1/2)*b^(1/2)*f^-1*(b+3a)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^3//2*csc(e+f*x)^2, x) == :(-1*f^-1*(a+b+b*tan(e+f*x)^2)^3//2*cot(e+f*x)+3//2*b*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)+3//2*b^(1/2)*f^-1*(a+b)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^3//2*csc(e+f*x)^4, x) == :((1/2)*b^(1/2)*f^-1*(3a+5b)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*f^-1*(3a+3b)^-1*(a+b+b*tan(e+f*x)^2)^5//2*cot(e+f*x)^3+-1*f^-1*(3a+3b)^-1*(a+b+b*tan(e+f*x)^2)^3//2*(3a+5b)*cot(e+f*x)+b*f^-1*(2a+2b)^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(3a+5b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^3//2*csc(e+f*x)^6, x) == :((1/2)*b^(1/2)*f^-1*(3a+7b)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*f^-1*(5a+5b)^-1*(a+b+b*tan(e+f*x)^2)^5//2*cot(e+f*x)^5+-2*f^-1*(3a+3b)^-1*(a+b+b*tan(e+f*x)^2)^5//2*cot(e+f*x)^3+-1*f^-1*(3a+3b)^-1*(a+b+b*tan(e+f*x)^2)^3//2*(3a+7b)*cot(e+f*x)+b*f^-1*(2a+2b)^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(3a+7b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*sin(e+f*x)^5, x) == :(-1//5*a^-1*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*cos(e+f*x)^5+-1//15*a^-3*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(8*b^2+15*a^2+20*a*b)*cos(e+f*x)+1//15*a^-2*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*cos(e+f*x)^3*(4b+10a))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*sin(e+f*x)^3, x) == :(1//3*a^-1*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*cos(e+f*x)^3+-1//3*a^-2*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(2b+3a)*cos(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*sin(e+f*x), x) == :(-1*a^-1*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*cos(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*csc(e+f*x), x) == :(-1*f^-1*(a+b)^-1//2*arctanh((a+b)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*csc(e+f*x)^3, x) == :(-1//2*a*f^-1*(a+b)^-3//2*arctanh((a+b)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(2a+2b)^-1*cot(e+f*x)*csc(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*csc(e+f*x)^5, x) == :(-3//8*a^2*f^-1*(a+b)^-5//2*arctanh((a+b)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(4a+4b)^-1*cot(e+f*x)^3*csc(e+f*x)+-1//8*f^-1*(a+b)^-2*(a+b*sec(e+f*x)^2)^(1/2)*(2b+5a)*cot(e+f*x)*csc(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*sin(e+f*x)^6, x) == :(5//16*a^-7//2*f^-1*(a+b)^3*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//6*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cos(e+f*x)^3*sin(e+f*x)^3+-1//48*a^-3*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(15*b^2+33*a^2+40*a*b)*cos(e+f*x)*sin(e+f*x)+1//24*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cos(e+f*x)^3*(5b+9a)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*sin(e+f*x)^4, x) == :(3//8*a^-5//2*f^-1*(a+b)^2*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//4*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cos(e+f*x)^3*sin(e+f*x)+-1//8*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(3b+5a)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*sin(e+f*x)^2, x) == :((1/2)*a^-3//2*f^-1*(a+b)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//2*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-1//2, x) == :(a^-1//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*csc(e+f*x)^2, x) == :(-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*csc(e+f*x)^4, x) == :(-1*f^-1*(3a+3b)^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^3+-1//3*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^(1/2)*(b+3a)*cot(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*csc(e+f*x)^6, x) == :(-1*f^-1*(5a+5b)^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^5+-1//15*f^-1*(a+b)^-3*(a+b+b*tan(e+f*x)^2)^(1/2)*(3*b^2+15*a^2+10*a*b)*cot(e+f*x)+-1//15*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^3*(6b+10a))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*sin(e+f*x)^5, x) == :(-1//5*a^-1*f^-1*(a+b*sec(e+f*x)^2)^-1//2*cos(e+f*x)^5+-1//15*a^-3*f^-1*(a+b*sec(e+f*x)^2)^-1//2*(15*a^2+24*b^2+40*a*b)*cos(e+f*x)+1//15*a^-2*f^-1*(a+b*sec(e+f*x)^2)^-1//2*cos(e+f*x)^3*(6b+10a)+-2//15*b*a^-4*f^-1*(a+b*sec(e+f*x)^2)^-1//2*(15*a^2+24*b^2+40*a*b)*sec(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*sin(e+f*x)^3, x) == :(1//3*a^-1*f^-1*(a+b*sec(e+f*x)^2)^-1//2*cos(e+f*x)^3+-1//3*a^-2*f^-1*(a+b*sec(e+f*x)^2)^-1//2*(3a+4b)*cos(e+f*x)+-2//3*b*a^-3*f^-1*(a+b*sec(e+f*x)^2)^-1//2*(3a+4b)*sec(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*sin(e+f*x), x) == :(-1*a^-1*f^-1*(a+b*sec(e+f*x)^2)^-1//2*cos(e+f*x)+-2*b*a^-2*f^-1*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*csc(e+f*x), x) == :(-1*f^-1*(a+b)^-3//2*arctanh((a+b)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1*b*a^-1*f^-1*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*csc(e+f*x)^3, x) == :(-1//2*f^-1*(a+b)^-5//2*(a+-2b)*arctanh((a+b)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1*f^-1*(a+b*sec(e+f*x)^2)^-1//2*(2a+2b)^-1*cot(e+f*x)*csc(e+f*x)+-3//2*b*f^-1*(a+b)^-2*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*csc(e+f*x)^5, x) == :(-1*f^-1*(a+b*sec(e+f*x)^2)^-1//2*(4a+4b)^-1*cot(e+f*x)^3*csc(e+f*x)+-3//8*a*f^-1*(a+b)^-7//2*(a+-4b)*arctanh((a+b)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-5//8*a*f^-1*(a+b)^-2*(a+b*sec(e+f*x)^2)^-1//2*cot(e+f*x)*csc(e+f*x)+-1//8*b*f^-1*(a+b)^-3*(a+b*sec(e+f*x)^2)^-1//2*(-2b+13a)*sec(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*sin(e+f*x)^6, x) == :(1//6*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-1//2*cos(e+f*x)^3*sin(e+f*x)^3+5//16*a^-9//2*f^-1*(a+b)^2*(a+7b)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//48*b*a^-4*f^-1*(a+b+b*tan(e+f*x)^2)^-1//2*(81*a^2+105*b^2+190*a*b)*tan(e+f*x)+1//24*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^-1//2*cos(e+f*x)^3*(7b+9a)*sin(e+f*x)+-1//48*a^-3*f^-1*(a+b+b*tan(e+f*x)^2)^-1//2*(a+b)*(33a+35b)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*sin(e+f*x)^4, x) == :(1//4*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-1//2*cos(e+f*x)^3*sin(e+f*x)+1//8*a^-7//2*f^-1*(a+5b)*(3a+3b)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//8*b*a^-3*f^-1*(a+b+b*tan(e+f*x)^2)^-1//2*(13a+15b)*tan(e+f*x)+-1//8*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^-1//2*(5a+5b)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*sin(e+f*x)^2, x) == :((1/2)*a^-5//2*f^-1*(a+3b)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-3//2*b*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)+-1//2*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-1//2*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3//2, x) == :(a^-3//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*b*a^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*csc(e+f*x)^2, x) == :(-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)+-2*b*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*csc(e+f*x)^4, x) == :(-1*f^-1*(3a+3b)^-1*(a+b+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)^3+-1//3*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1//2*(-1b+3a)*cot(e+f*x)+-1//3*b*f^-1*(a+b)^-3*(a+b+b*tan(e+f*x)^2)^-1//2*(-2b+6a)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*csc(e+f*x)^6, x) == :(-1*f^-1*(5a+5b)^-1*(a+b+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)^5+-1//15*f^-1*(a+b)^-3*(a+b+b*tan(e+f*x)^2)^-1//2*(-1*b^2+15*a^2+-10*a*b)*cot(e+f*x)+-1//15*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)^3*(4b+10a)+-2//15*b*f^-1*(a+b)^-4*(a+b+b*tan(e+f*x)^2)^-1//2*(-1*b^2+15*a^2+-10*a*b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*sin(e+f*x)^5, x) == :(-1//5*a^-1*f^-1*(a+b*sec(e+f*x)^2)^-3//2*cos(e+f*x)^5+-1//5*a^-3*f^-1*(a+b*sec(e+f*x)^2)^-3//2*(5*a^2+16*b^2+20*a*b)*cos(e+f*x)+1//15*a^-2*f^-1*(a+b*sec(e+f*x)^2)^-3//2*cos(e+f*x)^3*(8b+10a)+-8//15*b*a^-5*f^-1*(a+b*sec(e+f*x)^2)^-1//2*(5*a^2+16*b^2+20*a*b)*sec(e+f*x)+-4//15*b*a^-4*f^-1*(a+b*sec(e+f*x)^2)^-3//2*(5*a^2+16*b^2+20*a*b)*sec(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*sin(e+f*x)^3, x) == :(1//3*a^-1*f^-1*(a+b*sec(e+f*x)^2)^-3//2*cos(e+f*x)^3+-1*a^-2*f^-1*(a+b*sec(e+f*x)^2)^-3//2*(a+2b)*cos(e+f*x)+-8//3*b*a^-4*f^-1*(a+b*sec(e+f*x)^2)^-1//2*(a+2b)*sec(e+f*x)+-4//3*b*a^-3*f^-1*(a+b*sec(e+f*x)^2)^-3//2*(a+2b)*sec(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*sin(e+f*x), x) == :(-1*a^-1*f^-1*(a+b*sec(e+f*x)^2)^-3//2*cos(e+f*x)+-8//3*b*a^-3*f^-1*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x)+-4//3*b*a^-2*f^-1*(a+b*sec(e+f*x)^2)^-3//2*sec(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*csc(e+f*x), x) == :(-1*f^-1*(a+b)^-5//2*arctanh((a+b)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1//3*b*a^-1*f^-1*(a+b)^-1*(a+b*sec(e+f*x)^2)^-3//2*sec(e+f*x)+-1//3*b*a^-2*f^-1*(a+b)^-2*(a+b*sec(e+f*x)^2)^-1//2*(2b+5a)*sec(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*csc(e+f*x)^3, x) == :(-1//2*f^-1*(a+b)^-7//2*(a+-4b)*arctanh((a+b)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1*f^-1*(a+b*sec(e+f*x)^2)^-3//2*(2a+2b)^-1*cot(e+f*x)*csc(e+f*x)+-5//6*b*f^-1*(a+b)^-2*(a+b*sec(e+f*x)^2)^-3//2*sec(e+f*x)+-1//6*b*a^-1*f^-1*(a+b)^-3*(a+b*sec(e+f*x)^2)^-1//2*(-2b+13a)*sec(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*csc(e+f*x)^5, x) == :(-1//8*f^-1*(a+b)^-9//2*(3*a^2+8*b^2+-24*a*b)*arctanh((a+b)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x))+-1*f^-1*(a+b*sec(e+f*x)^2)^-3//2*(4a+4b)^-1*cot(e+f*x)^3*csc(e+f*x)+-1//8*f^-1*(a+b)^-2*(a+b*sec(e+f*x)^2)^-3//2*(-2b+5a)*cot(e+f*x)*csc(e+f*x)+-1//24*b*f^-1*(a+b)^-4*(a+b*sec(e+f*x)^2)^-1//2*(-50b+55a)*sec(e+f*x)+-1//24*b*f^-1*(a+b)^-3*(a+b*sec(e+f*x)^2)^-3//2*(-12b+23a)*sec(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*sin(e+f*x)^6, x) == :(1//6*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-3//2*cos(e+f*x)^3*sin(e+f*x)^3+1//16*a^-11//2*f^-1*(5a+5b)*(a^2+21*b^2+14*a*b)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//48*b*a^-5*f^-1*(a+b+b*tan(e+f*x)^2)^-1//2*(113*a^2+315*b^2+420*a*b)*tan(e+f*x)+1//8*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^-3//2*cos(e+f*x)^3*(3a+3b)*sin(e+f*x)+-7//48*b*a^-4*f^-1*(a+b+b*tan(e+f*x)^2)^-3//2*(a+b)*(7a+15b)*tan(e+f*x)+-1//16*a^-3*f^-1*(a+b+b*tan(e+f*x)^2)^-3//2*(a+b)*(11a+21b)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*sin(e+f*x)^4, x) == :(1//8*a^-9//2*f^-1*(3*a^2+35*b^2+30*a*b)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//4*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-3//2*cos(e+f*x)^3*sin(e+f*x)+-5//24*b*a^-4*f^-1*(a+b+b*tan(e+f*x)^2)^-1//2*(11a+21b)*tan(e+f*x)+-1//8*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^-3//2*(5a+7b)*cos(e+f*x)*sin(e+f*x)+-1//24*b*a^-3*f^-1*(a+b+b*tan(e+f*x)^2)^-3//2*(23a+35b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*sin(e+f*x)^2, x) == :((1/2)*a^-7//2*f^-1*(a+5b)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-5//6*b*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^-3//2*tan(e+f*x)+-1//2*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-3//2*cos(e+f*x)*sin(e+f*x)+-1//6*b*a^-3*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1//2*(13a+15b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-5//2, x) == :(a^-5//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//3*b*a^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-3//2*tan(e+f*x)+-1//3*b*a^-2*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1//2*(3b+5a)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*csc(e+f*x)^2, x) == :(-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-3//2*cot(e+f*x)+-8//3*b*f^-1*(a+b)^-3*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)+-4//3*b*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-3//2*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*csc(e+f*x)^4, x) == :(-1*f^-1*(3a+3b)^-1*(a+b+b*tan(e+f*x)^2)^-3//2*cot(e+f*x)^3+-1*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-3//2*(a+-1b)*cot(e+f*x)+-1//3*b*f^-1*(a+b)^-4*(a+b+b*tan(e+f*x)^2)^-1//2*(-8b+8a)*tan(e+f*x)+-1//3*b*f^-1*(a+b)^-3*(a+b+b*tan(e+f*x)^2)^-3//2*(-4b+4a)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*csc(e+f*x)^6, x) == :(-1*f^-1*(5a+5b)^-1*(a+b+b*tan(e+f*x)^2)^-3//2*cot(e+f*x)^5+-1//5*f^-1*(a+b)^-3*(a+b+b*tan(e+f*x)^2)^-3//2*(b^2+5*a^2+-10*a*b)*cot(e+f*x)+-1//15*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-3//2*cot(e+f*x)^3*(2b+10a)+-8//15*b*f^-1*(a+b)^-5*(a+b+b*tan(e+f*x)^2)^-1//2*(b^2+5*a^2+-10*a*b)*tan(e+f*x)+-4//15*b*f^-1*(a+b)^-4*(a+b+b*tan(e+f*x)^2)^-3//2*(b^2+5*a^2+-10*a*b)*tan(e+f*x))
@test integrate((a+-1*a*sec(c+d*x)^2)^4, x) == :(x*a^4+-1*a^4*d^-1*tan(c+d*x)+-1//5*a^4*d^-1*tan(c+d*x)^5+1//3*a^4*d^-1*tan(c+d*x)^3+1//7*a^4*d^-1*tan(c+d*x)^7)
@test integrate((a+-1*a*sec(c+d*x)^2)^3, x) == :(x*a^3+-1*a^3*d^-1*tan(c+d*x)+-1//5*a^3*d^-1*tan(c+d*x)^5+1//3*a^3*d^-1*tan(c+d*x)^3)
@test integrate((a+-1*a*sec(c+d*x)^2)^2, x) == :(x*a^2+-1*a^2*d^-1*tan(c+d*x)+1//3*a^2*d^-1*tan(c+d*x)^3)
@test integrate(a+-1*a*sec(c+d*x)^2, x) == :(a*x+-1*a*d^-1*tan(c+d*x))
@test integrate((a+-1*a*sec(c+d*x)^2)^-1, x) == :(x*a^-1+a^-1*d^-1*cot(c+d*x))
@test integrate((a+-1*a*sec(c+d*x)^2)^-2, x) == :(x*a^-2+a^-2*d^-1*cot(c+d*x)+-1//3*a^-2*d^-1*cot(c+d*x)^3)
@test integrate((a+-1*a*sec(c+d*x)^2)^-3, x) == :(x*a^-3+a^-3*d^-1*cot(c+d*x)+-1//3*a^-3*d^-1*cot(c+d*x)^3+1//5*a^-3*d^-1*cot(c+d*x)^5)
@test integrate((a+-1*a*sec(c+d*x)^2)^-4, x) == :(x*a^-4+a^-4*d^-1*cot(c+d*x)+-1//3*a^-4*d^-1*cot(c+d*x)^3+-1//7*a^-4*d^-1*cot(c+d*x)^7+1//5*a^-4*d^-1*cot(c+d*x)^5)
@test integrate(sec(e+f*x)^5*(a+b*sec(e+f*x)^2), x) == :(1//16*f^-1*(5b+6a)*arctanh(sin(e+f*x))+1//6*b*f^-1*sec(e+f*x)^5*tan(e+f*x)+1//16*f^-1*(5b+6a)*sec(e+f*x)*tan(e+f*x)+1//24*f^-1*sec(e+f*x)^3*(5b+6a)*tan(e+f*x))
@test integrate(sec(e+f*x)^3*(a+b*sec(e+f*x)^2), x) == :(1//8*f^-1*(3b+4a)*arctanh(sin(e+f*x))+1//4*b*f^-1*sec(e+f*x)^3*tan(e+f*x)+1//8*f^-1*(3b+4a)*sec(e+f*x)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)*sec(e+f*x), x) == :((1/2)*f^-1*(b+2a)*arctanh(sin(e+f*x))+(1/2)*b*f^-1*sec(e+f*x)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)*cos(e+f*x), x) == :(a*f^-1*sin(e+f*x)+b*f^-1*arctanh(sin(e+f*x)))
@test integrate(cos(e+f*x)^3*(a+b*sec(e+f*x)^2), x) == :(f^-1*(a+b)*sin(e+f*x)+-1//3*a*f^-1*sin(e+f*x)^3)
@test integrate(cos(e+f*x)^5*(a+b*sec(e+f*x)^2), x) == :(f^-1*(a+b)*sin(e+f*x)+-1//3*f^-1*sin(e+f*x)^3*(b+2a)+1//5*a*f^-1*sin(e+f*x)^5)
@test integrate(sec(e+f*x)^6*(a+b*sec(e+f*x)^2), x) == :(1//7*f^-1*(6b+7a)*tan(e+f*x)+1//21*f^-1*tan(e+f*x)^3*(12b+14a)+1//35*f^-1*tan(e+f*x)^5*(6b+7a)+1//7*b*f^-1*sec(e+f*x)^6*tan(e+f*x))
@test integrate(sec(e+f*x)^4*(a+b*sec(e+f*x)^2), x) == :(1//5*f^-1*(4b+5a)*tan(e+f*x)+1//15*f^-1*tan(e+f*x)^3*(4b+5a)+1//5*b*f^-1*sec(e+f*x)^4*tan(e+f*x))
@test integrate(sec(e+f*x)^2*(a+b*sec(e+f*x)^2), x) == :(1//3*f^-1*(2b+3a)*tan(e+f*x)+1//3*b*f^-1*sec(e+f*x)^2*tan(e+f*x))
@test integrate(a+b*sec(e+f*x)^2, x) == :(a*x+b*f^-1*tan(e+f*x))
@test integrate(cos(e+f*x)^2*(a+b*sec(e+f*x)^2), x) == :((1/2)*x*(a+2b)+(1/2)*a*f^-1*cos(e+f*x)*sin(e+f*x))
@test integrate(cos(e+f*x)^4*(a+b*sec(e+f*x)^2), x) == :(1//8*x*(3a+4b)+1//4*a*f^-1*cos(e+f*x)^3*sin(e+f*x)+1//8*f^-1*(3a+4b)*cos(e+f*x)*sin(e+f*x))
@test integrate(cos(e+f*x)^6*(a+b*sec(e+f*x)^2), x) == :(1//16*x*(5a+6b)+1//6*a*f^-1*cos(e+f*x)^5*sin(e+f*x)+1//16*f^-1*(5a+6b)*cos(e+f*x)*sin(e+f*x)+1//24*f^-1*cos(e+f*x)^3*(5a+6b)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^2*sec(e+f*x)^5, x) == :(1//128*f^-1*(35*b^2+48*a^2+80*a*b)*arctanh(sin(e+f*x))+1//128*f^-1*(35*b^2+48*a^2+80*a*b)*sec(e+f*x)*tan(e+f*x)+1//192*f^-1*sec(e+f*x)^3*(35*b^2+48*a^2+80*a*b)*tan(e+f*x)+1//8*b*f^-1*sec(e+f*x)^7*(a+b+-1*a*sin(e+f*x)^2)*tan(e+f*x)+1//48*b*f^-1*sec(e+f*x)^5*(7b+10a)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^2*sec(e+f*x)^3, x) == :(1//16*f^-1*(5*b^2+8*a^2+12*a*b)*arctanh(sin(e+f*x))+1//16*f^-1*(5*b^2+8*a^2+12*a*b)*sec(e+f*x)*tan(e+f*x)+1//6*b*f^-1*sec(e+f*x)^5*(a+b+-1*a*sin(e+f*x)^2)*tan(e+f*x)+1//24*b*f^-1*sec(e+f*x)^3*(5b+8a)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^2*sec(e+f*x), x) == :(1//8*f^-1*(3*b^2+8*a^2+8*a*b)*arctanh(sin(e+f*x))+1//4*b*f^-1*sec(e+f*x)^3*(a+b+-1*a*sin(e+f*x)^2)*tan(e+f*x)+3//8*b*f^-1*(b+2a)*sec(e+f*x)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^2*cos(e+f*x), x) == :(a^2*f^-1*sin(e+f*x)+(1/2)*b*f^-1*(b+4a)*arctanh(sin(e+f*x))+(1/2)*b^2*f^-1*sec(e+f*x)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^2*cos(e+f*x)^3, x) == :(b^2*f^-1*arctanh(sin(e+f*x))+-1//3*a^2*f^-1*sin(e+f*x)^3+a*f^-1*(a+2b)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^2*cos(e+f*x)^5, x) == :(f^-1*(a+b)^2*sin(e+f*x)+1//5*a^2*f^-1*sin(e+f*x)^5+-2//3*a*f^-1*sin(e+f*x)^3*(a+b))
@test integrate((a+b*sec(e+f*x)^2)^2*sec(e+f*x)^6, x) == :(f^-1*(a+b)^2*tan(e+f*x)+1//5*f^-1*tan(e+f*x)^5*(a^2+6*b^2+6*a*b)+1//9*b^2*f^-1*tan(e+f*x)^9+1//3*f^-1*tan(e+f*x)^3*(a+2b)*(2a+2b)+2//7*b*f^-1*tan(e+f*x)^7*(a+2b))
@test integrate((a+b*sec(e+f*x)^2)^2*sec(e+f*x)^4, x) == :(f^-1*(a+b)^2*tan(e+f*x)+1//7*b^2*f^-1*tan(e+f*x)^7+1//3*f^-1*tan(e+f*x)^3*(a+b)*(a+3b)+1//5*b*f^-1*tan(e+f*x)^5*(2a+3b))
@test integrate((a+b*sec(e+f*x)^2)^2*sec(e+f*x)^2, x) == :(f^-1*(a+b)^2*tan(e+f*x)+1//5*b^2*f^-1*tan(e+f*x)^5+2//3*b*f^-1*tan(e+f*x)^3*(a+b))
@test integrate((a+b*sec(e+f*x)^2)^2, x) == :(x*a^2+1//3*b^2*f^-1*tan(e+f*x)^3+b*f^-1*(b+2a)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^2*cos(e+f*x)^2, x) == :(b^2*f^-1*tan(e+f*x)+(1/2)*a*x*(a+4b)+(1/2)*a^2*f^-1*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^2*cos(e+f*x)^4, x) == :(1//8*x*(3*a^2+8*b^2+8*a*b)+1//4*a*f^-1*cos(e+f*x)^3*(a+b+b*tan(e+f*x)^2)*sin(e+f*x)+3//8*a*f^-1*(a+2b)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^2*cos(e+f*x)^6, x) == :(1//16*x*(5*a^2+8*b^2+12*a*b)+1//16*f^-1*(5*a^2+8*b^2+12*a*b)*cos(e+f*x)*sin(e+f*x)+1//6*a*f^-1*cos(e+f*x)^5*(a+b+b*tan(e+f*x)^2)*sin(e+f*x)+1//24*a*f^-1*cos(e+f*x)^3*(5a+8b)*sin(e+f*x))
@test integrate((a+b*sec(c+d*x)^2)^3, x) == :(x*a^3+1//5*b^3*d^-1*tan(c+d*x)^5+b*d^-1*(b^2+3*a^2+3*a*b)*tan(c+d*x)+1//3*b^2*d^-1*tan(c+d*x)^3*(2b+3a))
@test integrate((a+b*sec(c+d*x)^2)^4, x) == :(x*a^4+1//7*b^4*d^-1*tan(c+d*x)^7+1//3*b^2*d^-1*tan(c+d*x)^3*(3*b^2+6*a^2+8*a*b)+1//5*b^3*d^-1*tan(c+d*x)^5*(3b+4a)+b*d^-1*(b+2a)*(b^2+2*a^2+2*a*b)*tan(c+d*x))
@test integrate((a+b*sec(e+f*x)^2)^-1*sec(e+f*x)^5, x) == :((1/2)*b^-1*f^-1*sec(e+f*x)*tan(e+f*x)+-1//2*b^-2*f^-1*(-1b+2a)*arctanh(sin(e+f*x))+a^3//2*b^-2*f^-1*(a+b)^-1//2*arctanh(a^(1/2)*(a+b)^-1//2*sin(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1*sec(e+f*x)^3, x) == :(b^-1*f^-1*arctanh(sin(e+f*x))+-1*a^(1/2)*b^-1*f^-1*(a+b)^-1//2*arctanh(a^(1/2)*(a+b)^-1//2*sin(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1*sec(e+f*x), x) == :(a^-1//2*f^-1*(a+b)^-1//2*arctanh(a^(1/2)*(a+b)^-1//2*sin(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1*cos(e+f*x), x) == :(a^-1*f^-1*sin(e+f*x)+-1*b*a^-3//2*f^-1*(a+b)^-1//2*arctanh(a^(1/2)*(a+b)^-1//2*sin(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1*cos(e+f*x)^3, x) == :(-1//3*a^-1*f^-1*sin(e+f*x)^3+a^-2*f^-1*(a+-1b)*sin(e+f*x)+a^-5//2*b^2*f^-1*(a+b)^-1//2*arctanh(a^(1/2)*(a+b)^-1//2*sin(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1*cos(e+f*x)^5, x) == :(1//5*a^-1*f^-1*sin(e+f*x)^5+a^-3*f^-1*(a^2+b^2+-1*a*b)*sin(e+f*x)+-1//3*a^-2*f^-1*sin(e+f*x)^3*(-1b+2a)+-1*a^-7//2*b^3*f^-1*(a+b)^-1//2*arctanh(a^(1/2)*(a+b)^-1//2*sin(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1*sec(e+f*x)^6, x) == :(1//3*b^-1*f^-1*tan(e+f*x)^3+-1*b^-2*f^-1*(a+-1b)*tan(e+f*x)+a^2*b^-5//2*f^-1*(a+b)^-1//2*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1*sec(e+f*x)^4, x) == :(b^-1*f^-1*tan(e+f*x)+-1*a*b^-3//2*f^-1*(a+b)^-1//2*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1*sec(e+f*x)^2, x) == :(b^-1//2*f^-1*(a+b)^-1//2*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1, x) == :(x*a^-1+a^-1*b^(1/2)*f^-1*(a+b)^-1//2*arctan(b^-1//2*(a+b)^(1/2)*cot(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1*cos(e+f*x)^2, x) == :((1/2)*x*a^-2*(a+-2b)+(1/2)*a^-1*f^-1*cos(e+f*x)*sin(e+f*x)+a^-2*b^3//2*f^-1*(a+b)^-1//2*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1*cos(e+f*x)^4, x) == :(1//8*x*a^-3*(3*a^2+8*b^2+-4*a*b)+1//4*a^-1*f^-1*cos(e+f*x)^3*sin(e+f*x)+-1*a^-3*b^5//2*f^-1*(a+b)^-1//2*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+1//8*a^-2*f^-1*(-4b+3a)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-1*cos(e+f*x)^6, x) == :(1//16*x*a^-4*(-16*b^3+5*a^3+-6*b*a^2+8*a*b^2)+1//6*a^-1*f^-1*cos(e+f*x)^5*sin(e+f*x)+a^-4*b^7//2*f^-1*(a+b)^-1//2*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+1//16*a^-3*f^-1*(5*a^2+8*b^2+-6*a*b)*cos(e+f*x)*sin(e+f*x)+1//24*a^-2*f^-1*cos(e+f*x)^3*(-6b+5a)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-2*sec(e+f*x)^5, x) == :(b^-2*f^-1*arctanh(sin(e+f*x))+-1//2*a*b^-1*f^-1*(a+b)^-1*(a+b+-1*a*sin(e+f*x)^2)^-1*sin(e+f*x)+-1//2*a^(1/2)*b^-2*f^-1*(a+b)^-3//2*(2a+3b)*arctanh(a^(1/2)*(a+b)^-1//2*sin(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-2*sec(e+f*x)^3, x) == :(f^-1*(2a+2b)^-1*(a+b+-1*a*sin(e+f*x)^2)^-1*sin(e+f*x)+(1/2)*a^-1//2*f^-1*(a+b)^-3//2*arctanh(a^(1/2)*(a+b)^-1//2*sin(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-2*sec(e+f*x), x) == :((1/2)*a^-3//2*f^-1*(a+b)^-3//2*(b+2a)*arctanh(a^(1/2)*(a+b)^-1//2*sin(e+f*x))+-1//2*b*a^-1*f^-1*(a+b)^-1*(a+b+-1*a*sin(e+f*x)^2)^-1*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-2*cos(e+f*x), x) == :(a^-2*f^-1*sin(e+f*x)+(1/2)*a^-2*b^2*f^-1*(a+b)^-1*(a+b+-1*a*sin(e+f*x)^2)^-1*sin(e+f*x)+-1//2*b*a^-5//2*f^-1*(a+b)^-3//2*(3b+4a)*arctanh(a^(1/2)*(a+b)^-1//2*sin(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-2*cos(e+f*x)^3, x) == :(-1//3*a^-2*f^-1*sin(e+f*x)^3+a^-3*f^-1*(a+-2b)*sin(e+f*x)+(1/2)*a^-7//2*b^2*f^-1*(a+b)^-3//2*(5b+6a)*arctanh(a^(1/2)*(a+b)^-1//2*sin(e+f*x))+-1//2*a^-3*b^3*f^-1*(a+b)^-1*(a+b+-1*a*sin(e+f*x)^2)^-1*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-2*cos(e+f*x)^5, x) == :(1//5*a^-2*f^-1*sin(e+f*x)^5+a^-4*f^-1*(a^2+3*b^2+-2*a*b)*sin(e+f*x)+-1//3*a^-3*f^-1*sin(e+f*x)^3*(-2b+2a)+(1/2)*a^-4*b^4*f^-1*(a+b)^-1*(a+b+-1*a*sin(e+f*x)^2)^-1*sin(e+f*x)+-1//2*a^-9//2*b^3*f^-1*(a+b)^-3//2*(7b+8a)*arctanh(a^(1/2)*(a+b)^-1//2*sin(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-2*sec(e+f*x)^6, x) == :(b^-2*f^-1*tan(e+f*x)+(1/2)*a^2*b^-2*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1*tan(e+f*x)+-1//2*a*b^-5//2*f^-1*(a+b)^-3//2*(3a+4b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-2*sec(e+f*x)^4, x) == :((1/2)*b^-3//2*f^-1*(a+b)^-3//2*(a+2b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+-1//2*a*b^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-2*sec(e+f*x)^2, x) == :(f^-1*(2a+2b)^-1*(a+b+b*tan(e+f*x)^2)^-1*tan(e+f*x)+(1/2)*b^-1//2*f^-1*(a+b)^-3//2*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-2, x) == :(x*a^-2+-1//2*b*a^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1*tan(e+f*x)+-1//2*a^-2*b^(1/2)*f^-1*(a+b)^-3//2*(2b+3a)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-2*cos(e+f*x)^2, x) == :((1/2)*x*a^-3*(a+-4b)+(1/2)*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-1*cos(e+f*x)*sin(e+f*x)+(1/2)*a^-3*b^3//2*f^-1*(a+b)^-3//2*(4b+5a)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+(1/2)*b*a^-2*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1*(a+2b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-2*cos(e+f*x)^4, x) == :(1//8*x*a^-4*(3*a^2+24*b^2+-8*a*b)+1//4*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-1*cos(e+f*x)^3*sin(e+f*x)+-1//2*a^-4*b^5//2*f^-1*(a+b)^-3//2*(6b+7a)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+1//8*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^-1*(-6b+3a)*cos(e+f*x)*sin(e+f*x)+1//8*b*a^-3*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1*(a+-3b)*(3a+4b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-2*cos(e+f*x)^6, x) == :(1//16*x*a^-5*(-64*b^3+5*a^3+-12*b*a^2+24*a*b^2)+1//6*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-1*cos(e+f*x)^5*sin(e+f*x)+(1/2)*a^-5*b^7//2*f^-1*(a+b)^-3//2*(8b+9a)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+1//24*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^-1*cos(e+f*x)^3*(-8b+5a)*sin(e+f*x)+1//48*a^-3*f^-1*(a+b+b*tan(e+f*x)^2)^-1*(15*a^2+48*b^2+-26*a*b)*cos(e+f*x)*sin(e+f*x)+1//16*b*a^-4*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1*(5*a^3+32*b^3+-7*b*a^2+12*a*b^2)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3*sec(e+f*x)^5, x) == :(f^-1*(4a+4b)^-1*(a+b+-1*a*sin(e+f*x)^2)^-2*sin(e+f*x)+3//8*a^-1//2*f^-1*(a+b)^-5//2*arctanh(a^(1/2)*(a+b)^-1//2*sin(e+f*x))+3//8*f^-1*(a+b)^-2*(a+b+-1*a*sin(e+f*x)^2)^-1*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3*sec(e+f*x)^3, x) == :(1//8*a^-3//2*f^-1*(a+b)^-5//2*(b+4a)*arctanh(a^(1/2)*(a+b)^-1//2*sin(e+f*x))+-1//4*b*a^-1*f^-1*(a+b)^-1*(a+b+-1*a*sin(e+f*x)^2)^-2*sin(e+f*x)+1//8*a^-1*f^-1*(a+b)^-2*(a+b+-1*a*sin(e+f*x)^2)^-1*(b+4a)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3*sec(e+f*x), x) == :(1//8*a^-5//2*f^-1*(a+b)^-5//2*(3*b^2+8*a^2+8*a*b)*arctanh(a^(1/2)*(a+b)^-1//2*sin(e+f*x))+-3//8*b*a^-2*f^-1*(a+b)^-2*(a+b+-1*a*sin(e+f*x)^2)^-1*(b+2a)*sin(e+f*x)+-1//4*b*a^-1*f^-1*(a+b)^-1*(a+b+-1*a*sin(e+f*x)^2)^-2*cos(e+f*x)^2*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3*cos(e+f*x), x) == :(a^-3*f^-1*sin(e+f*x)+-3//8*b*a^-7//2*f^-1*(a+b)^-5//2*((b+2a)^2+4*(a+b)^2)*arctanh(a^(1/2)*(a+b)^-1//2*sin(e+f*x))+-1//4*a^-3*b^3*f^-1*(a+b)^-1*(a+b+-1*a*sin(e+f*x)^2)^-2*sin(e+f*x)+3//8*a^-3*b^2*f^-1*(a+b)^-2*(a+b+-1*a*sin(e+f*x)^2)^-1*(3b+4a)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3*cos(e+f*x)^3, x) == :(-1//3*a^-3*f^-1*sin(e+f*x)^3+a^-4*f^-1*(a+-3b)*sin(e+f*x)+1//4*a^-4*b^4*f^-1*(a+b)^-1*(a+b+-1*a*sin(e+f*x)^2)^-2*sin(e+f*x)+1//8*a^-9//2*b^2*f^-1*(a+b)^-5//2*(35*b^2+48*a^2+80*a*b)*arctanh(a^(1/2)*(a+b)^-1//2*sin(e+f*x))+-1//8*a^-4*b^3*f^-1*(a+b)^-2*(a+b+-1*a*sin(e+f*x)^2)^-1*(13b+16a)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3*cos(e+f*x)^5, x) == :(1//5*a^-3*f^-1*sin(e+f*x)^5+a^-5*f^-1*(a^2+6*b^2+-3*a*b)*sin(e+f*x)+-1//3*a^-4*f^-1*sin(e+f*x)^3*(-3b+2a)+-1//4*a^-5*b^5*f^-1*(a+b)^-1*(a+b+-1*a*sin(e+f*x)^2)^-2*sin(e+f*x)+-1//8*a^-11//2*b^3*f^-1*(a+b)^-5//2*(63*b^2+80*a^2+140*a*b)*arctanh(a^(1/2)*(a+b)^-1//2*sin(e+f*x))+1//8*a^-5*b^4*f^-1*(a+b)^-2*(a+b+-1*a*sin(e+f*x)^2)^-1*(17b+20a)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3*sec(e+f*x)^6, x) == :(1//8*b^-5//2*f^-1*(a+b)^-5//2*(3*a^2+8*b^2+8*a*b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+-3//8*a*b^-2*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1*(a+2b)*tan(e+f*x)+-1//4*a*b^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-2*sec(e+f*x)^2*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3*sec(e+f*x)^4, x) == :(1//8*b^-3//2*f^-1*(a+b)^-5//2*(a+4b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+-1//4*a*b^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-2*tan(e+f*x)+1//8*b^-1*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1*(a+4b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3*sec(e+f*x)^2, x) == :(f^-1*(4a+4b)^-1*(a+b+b*tan(e+f*x)^2)^-2*tan(e+f*x)+3//8*b^-1//2*f^-1*(a+b)^-5//2*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+3//8*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3, x) == :(x*a^-3+-1//4*b*a^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-2*tan(e+f*x)+-1//8*a^-3*b^(1/2)*f^-1*(a+b)^-5//2*(8*b^2+15*a^2+20*a*b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+-1//8*b*a^-2*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1*(4b+7a)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3*cos(e+f*x)^2, x) == :((1/2)*x*a^-4*(a+-6b)+(1/2)*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-2*cos(e+f*x)*sin(e+f*x)+1//8*a^-4*b^3//2*f^-1*(a+b)^-5//2*(24*b^2+35*a^2+56*a*b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+1//4*b*a^-2*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-2*(2a+3b)*tan(e+f*x)+1//8*b*a^-3*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1*(a+4b)*(3b+4a)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3*cos(e+f*x)^4, x) == :(1//8*x*a^-5*(3*a^2+48*b^2+-12*a*b)+1//4*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-2*cos(e+f*x)^3*sin(e+f*x)+-3//8*a^-5*b^5//2*f^-1*(a+b)^-5//2*(16*b^2+21*a^2+36*a*b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+1//8*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^-2*(-8b+3a)*cos(e+f*x)*sin(e+f*x)+1//8*b*a^-3*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-2*(-12*b^2+3*a^2+-7*a*b)*tan(e+f*x)+3//8*b*a^-4*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1*(a+2b)*(a^2+-4*b^2+-4*a*b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3*cos(e+f*x)^6, x) == :(1//16*x*a^-6*(-160*b^3+5*a^3+-18*b*a^2+48*a*b^2)+1//6*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-2*cos(e+f*x)^5*sin(e+f*x)+1//8*a^-6*b^7//2*f^-1*(a+b)^-5//2*(80*b^2+99*a^2+176*a*b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+1//24*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^-2*cos(e+f*x)^3*(-10b+5a)*sin(e+f*x)+1//48*a^-3*f^-1*(a+b+b*tan(e+f*x)^2)^-2*(15*a^2+80*b^2+-34*a*b)*cos(e+f*x)*sin(e+f*x)+1//16*b*a^-5*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1*(5*a^4+80*b^4+-8*b*a^3+17*a^2*b^2+116*a*b^3)*tan(e+f*x)+1//48*b*a^-4*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-2*(15*a^3+120*b^3+-29*b*a^2+64*a*b^2)*tan(e+f*x))
@test integrate((a+b*sec(c+d*x)^2)^-4, x) == :(x*a^-4+-1//6*b*a^-1*d^-1*(a+b)^-1*(a+b+b*tan(c+d*x)^2)^-3*tan(c+d*x)+-1//16*a^-4*b^(1/2)*d^-1*(a+b)^-7//2*(16*b^3+35*a^3+56*a*b^2+70*b*a^2)*arctan(b^(1/2)*(a+b)^-1//2*tan(c+d*x))+-1//16*b*a^-3*d^-1*(a+b)^-3*(a+b+b*tan(c+d*x)^2)^-1*(8*b^2+19*a^2+22*a*b)*tan(c+d*x)+-1//24*b*a^-2*d^-1*(a+b)^-2*(a+b+b*tan(c+d*x)^2)^-2*(6b+11a)*tan(c+d*x))
@test integrate((a+-1*a*sec(c+d*x)^2)^7//2, x) == :(-1//2*a^3*d^-1*(-1*a*tan(c+d*x)^2)^(1/2)*tan(c+d*x)+-1//6*a^3*d^-1*(-1*a*tan(c+d*x)^2)^(1/2)*tan(c+d*x)^5+1//4*a^3*d^-1*(-1*a*tan(c+d*x)^2)^(1/2)*tan(c+d*x)^3+-1*a^3*d^-1*(-1*a*tan(c+d*x)^2)^(1/2)*cot(c+d*x)*log(cos(c+d*x)))
@test integrate((a+-1*a*sec(c+d*x)^2)^5//2, x) == :(-1//2*a^2*d^-1*(-1*a*tan(c+d*x)^2)^(1/2)*tan(c+d*x)+1//4*a^2*d^-1*(-1*a*tan(c+d*x)^2)^(1/2)*tan(c+d*x)^3+-1*a^2*d^-1*(-1*a*tan(c+d*x)^2)^(1/2)*cot(c+d*x)*log(cos(c+d*x)))
@test integrate((a+-1*a*sec(c+d*x)^2)^3//2, x) == :(-1//2*a*d^-1*(-1*a*tan(c+d*x)^2)^(1/2)*tan(c+d*x)+-1*a*d^-1*(-1*a*tan(c+d*x)^2)^(1/2)*cot(c+d*x)*log(cos(c+d*x)))
@test integrate((a+-1*a*sec(c+d*x)^2)^(1/2), x) == :(-1*d^-1*(-1*a*tan(c+d*x)^2)^(1/2)*cot(c+d*x)*log(cos(c+d*x)))
@test integrate((a+-1*a*sec(c+d*x)^2)^-1//2, x) == :(d^-1*(-1*a*tan(c+d*x)^2)^-1//2*log(sin(c+d*x))*tan(c+d*x))
@test integrate((a+-1*a*sec(c+d*x)^2)^-3//2, x) == :((1/2)*a^-1*d^-1*(-1*a*tan(c+d*x)^2)^-1//2*cot(c+d*x)+a^-1*d^-1*(-1*a*tan(c+d*x)^2)^-1//2*log(sin(c+d*x))*tan(c+d*x))
@test integrate((a+-1*a*sec(c+d*x)^2)^-5//2, x) == :((1/2)*a^-2*d^-1*(-1*a*tan(c+d*x)^2)^-1//2*cot(c+d*x)+-1//4*a^-2*d^-1*(-1*a*tan(c+d*x)^2)^-1//2*cot(c+d*x)^3+a^-2*d^-1*(-1*a*tan(c+d*x)^2)^-1//2*log(sin(c+d*x))*tan(c+d*x))
@test integrate((a+-1*a*sec(c+d*x)^2)^-7//2, x) == :((1/2)*a^-3*d^-1*(-1*a*tan(c+d*x)^2)^-1//2*cot(c+d*x)+-1//4*a^-3*d^-1*(-1*a*tan(c+d*x)^2)^-1//2*cot(c+d*x)^3+1//6*a^-3*d^-1*(-1*a*tan(c+d*x)^2)^-1//2*cot(c+d*x)^5+a^-3*d^-1*(-1*a*tan(c+d*x)^2)^-1//2*log(sin(c+d*x))*tan(c+d*x))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*sec(e+f*x)^5, x) == :(1//5*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*sec(e+f*x)^3*tan(e+f*x)+-1//15*b^-2*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(-8*b^2+2*a^2+-3*a*b)*sin(e+f*x)+1//15*b^-1*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(a+4b)*sec(e+f*x)*tan(e+f*x)+1//15*b^-2*f^-1*(cos(e+f*x)^2)^(1/2)*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(-8*b^2+2*a^2+-3*a*b)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1)+-1//15*b^-1*f^-1*(cos(e+f*x)^2)^(1/2)*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^-1//2*(a+b)*(a+-8b)*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*sec(e+f*x)^3, x) == :(1//3*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*sec(e+f*x)*tan(e+f*x)+1//3*b^-1*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(a+2b)*sin(e+f*x)+1//3*f^-1*(cos(e+f*x)^2)^(1/2)*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^-1//2*(2a+2b)*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1)+-1//3*b^-1*f^-1*(cos(e+f*x)^2)^(1/2)*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(a+2b)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*sec(e+f*x), x) == :(f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*sin(e+f*x)+-1*f^-1*(cos(e+f*x)^2)^(1/2)*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1)+f^-1*(cos(e+f*x)^2)^(1/2)*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^-1//2*(a+b)*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*cos(e+f*x), x) == :(f^-1*(cos(e+f*x)^2)^(1/2)*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*cos(e+f*x)^3, x) == :(1//3*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*cos(e+f*x)^2*sin(e+f*x)+1//3*a^-1*f^-1*(cos(e+f*x)^2)^(1/2)*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(b+2a)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1)+-1//3*b*a^-1*f^-1*(cos(e+f*x)^2)^(1/2)*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^-1//2*(a+b)*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*cos(e+f*x)^5, x) == :(1//5*a^-1*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^3//2*cos(e+f*x)^2*sin(e+f*x)+1//15*a^-1*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*cos(e+f*x)^2*(-2b+4a)*sin(e+f*x)+1//15*a^-2*f^-1*(cos(e+f*x)^2)^(1/2)*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(-2*b^2+8*a^2+3*a*b)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1)+-1//15*b*a^-2*f^-1*(cos(e+f*x)^2)^(1/2)*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^-1//2*(a+b)*(-2b+4a)*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*sec(e+f*x)^6, x) == :(-1//24*b^-2*f^-1*(a+b+b*tan(e+f*x)^2)^3//2*(-5b+3a)*tan(e+f*x)+1//6*b^-1*f^-1*(a+b+b*tan(e+f*x)^2)^3//2*sec(e+f*x)^2*tan(e+f*x)+1//16*b^-2*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(a^2+5*b^2+-2*a*b)*tan(e+f*x)+1//16*b^-5//2*f^-1*(a+b)*(a^2+5*b^2+-2*a*b)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*sec(e+f*x)^4, x) == :(1//4*b^-1*f^-1*(a+b+b*tan(e+f*x)^2)^3//2*tan(e+f*x)+-1//8*b^-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(a+-3b)*tan(e+f*x)+-1//8*b^-3//2*f^-1*(a+b)*(a+-3b)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*sec(e+f*x)^2, x) == :((1/2)*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)+(1/2)*b^-1//2*f^-1*(a+b)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^(1/2), x) == :(a^(1/2)*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+b^(1/2)*f^-1*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*cos(e+f*x)^2, x) == :((1/2)*a^-1//2*f^-1*(a+b)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+(1/2)*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*cos(e+f*x)^4, x) == :(1//4*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^3//2*cos(e+f*x)^3*sin(e+f*x)+1//8*a^-3//2*f^-1*(a+b)*(-1b+3a)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//8*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(-1b+3a)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*cos(e+f*x)^6, x) == :(1//6*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cos(e+f*x)^5*sin(e+f*x)+1//16*a^-5//2*f^-1*(a+b)*(b^2+5*a^2+-2*a*b)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//24*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cos(e+f*x)^3*(b+5a)*sin(e+f*x)+1//48*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(-1b+3a)*(3b+5a)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^3//2*sec(e+f*x)^5, x) == :(1//7*b*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*sec(e+f*x)^5*tan(e+f*x)+1//35*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*sec(e+f*x)^3*(6b+8a)*tan(e+f*x)+1//35*b^-1*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(a^2+8*b^2+11*a*b)*sec(e+f*x)*tan(e+f*x)+1//35*b^-2*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(-4b+-2a)*(a^2+-4*b^2+-4*a*b)*sin(e+f*x)+-1//35*b^-1*f^-1*(cos(e+f*x)^2)^(1/2)*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^-1//2*(a+b)*(a^2+-16*b^2+-16*a*b)*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1)+1//35*b^-2*f^-1*(cos(e+f*x)^2)^(1/2)*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(2a+4b)*(a^2+-4*b^2+-4*a*b)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^3//2*sec(e+f*x)^3, x) == :(1//5*b*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*sec(e+f*x)^3*tan(e+f*x)+1//15*b^-1*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(3*a^2+8*b^2+13*a*b)*sin(e+f*x)+1//15*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(4b+6a)*sec(e+f*x)*tan(e+f*x)+-1//15*b^-1*f^-1*(cos(e+f*x)^2)^(1/2)*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(3*a^2+8*b^2+13*a*b)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1)+1//15*f^-1*(cos(e+f*x)^2)^(1/2)*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^-1//2*(a+b)*(8b+9a)*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^3//2*sec(e+f*x), x) == :(1//3*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(2b+4a)*sin(e+f*x)+1//3*b*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*sec(e+f*x)*tan(e+f*x)+-1//3*f^-1*(cos(e+f*x)^2)^(1/2)*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(2b+4a)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1)+1//3*f^-1*(cos(e+f*x)^2)^(1/2)*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^-1//2*(a+b)*(2b+3a)*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^3//2*cos(e+f*x), x) == :(b*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*sin(e+f*x)+f^-1*(cos(e+f*x)^2)^(1/2)*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(a+-1b)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1)+b*f^-1*(cos(e+f*x)^2)^(1/2)*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^-1//2*(a+b)*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^3//2*cos(e+f*x)^3, x) == :(1//3*a*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*cos(e+f*x)^2*sin(e+f*x)+1//3*f^-1*(cos(e+f*x)^2)^(1/2)*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(2a+4b)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1)+-1//3*b*f^-1*(cos(e+f*x)^2)^(1/2)*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^-1//2*(a+b)*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^3//2*cos(e+f*x)^5, x) == :(1//5*a*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*cos(e+f*x)^4*sin(e+f*x)+1//15*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*cos(e+f*x)^2*(4a+6b)*sin(e+f*x)+1//15*a^-1*f^-1*(cos(e+f*x)^2)^(1/2)*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(3*b^2+8*a^2+13*a*b)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1)+-1//15*b*a^-1*f^-1*(cos(e+f*x)^2)^(1/2)*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b*sec(e+f*x)^2)^(1/2)*(b+a*cos(e+f*x)^2)^-1//2*(a+b+-1*a*sin(e+f*x)^2)^-1//2*(a+b)*(3b+4a)*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^3//2*sec(e+f*x)^6, x) == :(-1//48*b^-2*f^-1*(a+b+b*tan(e+f*x)^2)^5//2*(-7b+3a)*tan(e+f*x)+1//8*b^-1*f^-1*(a+b+b*tan(e+f*x)^2)^5//2*sec(e+f*x)^2*tan(e+f*x)+1//128*b^-5//2*f^-1*(a+b)^2*(3*a^2+35*b^2+-10*a*b)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//192*b^-2*f^-1*(a+b+b*tan(e+f*x)^2)^3//2*(3*a^2+35*b^2+-10*a*b)*tan(e+f*x)+1//128*b^-2*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(a+b)*(3*a^2+35*b^2+-10*a*b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^3//2*sec(e+f*x)^4, x) == :(1//6*b^-1*f^-1*(a+b+b*tan(e+f*x)^2)^5//2*tan(e+f*x)+-1//16*b^-3//2*f^-1*(a+b)^2*(a+-5b)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//24*b^-1*f^-1*(a+b+b*tan(e+f*x)^2)^3//2*(a+-5b)*tan(e+f*x)+-1//16*b^-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(a+b)*(a+-5b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^3//2*sec(e+f*x)^2, x) == :(1//4*f^-1*(a+b+b*tan(e+f*x)^2)^3//2*tan(e+f*x)+1//8*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(3a+3b)*tan(e+f*x)+3//8*b^-1//2*f^-1*(a+b)^2*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^3//2, x) == :(a^3//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+(1/2)*b*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)+(1/2)*b^(1/2)*f^-1*(b+3a)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^3//2*cos(e+f*x)^2, x) == :(b^3//2*f^-1*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+(1/2)*a^(1/2)*f^-1*(a+3b)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+(1/2)*a*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^3//2*cos(e+f*x)^4, x) == :(1//4*f^-1*(a+b+b*tan(e+f*x)^2)^3//2*cos(e+f*x)^3*sin(e+f*x)+3//8*a^-1//2*f^-1*(a+b)^2*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//8*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(3a+3b)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^3//2*cos(e+f*x)^6, x) == :(1//6*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^5//2*cos(e+f*x)^5*sin(e+f*x)+1//16*a^-3//2*f^-1*(a+b)^2*(-1b+5a)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//24*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^3//2*cos(e+f*x)^3*(-1b+5a)*sin(e+f*x)+1//16*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(a+b)*(-1b+5a)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(c+d*x)^2)^5//2, x) == :(a^5//2*d^-1*arctan(a^(1/2)*(a+b+b*tan(c+d*x)^2)^-1//2*tan(c+d*x))+1//4*b*d^-1*(a+b+b*tan(c+d*x)^2)^3//2*tan(c+d*x)+1//8*b^(1/2)*d^-1*(3*b^2+15*a^2+10*a*b)*arctanh(b^(1/2)*(a+b+b*tan(c+d*x)^2)^-1//2*tan(c+d*x))+1//8*b*d^-1*(a+b+b*tan(c+d*x)^2)^(1/2)*(3b+7a)*tan(c+d*x))
@test integrate((1+sec(x)^2)^3//2, x) == :(2*arcsinh((1/2)*2^(1/2)*tan(x))+(1/2)*(2+tan(x)^2)^(1/2)*tan(x)+arctan((2+tan(x)^2)^-1//2*tan(x)))
@test integrate((1+sec(x)^2)^(1/2), x) == :(arcsinh((1/2)*2^(1/2)*tan(x))+arctan((2+tan(x)^2)^-1//2*tan(x)))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x)^5, x) == :(1//3*b^-1*f^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*sec(e+f*x)^3*tan(e+f*x)+-1//3*b^-2*f^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(-2b+2a)*sec(e+f*x)*tan(e+f*x)+-1//3*b^-1*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*(a+-2b)*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1)+1//3*b^-2*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(-2b+2a)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x)^3, x) == :(b^-1*f^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*sec(e+f*x)*tan(e+f*x)+-1*a^(1/2)*b^-1*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*Elliptic.E(arcsin(a^(1/2)*(a+b)^-1//2*sin(e+f*x)),a^-1*(a+b)))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x), x) == :(f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*cos(e+f*x), x) == :(a^-1//2*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*Elliptic.E(arcsin(a^(1/2)*(a+b)^-1//2*sin(e+f*x)),a^-1*(a+b)))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*cos(e+f*x)^3, x) == :(1//3*a^-1*f^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*sin(e+f*x)+1//3*a^-2*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(-2b+2a)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1)+-1//3*b*a^-2*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*(a+-2b)*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*cos(e+f*x)^5, x) == :(1//5*a^-1*f^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*cos(e+f*x)^2*sin(e+f*x)+1//15*a^-2*f^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(-4b+4a)*sin(e+f*x)+1//15*a^-3*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(8*a^2+8*b^2+-7*a*b)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1)+-1//15*b*a^-3*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*(4*a^2+8*b^2+-3*a*b)*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x)^6, x) == :(1//8*b^-5//2*f^-1*(3*a^2+3*b^2+-2*a*b)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//8*b^-2*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(-3b+3a)*tan(e+f*x)+1//4*b^-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*sec(e+f*x)^2*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x)^4, x) == :((1/2)*b^-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)+-1//2*b^-3//2*f^-1*(a+-1b)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*sec(e+f*x)^2, x) == :(b^-1//2*f^-1*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1//2, x) == :(a^-1//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*cos(e+f*x)^2, x) == :((1/2)*a^-3//2*f^-1*(a+-1b)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+(1/2)*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*cos(e+f*x)^4, x) == :(1//8*a^-5//2*f^-1*(3*a^2+3*b^2+-2*a*b)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//4*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cos(e+f*x)^3*sin(e+f*x)+1//8*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(-3b+3a)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*cos(e+f*x)^6, x) == :(1//6*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cos(e+f*x)^5*sin(e+f*x)+1//16*a^-7//2*f^-1*(a+-1b)*(5*a^2+5*b^2+2*a*b)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//24*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cos(e+f*x)^3*(-5b+5a)*sin(e+f*x)+1//48*a^-3*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(15*a^2+15*b^2+-14*a*b)*cos(e+f*x)*sin(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*sec(e+f*x)^5, x) == :(b^-1*f^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*sec(e+f*x)*tan(e+f*x)+b^-1*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1)+a*b^-2*f^-1*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*(b+2a)*sin(e+f*x)+-1*b^-2*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(b+2a)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*sec(e+f*x)^3, x) == :(-1*a*b^-1*f^-1*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*sin(e+f*x)+b^-1*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*sec(e+f*x), x) == :(f^-1*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*sin(e+f*x)+a^-1*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1)+-1*a^-1*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*cos(e+f*x), x) == :(-1*b*a^-1*f^-1*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*sin(e+f*x)+-2*b*a^-2*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1)+a^-2*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(a+2b)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*cos(e+f*x)^3, x) == :(1//3*a^-2*f^-1*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(a+4b)*sin(e+f*x)+-1*b*a^-1*f^-1*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*cos(e+f*x)^2*sin(e+f*x)+-1//3*b*a^-3*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*(a+-8b)*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1)+1//3*a^-3*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(-8*b^2+2*a^2+-3*a*b)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*cos(e+f*x)^5, x) == :(1//15*a^-3*f^-1*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(-24*b^2+4*a^2+-5*a*b)*sin(e+f*x)+-1*b*a^-1*f^-1*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*cos(e+f*x)^4*sin(e+f*x)+1//5*a^-2*f^-1*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*cos(e+f*x)^2*(a+6b)*sin(e+f*x)+-4//15*b*a^-4*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*(a^2+12*b^2+-2*a*b)*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1)+1//15*a^-4*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(8*a^3+48*b^3+-9*b*a^2+16*a*b^2)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*sec(e+f*x)^6, x) == :(-1//2*b^-5//2*f^-1*(-1b+3a)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+(1/2)*b^-2*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(b+3a)*tan(e+f*x)+-1*a*b^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1//2*sec(e+f*x)^2*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*sec(e+f*x)^4, x) == :(b^-3//2*f^-1*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*a*b^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*sec(e+f*x)^2, x) == :(f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3//2, x) == :(a^-3//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*b*a^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*cos(e+f*x)^2, x) == :((1/2)*a^-5//2*f^-1*(a+-3b)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+(1/2)*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-1//2*cos(e+f*x)*sin(e+f*x)+(1/2)*b*a^-2*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1//2*(a+3b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*cos(e+f*x)^4, x) == :(1//8*a^-7//2*f^-1*(3*a^2+15*b^2+-6*a*b)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//4*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-1//2*cos(e+f*x)^3*sin(e+f*x)+1//8*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^-1//2*(-5b+3a)*cos(e+f*x)*sin(e+f*x)+1//8*b*a^-3*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1//2*(a+-3b)*(3a+5b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*cos(e+f*x)^6, x) == :(1//16*a^-9//2*f^-1*(-35*b^3+5*a^3+-9*b*a^2+15*a*b^2)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//6*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-1//2*cos(e+f*x)^5*sin(e+f*x)+1//24*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^-1//2*cos(e+f*x)^3*(-7b+5a)*sin(e+f*x)+1//48*a^-3*f^-1*(a+b+b*tan(e+f*x)^2)^-1//2*(15*a^2+35*b^2+-22*a*b)*cos(e+f*x)*sin(e+f*x)+1//48*b*a^-4*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1//2*(15*a^3+105*b^3+-17*b*a^2+25*a*b^2)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*sec(e+f*x)^5, x) == :(-1//3*a*b^-1*f^-1*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-3//2*sin(e+f*x)+-2//3*a*b^-2*f^-1*(a+b)^-2*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*(a+2b)*sin(e+f*x)+-1//3*b^-1*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1)+1//3*b^-2*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b)^-2*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(2a+4b)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*sec(e+f*x)^3, x) == :(f^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(3a+3b)^-1*(a+b+-1*a*sin(e+f*x)^2)^-3//2*sin(e+f*x)+-1//3*b^-1*f^-1*(a+b)^-2*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*(a+-1b)*sin(e+f*x)+1//3*a^-1*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1)+1//3*a^-1*b^-1*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b)^-2*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(a+-1b)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*sec(e+f*x), x) == :(-1//3*b*a^-1*f^-1*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-3//2*sin(e+f*x)+1//3*a^-1*f^-1*(a+b)^-2*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*(2b+4a)*sin(e+f*x)+-1//3*a^-2*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b)^-2*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(2b+4a)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1)+1//3*a^-2*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*(2b+3a)*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*cos(e+f*x), x) == :(-2//3*b*a^-2*f^-1*(a+b)^-2*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*(2b+3a)*sin(e+f*x)+-1//3*b*a^-1*f^-1*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-3//2*cos(e+f*x)^2*sin(e+f*x)+1//3*a^-3*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b)^-2*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(3*a^2+8*b^2+13*a*b)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1)+-1//3*b*a^-3*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*(8b+9a)*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*cos(e+f*x)^3, x) == :(1//3*a^-3*f^-1*(a+b)^-2*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(a^2+8*b^2+11*a*b)*sin(e+f*x)+-1//3*b*a^-1*f^-1*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-3//2*cos(e+f*x)^4*sin(e+f*x)+-2//3*b*a^-2*f^-1*(a+b)^-2*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*cos(e+f*x)^2*(3b+4a)*sin(e+f*x)+-1//3*b*a^-4*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*(a^2+-16*b^2+-16*a*b)*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1)+1//3*a^-4*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b)^-2*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(2a+4b)*(a^2+-4*b^2+-4*a*b)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*cos(e+f*x)^5, x) == :(1//15*a^-4*f^-1*(a+b)^-2*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(-64*b^3+4*a^3+-84*a*b^2+-6*b*a^2)*sin(e+f*x)+-1//3*b*a^-1*f^-1*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-3//2*cos(e+f*x)^6*sin(e+f*x)+1//15*a^-3*f^-1*(a+b)^-2*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*cos(e+f*x)^2*(3*a^2+48*b^2+61*a*b)*sin(e+f*x)+-2//3*b*a^-2*f^-1*(a+b)^-2*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*cos(e+f*x)^4*(4b+5a)*sin(e+f*x)+1//15*a^-5*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^-1//2*(a+b)^-2*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^(1/2)*(8*a^4+128*b^4+-11*b*a^3+27*a^2*b^2+184*a*b^3)*Elliptic.E(arcsin(sin(e+f*x)),a*(a+b)^-1)+-1//15*b*a^-5*f^-1*(cos(e+f*x)^2)^-1//2*(1+-1*a*(a+b)^-1*sin(e+f*x)^2)^(1/2)*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2*(b+a*cos(e+f*x)^2)^(1/2)*(a+b+-1*a*sin(e+f*x)^2)^-1//2*(4*a^3+128*b^3+-9*b*a^2+120*a*b^2)*Elliptic.F(arcsin(sin(e+f*x)),a*(a+b)^-1))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*sec(e+f*x)^6, x) == :(b^-5//2*f^-1*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//3*a*b^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-3//2*sec(e+f*x)^2*tan(e+f*x)+-1//3*a*b^-2*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1//2*(3a+5b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*sec(e+f*x)^4, x) == :(2//3*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)+f^-1*(3a+3b)^-1*(a+b+b*tan(e+f*x)^2)^-3//2*sec(e+f*x)^2*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*sec(e+f*x)^2, x) == :(f^-1*(3a+3b)^-1*(a+b+b*tan(e+f*x)^2)^-3//2*tan(e+f*x)+2//3*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-5//2, x) == :(a^-5//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//3*b*a^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-3//2*tan(e+f*x)+-1//3*b*a^-2*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1//2*(3b+5a)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*cos(e+f*x)^2, x) == :((1/2)*a^-7//2*f^-1*(a+-5b)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+(1/2)*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-3//2*cos(e+f*x)*sin(e+f*x)+1//6*b*a^-3*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1//2*(3*a^2+15*b^2+22*a*b)*tan(e+f*x)+1//6*b*a^-2*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-3//2*(3a+5b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*cos(e+f*x)^4, x) == :(1//8*a^-9//2*f^-1*(3*a^2+35*b^2+-10*a*b)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//4*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-3//2*cos(e+f*x)^3*sin(e+f*x)+1//8*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^-3//2*(-7b+3a)*cos(e+f*x)*sin(e+f*x)+1//24*b*a^-4*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1//2*(-105*b^3+9*a^3+-145*a*b^2+-15*b*a^2)*tan(e+f*x)+1//24*b*a^-3*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-3//2*(-35*b^2+9*a^2+-18*a*b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*cos(e+f*x)^6, x) == :(1//6*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-3//2*cos(e+f*x)^5*sin(e+f*x)+1//16*a^-11//2*f^-1*(a^2+7*b^2)*(-15b+5a)*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//16*a^-3*f^-1*(a+b+b*tan(e+f*x)^2)^-3//2*(5*a^2+21*b^2+-10*a*b)*cos(e+f*x)*sin(e+f*x)+1//24*a^-2*f^-1*(a+b+b*tan(e+f*x)^2)^-3//2*cos(e+f*x)^3*(-9b+5a)*sin(e+f*x)+1//48*b*a^-5*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1//2*(15*a^4+315*b^4+-20*b*a^3+38*a^2*b^2+420*a*b^3)*tan(e+f*x)+1//48*b*a^-4*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-3//2*(15*a^3+105*b^3+-25*b*a^2+49*a*b^2)*tan(e+f*x))
@test integrate((a+b*sec(c+d*x)^2)^-7//2, x) == :(a^-7//2*d^-1*arctan(a^(1/2)*(a+b+b*tan(c+d*x)^2)^-1//2*tan(c+d*x))+-1//5*b*a^-1*d^-1*(a+b)^-1*(a+b+b*tan(c+d*x)^2)^-5//2*tan(c+d*x)+-1//15*b*a^-3*d^-1*(a+b)^-3*(a+b+b*tan(c+d*x)^2)^-1//2*(15*b^2+33*a^2+40*a*b)*tan(c+d*x)+-1//15*b*a^-2*d^-1*(a+b)^-2*(a+b+b*tan(c+d*x)^2)^-3//2*(5b+9a)*tan(c+d*x))
@test integrate((1+sec(x)^2)^-1//2, x) == :(arctan((2+tan(x)^2)^-1//2*tan(x)))
@test integrate(tan(e+f*x)^5*(a+b*sec(e+f*x)^2), x) == :(-1*a*f^-1*log(cos(e+f*x))+-1//2*f^-1*sec(e+f*x)^2*(-1b+2a)+1//4*f^-1*sec(e+f*x)^4*(a+-2b)+1//6*b*f^-1*sec(e+f*x)^6)
@test integrate(tan(e+f*x)^3*(a+b*sec(e+f*x)^2), x) == :(a*f^-1*log(cos(e+f*x))+(1/2)*f^-1*sec(e+f*x)^2*(a+-1b)+1//4*b*f^-1*sec(e+f*x)^4)
@test integrate((a+b*sec(e+f*x)^2)*tan(e+f*x), x) == :((1/2)*b*f^-1*sec(e+f*x)^2+-1*a*f^-1*log(cos(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)*cot(e+f*x), x) == :(f^-1*(a+b)*log(sin(e+f*x))+-1*b*f^-1*log(cos(e+f*x)))
@test integrate(cot(e+f*x)^3*(a+b*sec(e+f*x)^2), x) == :(-1*a*f^-1*log(sin(e+f*x))+-1//2*f^-1*csc(e+f*x)^2*(a+b))
@test integrate(cot(e+f*x)^5*(a+b*sec(e+f*x)^2), x) == :(a*f^-1*log(sin(e+f*x))+(1/2)*f^-1*csc(e+f*x)^2*(b+2a)+-1//4*f^-1*csc(e+f*x)^4*(a+b))
@test integrate(tan(e+f*x)^6*(a+b*sec(e+f*x)^2), x) == :(-1*a*x+a*f^-1*tan(e+f*x)+-1//3*a*f^-1*tan(e+f*x)^3+1//5*a*f^-1*tan(e+f*x)^5+1//7*b*f^-1*tan(e+f*x)^7)
@test integrate(tan(e+f*x)^4*(a+b*sec(e+f*x)^2), x) == :(a*x+-1*a*f^-1*tan(e+f*x)+1//3*a*f^-1*tan(e+f*x)^3+1//5*b*f^-1*tan(e+f*x)^5)
@test integrate(tan(e+f*x)^2*(a+b*sec(e+f*x)^2), x) == :(-1*a*x+a*f^-1*tan(e+f*x)+1//3*b*f^-1*tan(e+f*x)^3)
@test integrate(a+b*sec(e+f*x)^2, x) == :(a*x+b*f^-1*tan(e+f*x))
@test integrate(cot(e+f*x)^2*(a+b*sec(e+f*x)^2), x) == :(-1*a*x+-1*f^-1*(a+b)*cot(e+f*x))
@test integrate(cot(e+f*x)^4*(a+b*sec(e+f*x)^2), x) == :(a*x+a*f^-1*cot(e+f*x)+-1//3*f^-1*cot(e+f*x)^3*(a+b))
@test integrate(cot(e+f*x)^6*(a+b*sec(e+f*x)^2), x) == :(-1*a*x+-1*a*f^-1*cot(e+f*x)+-1//5*f^-1*cot(e+f*x)^5*(a+b)+1//3*a*f^-1*cot(e+f*x)^3)
@test integrate((a+b*sec(e+f*x)^2)^2*tan(e+f*x)^5, x) == :(-1*a^2*f^-1*log(cos(e+f*x))+1//4*f^-1*sec(e+f*x)^4*(a^2+b^2+-4*a*b)+1//8*b^2*f^-1*sec(e+f*x)^8+-1*a*f^-1*sec(e+f*x)^2*(a+-1b)+1//3*b*f^-1*sec(e+f*x)^6*(a+-1b))
@test integrate((a+b*sec(e+f*x)^2)^2*tan(e+f*x)^3, x) == :(a^2*f^-1*log(cos(e+f*x))+1//6*b^2*f^-1*sec(e+f*x)^6+(1/2)*a*f^-1*sec(e+f*x)^2*(a+-2b)+1//4*b*f^-1*sec(e+f*x)^4*(-1b+2a))
@test integrate((a+b*sec(e+f*x)^2)^2*tan(e+f*x), x) == :(-1*a^2*f^-1*log(cos(e+f*x))+1//4*b^2*f^-1*sec(e+f*x)^4+a*b*f^-1*sec(e+f*x)^2)
@test integrate((a+b*sec(e+f*x)^2)^2*cot(e+f*x), x) == :(f^-1*(a+b)^2*log(sin(e+f*x))+(1/2)*b^2*f^-1*sec(e+f*x)^2+-1*b*f^-1*(b+2a)*log(cos(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^2*cot(e+f*x)^3, x) == :(-1*b^2*f^-1*log(cos(e+f*x))+-1*f^-1*(a^2+-1*b^2)*log(sin(e+f*x))+-1//2*f^-1*(a+b)^2*csc(e+f*x)^2)
@test integrate((a+b*sec(e+f*x)^2)^2*cot(e+f*x)^5, x) == :(a^2*f^-1*log(sin(e+f*x))+-1//4*f^-1*(a+b)^2*csc(e+f*x)^4+a*f^-1*csc(e+f*x)^2*(a+b))
@test integrate((a+b*sec(e+f*x)^2)^2*tan(e+f*x)^6, x) == :(-1*x*a^2+a^2*f^-1*tan(e+f*x)+-1//3*a^2*f^-1*tan(e+f*x)^3+1//5*a^2*f^-1*tan(e+f*x)^5+1//9*b^2*f^-1*tan(e+f*x)^9+1//7*b*f^-1*tan(e+f*x)^7*(b+2a))
@test integrate((a+b*sec(e+f*x)^2)^2*tan(e+f*x)^4, x) == :(x*a^2+-1*a^2*f^-1*tan(e+f*x)+1//3*a^2*f^-1*tan(e+f*x)^3+1//7*b^2*f^-1*tan(e+f*x)^7+1//5*b*f^-1*tan(e+f*x)^5*(b+2a))
@test integrate((a+b*sec(e+f*x)^2)^2*tan(e+f*x)^2, x) == :(-1*x*a^2+a^2*f^-1*tan(e+f*x)+1//5*b^2*f^-1*tan(e+f*x)^5+1//3*b*f^-1*tan(e+f*x)^3*(b+2a))
@test integrate((a+b*sec(e+f*x)^2)^2, x) == :(x*a^2+1//3*b^2*f^-1*tan(e+f*x)^3+b*f^-1*(b+2a)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^2*cot(e+f*x)^2, x) == :(-1*x*a^2+b^2*f^-1*tan(e+f*x)+-1*f^-1*(a+b)^2*cot(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^2*cot(e+f*x)^4, x) == :(x*a^2+f^-1*(a^2+-1*b^2)*cot(e+f*x)+-1//3*f^-1*(a+b)^2*cot(e+f*x)^3)
@test integrate((a+b*sec(e+f*x)^2)^2*cot(e+f*x)^6, x) == :(-1*x*a^2+-1*a^2*f^-1*cot(e+f*x)+-1//5*f^-1*(a+b)^2*cot(e+f*x)^5+1//3*f^-1*cot(e+f*x)^3*(a^2+-1*b^2))
@test integrate((a+b*sec(e+f*x)^2)^-1*tan(e+f*x)^5, x) == :((1/2)*b^-1*f^-1*sec(e+f*x)^2+b^-2*f^-1*(a+2b)*log(cos(e+f*x))+-1//2*a^-1*b^-2*f^-1*(a+b)^2*log(b+a*cos(e+f*x)^2))
@test integrate((a+b*sec(e+f*x)^2)^-1*tan(e+f*x)^3, x) == :(-1*b^-1*f^-1*log(cos(e+f*x))+(1/2)*a^-1*b^-1*f^-1*(a+b)*log(b+a*cos(e+f*x)^2))
@test integrate((a+b*sec(e+f*x)^2)^-1*tan(e+f*x), x) == :(-1//2*a^-1*f^-1*log(b+a*cos(e+f*x)^2))
@test integrate((a+b*sec(e+f*x)^2)^-1*cot(e+f*x), x) == :(f^-1*(a+b)^-1*log(sin(e+f*x))+(1/2)*b*a^-1*f^-1*(a+b)^-1*log(b+a*cos(e+f*x)^2))
@test integrate((a+b*sec(e+f*x)^2)^-1*cot(e+f*x)^3, x) == :(-1*f^-1*(2a+2b)^-1*csc(e+f*x)^2+-1*f^-1*(a+b)^-2*(a+2b)*log(sin(e+f*x))+-1//2*a^-1*b^2*f^-1*(a+b)^-2*log(b+a*cos(e+f*x)^2))
@test integrate((a+b*sec(e+f*x)^2)^-1*cot(e+f*x)^5, x) == :(-1*f^-1*(4a+4b)^-1*csc(e+f*x)^4+f^-1*(a+b)^-3*(a^2+3*b^2+3*a*b)*log(sin(e+f*x))+(1/2)*f^-1*(a+b)^-2*csc(e+f*x)^2*(2a+3b)+(1/2)*a^-1*b^3*f^-1*(a+b)^-3*log(b+a*cos(e+f*x)^2))
@test integrate((a+b*sec(e+f*x)^2)^-1*tan(e+f*x)^6, x) == :(-1*x*a^-1+1//3*b^-1*f^-1*tan(e+f*x)^3+-1*b^-2*f^-1*(a+2b)*tan(e+f*x)+a^-1*b^-5//2*f^-1*(a+b)^5//2*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1*tan(e+f*x)^4, x) == :(x*a^-1+b^-1*f^-1*tan(e+f*x)+-1*a^-1*b^-3//2*f^-1*(a+b)^3//2*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1*tan(e+f*x)^2, x) == :(-1*x*a^-1+a^-1*b^-1//2*f^-1*(a+b)^(1/2)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1, x) == :(x*a^-1+a^-1*b^(1/2)*f^-1*(a+b)^-1//2*arctan(b^-1//2*(a+b)^(1/2)*cot(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1*cot(e+f*x)^2, x) == :(-1*x*a^-1+-1*f^-1*(a+b)^-1*cot(e+f*x)+a^-1*b^3//2*f^-1*(a+b)^-3//2*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1*cot(e+f*x)^4, x) == :(x*a^-1+-1*f^-1*(3a+3b)^-1*cot(e+f*x)^3+f^-1*(a+b)^-2*(a+2b)*cot(e+f*x)+-1*a^-1*b^5//2*f^-1*(a+b)^-5//2*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1*cot(e+f*x)^6, x) == :(-1*x*a^-1+-1*f^-1*(5a+5b)^-1*cot(e+f*x)^5+-1*f^-1*(a+b)^-3*(a^2+3*b^2+3*a*b)*cot(e+f*x)+1//3*f^-1*(a+b)^-2*cot(e+f*x)^3*(a+2b)+a^-1*b^7//2*f^-1*(a+b)^-7//2*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-2*tan(e+f*x)^5, x) == :(-1*b^-2*f^-1*log(cos(e+f*x))+-1//2*f^-1*(a^-2+-1*b^-2)*log(b+a*cos(e+f*x)^2)+-1//2*a^-2*b^-1*f^-1*(a+b)^2*(b+a*cos(e+f*x)^2)^-1)
@test integrate((a+b*sec(e+f*x)^2)^-2*tan(e+f*x)^3, x) == :((1/2)*a^-2*f^-1*log(b+a*cos(e+f*x)^2)+(1/2)*a^-2*f^-1*(b+a*cos(e+f*x)^2)^-1*(a+b))
@test integrate((a+b*sec(e+f*x)^2)^-2*tan(e+f*x), x) == :(-1//2*a^-2*f^-1*log(b+a*cos(e+f*x)^2)+-1//2*b*a^-2*f^-1*(b+a*cos(e+f*x)^2)^-1)
@test integrate((a+b*sec(e+f*x)^2)^-2*cot(e+f*x), x) == :(f^-1*(a+b)^-2*log(sin(e+f*x))+(1/2)*a^-2*b^2*f^-1*(a+b)^-1*(b+a*cos(e+f*x)^2)^-1+(1/2)*b*a^-2*f^-1*(a+b)^-2*(b+2a)*log(b+a*cos(e+f*x)^2))
@test integrate((a+b*sec(e+f*x)^2)^-2*cot(e+f*x)^3, x) == :(-1//2*f^-1*(a+b)^-2*csc(e+f*x)^2+-1*f^-1*(a+b)^-3*(a+3b)*log(sin(e+f*x))+-1//2*a^-2*b^3*f^-1*(a+b)^-2*(b+a*cos(e+f*x)^2)^-1+-1//2*a^-2*b^2*f^-1*(a+b)^-3*(b+3a)*log(b+a*cos(e+f*x)^2))
@test integrate((a+b*sec(e+f*x)^2)^-2*cot(e+f*x)^5, x) == :(-1//4*f^-1*(a+b)^-2*csc(e+f*x)^4+f^-1*(a+b)^-4*(a^2+6*b^2+4*a*b)*log(sin(e+f*x))+f^-1*(a+b)^-3*csc(e+f*x)^2*(a+2b)+(1/2)*a^-2*b^4*f^-1*(a+b)^-3*(b+a*cos(e+f*x)^2)^-1+(1/2)*a^-2*b^3*f^-1*(a+b)^-4*(b+4a)*log(b+a*cos(e+f*x)^2))
@test integrate((a+b*sec(e+f*x)^2)^-2*tan(e+f*x)^6, x) == :(-1*x*a^-2+(1/2)*a^-1*b^-2*f^-1*(b+3a)*tan(e+f*x)+-1//2*a^-1*b^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-1*tan(e+f*x)^3*(a+b)+-1//2*a^-2*b^-5//2*f^-1*(a+b)^3//2*(-2b+3a)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-2*tan(e+f*x)^4, x) == :(x*a^-2+(1/2)*a^-2*b^-3//2*f^-1*(a+b)^(1/2)*(a+-2b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+-1//2*a^-1*b^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-1*(a+b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-2*tan(e+f*x)^2, x) == :(-1*x*a^-2+(1/2)*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-1*tan(e+f*x)+(1/2)*a^-2*b^-1//2*f^-1*(a+b)^-1//2*(a+2b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-2, x) == :(x*a^-2+-1//2*b*a^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1*tan(e+f*x)+-1//2*a^-2*b^(1/2)*f^-1*(a+b)^-3//2*(2b+3a)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-2*cot(e+f*x)^2, x) == :(-1*x*a^-2+-1//2*a^-1*f^-1*(a+b)^-2*(-1b+2a)*cot(e+f*x)+(1/2)*a^-2*b^3//2*f^-1*(a+b)^-5//2*(2b+5a)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+-1//2*b*a^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1*cot(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-2*cot(e+f*x)^4, x) == :(x*a^-2+(1/2)*a^-1*f^-1*(a+b)^-3*(-1*b^2+2*a^2+6*a*b)*cot(e+f*x)+-1//6*a^-1*f^-1*(a+b)^-2*cot(e+f*x)^3*(-3b+2a)+-1//2*b*a^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1*cot(e+f*x)^3+-1//2*a^-2*b^5//2*f^-1*(a+b)^-7//2*(2b+7a)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-2*cot(e+f*x)^6, x) == :(-1*x*a^-2+-1//2*a^-1*f^-1*(a+b)^-4*(-1*b^3+2*a^3+8*b*a^2+12*a*b^2)*cot(e+f*x)+-1//10*a^-1*f^-1*(a+b)^-2*cot(e+f*x)^5*(-5b+2a)+1//6*a^-1*f^-1*(a+b)^-3*cot(e+f*x)^3*(-3*b^2+2*a^2+6*a*b)+(1/2)*a^-2*b^7//2*f^-1*(a+b)^-9//2*(2b+9a)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+-1//2*b*a^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1*cot(e+f*x)^5)
@test integrate((a+b*sec(e+f*x)^2)^-3*tan(e+f*x)^5, x) == :(-1//2*a^-3*f^-1*log(b+a*cos(e+f*x)^2)+-1*a^-3*f^-1*(b+a*cos(e+f*x)^2)^-1*(a+b)+1//4*a^-3*f^-1*(a+b)^2*(b+a*cos(e+f*x)^2)^-2)
@test integrate((a+b*sec(e+f*x)^2)^-3*tan(e+f*x)^3, x) == :((1/2)*a^-3*f^-1*log(b+a*cos(e+f*x)^2)+(1/2)*a^-3*f^-1*(b+a*cos(e+f*x)^2)^-1*(a+2b)+-1//4*b*a^-3*f^-1*(b+a*cos(e+f*x)^2)^-2*(a+b))
@test integrate((a+b*sec(e+f*x)^2)^-3*tan(e+f*x), x) == :(-1//2*a^-3*f^-1*log(b+a*cos(e+f*x)^2)+-1*b*a^-3*f^-1*(b+a*cos(e+f*x)^2)^-1+1//4*a^-3*b^2*f^-1*(b+a*cos(e+f*x)^2)^-2)
@test integrate((a+b*sec(e+f*x)^2)^-3*cot(e+f*x), x) == :(f^-1*(a+b)^-3*log(sin(e+f*x))+-1//4*a^-3*b^3*f^-1*(a+b)^-1*(b+a*cos(e+f*x)^2)^-2+(1/2)*b*a^-3*f^-1*(a+b)^-3*(b^2+3*a^2+3*a*b)*log(b+a*cos(e+f*x)^2)+(1/2)*a^-3*b^2*f^-1*(a+b)^-2*(b+a*cos(e+f*x)^2)^-1*(2b+3a))
@test integrate((a+b*sec(e+f*x)^2)^-3*cot(e+f*x)^3, x) == :(-1//2*f^-1*(a+b)^-3*csc(e+f*x)^2+-1*f^-1*(a+b)^-4*(a+4b)*log(sin(e+f*x))+1//4*a^-3*b^4*f^-1*(a+b)^-2*(b+a*cos(e+f*x)^2)^-2+-1*a^-3*b^3*f^-1*(a+b)^-3*(b+a*cos(e+f*x)^2)^-1*(b+2a)+-1//2*a^-3*b^2*f^-1*(a+b)^-4*(b^2+6*a^2+4*a*b)*log(b+a*cos(e+f*x)^2))
@test integrate((a+b*sec(e+f*x)^2)^-3*cot(e+f*x)^5, x) == :(-1//4*f^-1*(a+b)^-3*csc(e+f*x)^4+f^-1*(a+b)^-5*(a^2+10*b^2+5*a*b)*log(sin(e+f*x))+(1/2)*f^-1*(a+b)^-4*csc(e+f*x)^2*(2a+5b)+-1//4*a^-3*b^5*f^-1*(a+b)^-3*(b+a*cos(e+f*x)^2)^-2+(1/2)*a^-3*b^3*f^-1*(a+b)^-5*(b^2+10*a^2+5*a*b)*log(b+a*cos(e+f*x)^2)+(1/2)*a^-3*b^4*f^-1*(a+b)^-4*(b+a*cos(e+f*x)^2)^-1*(2b+5a))
@test integrate((a+b*sec(e+f*x)^2)^-3*tan(e+f*x)^6, x) == :(-1*x*a^-3+-1//4*a^-1*b^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-2*tan(e+f*x)^3*(a+b)+1//8*a^-3*b^-5//2*f^-1*(a+b)^(1/2)*(3*a^2+8*b^2+-4*a*b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+-1//8*a^-2*b^-2*f^-1*(a+b+b*tan(e+f*x)^2)^-1*(a+b)*(-4b+3a)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3*tan(e+f*x)^4, x) == :(x*a^-3+-1//4*a^-1*b^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-2*(a+b)*tan(e+f*x)+1//8*a^-3*b^-3//2*f^-1*(a+b)^-1//2*(a^2+-8*b^2+-4*a*b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+1//8*a^-2*b^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-1*(a+-4b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3*tan(e+f*x)^2, x) == :(-1*x*a^-3+1//4*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-2*tan(e+f*x)+1//8*a^-3*b^-1//2*f^-1*(a+b)^-3//2*(3*a^2+8*b^2+12*a*b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+1//8*a^-2*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1*(3a+4b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3, x) == :(x*a^-3+-1//4*b*a^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-2*tan(e+f*x)+-1//8*a^-3*b^(1/2)*f^-1*(a+b)^-5//2*(8*b^2+15*a^2+20*a*b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+-1//8*b*a^-2*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1*(4b+7a)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3*cot(e+f*x)^2, x) == :(-1*x*a^-3+-1//8*a^-2*f^-1*(a+b)^-3*(-4*b^2+8*a^2+-11*a*b)*cot(e+f*x)+-1//4*b*a^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-2*cot(e+f*x)+1//8*a^-3*b^3//2*f^-1*(a+b)^-7//2*(8*b^2+35*a^2+28*a*b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+-1//8*b*a^-2*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1*(4b+9a)*cot(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3*cot(e+f*x)^4, x) == :(x*a^-3+-1//24*a^-2*f^-1*(a+b)^-3*cot(e+f*x)^3*(-12*b^2+8*a^2+-39*a*b)+1//8*a^-2*f^-1*(a+b)^-4*(-4*b^3+8*a^3+-15*a*b^2+32*b*a^2)*cot(e+f*x)+-1//4*b*a^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-2*cot(e+f*x)^3+-1//8*a^-3*b^5//2*f^-1*(a+b)^-9//2*(8*b^2+63*a^2+36*a*b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+-1//8*b*a^-2*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1*cot(e+f*x)^3*(4b+11a))
@test integrate((a+b*sec(e+f*x)^2)^-3*cot(e+f*x)^6, x) == :(-1*x*a^-3+-1//8*a^-2*f^-1*(a+b)^-5*(-4*b^4+8*a^4+-19*a*b^3+40*b*a^3+80*a^2*b^2)*cot(e+f*x)+-1//40*a^-2*f^-1*(a+b)^-3*cot(e+f*x)^5*(-20*b^2+8*a^2+-75*a*b)+1//24*a^-2*f^-1*(a+b)^-4*cot(e+f*x)^3*(-12*b^3+8*a^3+-51*a*b^2+32*b*a^2)+-1//4*b*a^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-2*cot(e+f*x)^5+1//8*a^-3*b^7//2*f^-1*(a+b)^-11//2*(8*b^2+99*a^2+44*a*b)*arctan(b^(1/2)*(a+b)^-1//2*tan(e+f*x))+-1//8*b*a^-2*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1*cot(e+f*x)^5*(4b+13a))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*tan(e+f*x)^5, x) == :(f^-1*(a+b*sec(e+f*x)^2)^(1/2)+-1*a^(1/2)*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+1//5*b^-2*f^-1*(a+b*sec(e+f*x)^2)^5//2+-1//3*b^-2*f^-1*(a+b*sec(e+f*x)^2)^3//2*(a+2b))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*tan(e+f*x)^3, x) == :(-1*f^-1*(a+b*sec(e+f*x)^2)^(1/2)+a^(1/2)*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+1//3*b^-1*f^-1*(a+b*sec(e+f*x)^2)^3//2)
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*tan(e+f*x), x) == :(f^-1*(a+b*sec(e+f*x)^2)^(1/2)+-1*a^(1/2)*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2)))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*cot(e+f*x), x) == :(a^(1/2)*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+-1*f^-1*(a+b)^(1/2)*arctanh((a+b)^-1//2*(a+b*sec(e+f*x)^2)^(1/2)))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*cot(e+f*x)^3, x) == :(-1*a^(1/2)*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+-1//2*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*cot(e+f*x)^2+(1/2)*f^-1*(a+b)^-1//2*(b+2a)*arctanh((a+b)^-1//2*(a+b*sec(e+f*x)^2)^(1/2)))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*cot(e+f*x)^5, x) == :(a^(1/2)*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+-1//4*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*cot(e+f*x)^4+-1//8*f^-1*(a+b)^-3//2*(3*b^2+8*a^2+12*a*b)*arctanh((a+b)^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(8a+8b)^-1*cot(e+f*x)^2*(3b+4a))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*tan(e+f*x)^6, x) == :(-1*a^(1/2)*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//6*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^5+1//16*b^-5//2*f^-1*(a^3+-5*b^3+5*b*a^2+15*a*b^2)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//24*b^-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^3*(a+-5b)+-1//16*b^-2*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(a+-1b)*(a+5b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*tan(e+f*x)^4, x) == :(a^(1/2)*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//4*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^3+-1//8*b^-3//2*f^-1*(a^2+-3*b^2+6*a*b)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//8*b^-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(a+-3b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*tan(e+f*x)^2, x) == :((1/2)*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)+-1*a^(1/2)*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+(1/2)*b^-1//2*f^-1*(a+-1b)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^(1/2), x) == :(a^(1/2)*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+b^(1/2)*f^-1*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*cot(e+f*x)^2, x) == :(-1*a^(1/2)*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*cot(e+f*x)^4, x) == :(a^(1/2)*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//3*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^3+f^-1*(3a+3b)^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(2b+3a)*cot(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^(1/2)*cot(e+f*x)^6, x) == :(-1*a^(1/2)*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//5*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^5+-1*f^-1*(15a+15b)^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^3*(-5a+-4b)+-1//15*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^(1/2)*(8*b^2+15*a^2+25*a*b)*cot(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^3//2*tan(e+f*x)^5, x) == :(1//3*f^-1*(a+b*sec(e+f*x)^2)^3//2+a*f^-1*(a+b*sec(e+f*x)^2)^(1/2)+-1*a^3//2*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+1//7*b^-2*f^-1*(a+b*sec(e+f*x)^2)^7//2+-1//5*b^-2*f^-1*(a+b*sec(e+f*x)^2)^5//2*(a+2b))
@test integrate((a+b*sec(e+f*x)^2)^3//2*tan(e+f*x)^3, x) == :(-1//3*f^-1*(a+b*sec(e+f*x)^2)^3//2+a^3//2*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+-1*a*f^-1*(a+b*sec(e+f*x)^2)^(1/2)+1//5*b^-1*f^-1*(a+b*sec(e+f*x)^2)^5//2)
@test integrate((a+b*sec(e+f*x)^2)^3//2*tan(e+f*x), x) == :(1//3*f^-1*(a+b*sec(e+f*x)^2)^3//2+a*f^-1*(a+b*sec(e+f*x)^2)^(1/2)+-1*a^3//2*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2)))
@test integrate((a+b*sec(e+f*x)^2)^3//2*cot(e+f*x), x) == :(b*f^-1*(a+b*sec(e+f*x)^2)^(1/2)+a^3//2*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+-1*f^-1*(a+b)^3//2*arctanh((a+b)^-1//2*(a+b*sec(e+f*x)^2)^(1/2)))
@test integrate((a+b*sec(e+f*x)^2)^3//2*cot(e+f*x)^3, x) == :(-1*a^3//2*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+(1/2)*f^-1*(a+b)^(1/2)*(-1b+2a)*arctanh((a+b)^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+-1//2*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*cot(e+f*x)^2*(a+b))
@test integrate((a+b*sec(e+f*x)^2)^3//2*cot(e+f*x)^5, x) == :(a^3//2*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+-1//4*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*cot(e+f*x)^4*(a+b)+-1//8*f^-1*(a+b)^-1//2*(-1*b^2+8*a^2+4*a*b)*arctanh((a+b)^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+1//8*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*cot(e+f*x)^2*(-1b+4a))
@test integrate((a+b*sec(e+f*x)^2)^3//2*tan(e+f*x)^6, x) == :(-1*a^3//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//8*b*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^7+1//48*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^5*(b+9a)+1//128*b^-5//2*f^-1*(-5*b^4+3*a^4+-60*a*b^3+20*b*a^3+90*a^2*b^2)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//128*b^-2*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(-5*b^3+3*a^3+-55*a*b^2+17*b*a^2)*tan(e+f*x)+1//192*b^-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^3*(-5*b^2+3*a^2+-50*a*b))
@test integrate((a+b*sec(e+f*x)^2)^3//2*tan(e+f*x)^4, x) == :(a^3//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//6*b*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^5+1//24*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^3*(b+7a)+-1//16*b^-3//2*f^-1*(a+-1b)*(a^2+b^2+10*a*b)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//16*b^-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(a^2+-1*b^2+-8*a*b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^3//2*tan(e+f*x)^2, x) == :(-1*a^3//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//4*b*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^3+1//8*b^-1//2*f^-1*(-1*b^2+3*a^2+-6*a*b)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//8*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(b+5a)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^3//2, x) == :(a^3//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+(1/2)*b*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)+(1/2)*b^(1/2)*f^-1*(b+3a)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^3//2*cot(e+f*x)^2, x) == :(b^3//2*f^-1*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*a^3//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(a+b)*cot(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^3//2*cot(e+f*x)^4, x) == :(a^3//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//3*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^3*(a+b)+1//3*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(-1b+3a)*cot(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^3//2*cot(e+f*x)^6, x) == :(-1*a^3//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//5*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^5*(a+b)+1//15*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^3*(-1b+5a)+-1*f^-1*(15a+15b)^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(-2*b^2+15*a^2+10*a*b)*cot(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*tan(e+f*x)^5, x) == :(-1*a^-1//2*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+1//3*b^-2*f^-1*(a+b*sec(e+f*x)^2)^3//2+-1*b^-2*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(a+2b))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*tan(e+f*x)^3, x) == :(a^-1//2*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+b^-1*f^-1*(a+b*sec(e+f*x)^2)^(1/2))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*tan(e+f*x), x) == :(-1*a^-1//2*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2)))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*cot(e+f*x), x) == :(a^-1//2*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+-1*f^-1*(a+b)^-1//2*arctanh((a+b)^-1//2*(a+b*sec(e+f*x)^2)^(1/2)))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*cot(e+f*x)^3, x) == :(-1*a^-1//2*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+(1/2)*f^-1*(a+b)^-3//2*(2a+3b)*arctanh((a+b)^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+-1*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(2a+2b)^-1*cot(e+f*x)^2)
@test integrate((a+b*sec(e+f*x)^2)^-1//2*cot(e+f*x)^5, x) == :(a^-1//2*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+-1*f^-1*(a+b*sec(e+f*x)^2)^(1/2)*(4a+4b)^-1*cot(e+f*x)^4+-1//8*f^-1*(a+b)^-5//2*(8*a^2+15*b^2+20*a*b)*arctanh((a+b)^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+1//8*f^-1*(a+b)^-2*(a+b*sec(e+f*x)^2)^(1/2)*cot(e+f*x)^2*(4a+7b))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*tan(e+f*x)^6, x) == :(-1*a^-1//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//4*b^-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)^3+1//8*b^-5//2*f^-1*(3*a^2+15*b^2+10*a*b)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//8*b^-2*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(3a+7b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*tan(e+f*x)^4, x) == :(a^-1//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+(1/2)*b^-1*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*tan(e+f*x)+-1//2*b^-3//2*f^-1*(a+3b)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*tan(e+f*x)^2, x) == :(b^-1//2*f^-1*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*a^-1//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1//2, x) == :(a^-1//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*cot(e+f*x)^2, x) == :(-1*a^-1//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*cot(e+f*x)^4, x) == :(a^-1//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*f^-1*(3a+3b)^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^3+1//3*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^(1/2)*(3a+5b)*cot(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-1//2*cot(e+f*x)^6, x) == :(-1*a^-1//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*f^-1*(5a+5b)^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^5+-1//15*f^-1*(a+b)^-3*(a+b+b*tan(e+f*x)^2)^(1/2)*(15*a^2+33*b^2+40*a*b)*cot(e+f*x)+1//15*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^3*(5a+9b))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*tan(e+f*x)^5, x) == :(b^-2*f^-1*(a+b*sec(e+f*x)^2)^(1/2)+-1*a^-3//2*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+a^-1*b^-2*f^-1*(a+b)^2*(a+b*sec(e+f*x)^2)^-1//2)
@test integrate((a+b*sec(e+f*x)^2)^-3//2*tan(e+f*x)^3, x) == :(a^-3//2*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+-1*a^-1*b^-1*f^-1*(a+b*sec(e+f*x)^2)^-1//2*(a+b))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*tan(e+f*x), x) == :(a^-1*f^-1*(a+b*sec(e+f*x)^2)^-1//2+-1*a^-3//2*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2)))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*cot(e+f*x), x) == :(a^-3//2*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+-1*f^-1*(a+b)^-3//2*arctanh((a+b)^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+-1*b*a^-1*f^-1*(a+b)^-1*(a+b*sec(e+f*x)^2)^-1//2)
@test integrate((a+b*sec(e+f*x)^2)^-3//2*cot(e+f*x)^3, x) == :(-1*a^-3//2*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+(1/2)*f^-1*(a+b)^-5//2*(2a+5b)*arctanh((a+b)^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+-1*f^-1*(a+b*sec(e+f*x)^2)^-1//2*(2a+2b)^-1*cot(e+f*x)^2+-1//2*b*a^-1*f^-1*(a+b)^-2*(a+b*sec(e+f*x)^2)^-1//2*(a+-2b))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*cot(e+f*x)^5, x) == :(a^-3//2*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+-1*f^-1*(a+b*sec(e+f*x)^2)^-1//2*(4a+4b)^-1*cot(e+f*x)^4+-1//8*f^-1*(a+b)^-7//2*(8*a^2+35*b^2+28*a*b)*arctanh((a+b)^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+1//8*f^-1*(a+b)^-2*(a+b*sec(e+f*x)^2)^-1//2*cot(e+f*x)^2*(4a+9b)+1//8*b*a^-1*f^-1*(a+b)^-3*(a+b*sec(e+f*x)^2)^-1//2*(-8*b^2+4*a^2+11*a*b))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*tan(e+f*x)^6, x) == :(-1*a^-3//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//2*b^-5//2*f^-1*(3a+5b)*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+(1/2)*a^-1*b^-2*f^-1*(a+b+b*tan(e+f*x)^2)^(1/2)*(2b+3a)*tan(e+f*x)+-1*a^-1*b^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x)^3*(a+b))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*tan(e+f*x)^4, x) == :(a^-3//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+b^-3//2*f^-1*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*a^-1*b^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-1//2*(a+b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*tan(e+f*x)^2, x) == :(-1*a^-3//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3//2, x) == :(a^-3//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*b*a^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*cot(e+f*x)^2, x) == :(-1*a^-3//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*b*a^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)+-1*a^-1*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^(1/2)*(a+-1b)*cot(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*cot(e+f*x)^4, x) == :(a^-3//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*b*a^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)^3+-1//3*a^-1*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^3*(a+-3b)+1//3*a^-1*f^-1*(a+b)^-3*(a+b+b*tan(e+f*x)^2)^(1/2)*(a+3b)*(-1b+3a)*cot(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-3//2*cot(e+f*x)^6, x) == :(-1*a^-3//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*b*a^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)^5+-1//5*a^-1*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^5*(a+-5b)+-1//15*a^-1*f^-1*(a+b)^-4*(a+b+b*tan(e+f*x)^2)^(1/2)*(-15*b^3+15*a^3+55*b*a^2+73*a*b^2)*cot(e+f*x)+1//15*a^-1*f^-1*(a+b)^-3*(a+b+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^3*(-15*b^2+5*a^2+14*a*b))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*tan(e+f*x)^5, x) == :(f^-1*(a+b*sec(e+f*x)^2)^-1//2*(a^-2+-1*b^-2)+-1*a^-5//2*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+1//3*a^-1*b^-2*f^-1*(a+b)^2*(a+b*sec(e+f*x)^2)^-3//2)
@test integrate((a+b*sec(e+f*x)^2)^-5//2*tan(e+f*x)^3, x) == :(a^-5//2*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+-1*a^-2*f^-1*(a+b*sec(e+f*x)^2)^-1//2+-1//3*a^-1*b^-1*f^-1*(a+b*sec(e+f*x)^2)^-3//2*(a+b))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*tan(e+f*x), x) == :(a^-2*f^-1*(a+b*sec(e+f*x)^2)^-1//2+-1*a^-5//2*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+1//3*a^-1*f^-1*(a+b*sec(e+f*x)^2)^-3//2)
@test integrate((a+b*sec(e+f*x)^2)^-5//2*cot(e+f*x), x) == :(a^-5//2*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+-1*f^-1*(a+b)^-5//2*arctanh((a+b)^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+-1//3*b*a^-1*f^-1*(a+b)^-1*(a+b*sec(e+f*x)^2)^-3//2+-1*b*a^-2*f^-1*(a+b)^-2*(a+b*sec(e+f*x)^2)^-1//2*(b+2a))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*cot(e+f*x)^3, x) == :(-1*a^-5//2*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+(1/2)*f^-1*(a+b)^-7//2*(2a+7b)*arctanh((a+b)^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+-1*f^-1*(a+b*sec(e+f*x)^2)^-3//2*(2a+2b)^-1*cot(e+f*x)^2+-1//2*b*a^-2*f^-1*(a+b)^-3*(a+b*sec(e+f*x)^2)^-1//2*(a^2+-2*b^2+-6*a*b)+-1//6*b*a^-1*f^-1*(a+b)^-2*(a+b*sec(e+f*x)^2)^-3//2*(-2b+3a))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*cot(e+f*x)^5, x) == :(a^-5//2*f^-1*arctanh(a^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+-1*f^-1*(a+b*sec(e+f*x)^2)^-3//2*(4a+4b)^-1*cot(e+f*x)^4+-1//8*f^-1*(a+b)^-9//2*(8*a^2+63*b^2+36*a*b)*arctanh((a+b)^-1//2*(a+b*sec(e+f*x)^2)^(1/2))+1//8*f^-1*(a+b)^-2*(a+b*sec(e+f*x)^2)^-3//2*cot(e+f*x)^2*(4a+11b)+1//8*b*a^-2*f^-1*(a+b)^-4*(a+b*sec(e+f*x)^2)^-1//2*(-8*b^3+4*a^3+-32*a*b^2+15*b*a^2)+1//24*b*a^-1*f^-1*(a+b)^-3*(a+b*sec(e+f*x)^2)^-3//2*(-8*b^2+12*a^2+39*a*b))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*tan(e+f*x)^6, x) == :(b^-5//2*f^-1*arctanh(b^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1*a^-5//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+f^-1*(a+b+b*tan(e+f*x)^2)^-1//2*(a^-2+-1*b^-2)*tan(e+f*x)+-1//3*a^-1*b^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-3//2*tan(e+f*x)^3*(a+b))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*tan(e+f*x)^4, x) == :(a^-5//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//3*a^-1*b^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-3//2*(a+b)*tan(e+f*x)+1//3*a^-2*b^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-1//2*(a+-3b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*tan(e+f*x)^2, x) == :(-1*a^-5//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+1//3*a^-1*f^-1*(a+b+b*tan(e+f*x)^2)^-3//2*tan(e+f*x)+1//3*a^-2*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-1//2*(2a+3b)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-5//2, x) == :(a^-5//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//3*b*a^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-3//2*tan(e+f*x)+-1//3*b*a^-2*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1//2*(3b+5a)*tan(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*cot(e+f*x)^2, x) == :(-1*a^-5//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//3*b*a^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-3//2*cot(e+f*x)+-1//3*b*a^-2*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1//2*(3b+7a)*cot(e+f*x)+-1//3*a^-2*f^-1*(a+b)^-3*(a+b+b*tan(e+f*x)^2)^(1/2)*(a+-3b)*(b+3a)*cot(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*cot(e+f*x)^4, x) == :(a^-5//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//3*b*a^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-3//2*cot(e+f*x)^3+-1//3*a^-2*f^-1*(a+b)^-3*(a+b+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^3*(a^2+-3*b^2+-10*a*b)+-1*b*a^-2*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)^3*(b+3a)+1//3*a^-2*f^-1*(a+b)^-4*(a+b+b*tan(e+f*x)^2)^(1/2)*(a+-1b)*(3*a^2+3*b^2+14*a*b)*cot(e+f*x))
@test integrate((a+b*sec(e+f*x)^2)^-5//2*cot(e+f*x)^6, x) == :(-1*a^-5//2*f^-1*arctan(a^(1/2)*(a+b+b*tan(e+f*x)^2)^-1//2*tan(e+f*x))+-1//3*b*a^-1*f^-1*(a+b)^-1*(a+b+b*tan(e+f*x)^2)^-3//2*cot(e+f*x)^5+-1//5*a^-2*f^-1*(a+b)^-3*(a+b+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^5*(a^2+-5*b^2+-20*a*b)+-1//15*a^-2*f^-1*(a+b)^-5*(a+b+b*tan(e+f*x)^2)^(1/2)*(-15*b^4+15*a^4+-70*a*b^3+70*b*a^3+128*a^2*b^2)*cot(e+f*x)+1//15*a^-2*f^-1*(a+b)^-4*(a+b+b*tan(e+f*x)^2)^(1/2)*cot(e+f*x)^3*(-15*b^3+5*a^3+-65*a*b^2+19*b*a^2)+-1//3*b*a^-2*f^-1*(a+b)^-2*(a+b+b*tan(e+f*x)^2)^-1//2*cot(e+f*x)^5*(3b+11a))
@test integrate(tan(e+f*x)^5*(a+b*sec(e+f*x)^3), x) == :(-1*a*f^-1*sec(e+f*x)^2+-1*a*f^-1*log(cos(e+f*x))+-2//5*b*f^-1*sec(e+f*x)^5+1//3*b*f^-1*sec(e+f*x)^3+1//4*a*f^-1*sec(e+f*x)^4+1//7*b*f^-1*sec(e+f*x)^7)
@test integrate(tan(e+f*x)^3*(a+b*sec(e+f*x)^3), x) == :(a*f^-1*log(cos(e+f*x))+(1/2)*a*f^-1*sec(e+f*x)^2+-1//3*b*f^-1*sec(e+f*x)^3+1//5*b*f^-1*sec(e+f*x)^5)
@test integrate((a+b*sec(e+f*x)^3)*tan(e+f*x), x) == :(-1*a*f^-1*log(cos(e+f*x))+1//3*b*f^-1*sec(e+f*x)^3)
@test integrate((a+b*sec(e+f*x)^3)*cot(e+f*x), x) == :(b*f^-1*sec(e+f*x)+(1/2)*f^-1*(a+b)*log(1+-1*cos(e+f*x))+(1/2)*f^-1*(a+-1b)*log(1+cos(e+f*x)))
@test integrate(cot(e+f*x)^3*(a+b*sec(e+f*x)^3), x) == :(-1//2*f^-1*csc(e+f*x)^2*(a+b*cos(e+f*x))+-1//4*f^-1*(b+2a)*log(1+cos(e+f*x))+-1//4*f^-1*(-1b+2a)*log(1+-1*cos(e+f*x)))
@test integrate((a+b*sec(e+f*x)^3)^-1*tan(e+f*x)^5, x) == :(b^-1*f^-1*sec(e+f*x)+-1//3*a^-1*f^-1*log(b+a*cos(e+f*x)^3)+-1//3*a^-1//3*b^-4//3*f^-1*(a^2//3+-2*b^2//3)*log(b^1//3+a^1//3*cos(e+f*x))+1//6*a^-1//3*b^-4//3*f^-1*(a^2//3+-2*b^2//3)*log(b^2//3+a^2//3*cos(e+f*x)^2+-1*a^1//3*b^1//3*cos(e+f*x))+-1//3*3^(1/2)*a^-1//3*b^-4//3*f^-1*(a^2//3+2*b^2//3)*arctan(1//3*3^(1/2)*b^-1//3*(b^1//3+-2*a^1//3*cos(e+f*x))))
@test integrate((a+b*sec(e+f*x)^3)^-1*tan(e+f*x)^3, x) == :(1//3*a^-1*f^-1*log(b+a*cos(e+f*x)^3)+-1//3*a^-1//3*b^-2//3*f^-1*log(b^1//3+a^1//3*cos(e+f*x))+1//6*a^-1//3*b^-2//3*f^-1*log(b^2//3+a^2//3*cos(e+f*x)^2+-1*a^1//3*b^1//3*cos(e+f*x))+1//3*3^(1/2)*a^-1//3*b^-2//3*f^-1*arctan(1//3*3^(1/2)*b^-1//3*(b^1//3+-2*a^1//3*cos(e+f*x))))
@test integrate((a+b*sec(e+f*x)^3)^-1*tan(e+f*x), x) == :(-1//3*a^-1*f^-1*log(b+a*cos(e+f*x)^3))
@test integrate((a+b*sec(e+f*x)^3)^-1*cot(e+f*x), x) == :(f^-1*(-2b+2a)^-1*log(1+cos(e+f*x))+f^-1*(2a+2b)^-1*log(1+-1*cos(e+f*x))+-1//3*a^-1*b^2*f^-1*(a^2+-1*b^2)^-1*log(b+a*cos(e+f*x)^3)+-1//3*3^(1/2)*a^-1//3*b^2//3*f^-1*(a^4//3+b^4//3+a^2//3*b^2//3)^-1*arctan(1//3*3^(1/2)*b^-1//3*(b^1//3+-2*a^1//3*cos(e+f*x)))+-1//3*a^-1//3*b^2//3*f^-1*(a^2+-1*b^2)^-1*(a^2//3+b^2//3)*log(b^1//3+a^1//3*cos(e+f*x))+1//6*a^-1//3*b^2//3*f^-1*(a^2+-1*b^2)^-1*(a^2//3+b^2//3)*log(b^2//3+a^2//3*cos(e+f*x)^2+-1*a^1//3*b^1//3*cos(e+f*x)))
@test integrate((a+b*sec(e+f*x)^3)^-1*cot(e+f*x)^3, x) == :(-1*f^-1*(1+-1*cos(e+f*x))^-1*(4a+4b)^-1+-1*f^-1*(1+cos(e+f*x))^-1*(-4b+4a)^-1+-1//4*f^-1*(a+b)^-2*(2a+5b)*log(1+-1*cos(e+f*x))+-1//4*f^-1*(a+-1b)^-2*(-5b+2a)*log(1+cos(e+f*x))+-1//3*a^-1*b^2*f^-1*(a^2+-1*b^2)^-2*(b^2+2*a^2)*log(b+a*cos(e+f*x)^3)+-1//3*a^-1//3*b^4//3*f^-1*(a^2+-1*b^2)^-2*(a^2+2*b^2+3*a^2//3*b^4//3)*log(b^1//3+a^1//3*cos(e+f*x))+1//6*a^-1//3*b^4//3*f^-1*(a^2+-1*b^2)^-2*(a^2+2*b^2+3*a^2//3*b^4//3)*log(b^2//3+a^2//3*cos(e+f*x)^2+-1*a^1//3*b^1//3*cos(e+f*x))+1//3*3^(1/2)*a^-1//3*b^4//3*f^-1*(a^2+-1*b^2)^-2*(a^2+2*b^2+-3*a^2//3*b^4//3)*arctan(1//3*3^(1/2)*b^-1//3*(b^1//3+-2*a^1//3*cos(e+f*x))))

max_stars_repo_path: test/4 Trig functions/4.5 Secant/4.5.7 (d trig)^m (a+b (c sec)^n)^p.jl