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

@test integrate(tan(c+d*x)^5*(a+im*a*tan(c+d*x)), x) == :(-1*im*a*x+-1*a*d^-1*log(cos(c+d*x))+-1//2*a*d^-1*tan(c+d*x)^2+1//4*a*d^-1*tan(c+d*x)^4+im*a*d^-1*tan(c+d*x)+-1//3*im*a*d^-1*tan(c+d*x)^3+1//5*im*a*d^-1*tan(c+d*x)^5)
@test integrate(tan(c+d*x)^4*(a+im*a*tan(c+d*x)), x) == :(a*x+-1*a*d^-1*tan(c+d*x)+1//3*a*d^-1*tan(c+d*x)^3+-1*im*a*d^-1*log(cos(c+d*x))+-1//2*im*a*d^-1*tan(c+d*x)^2+1//4*im*a*d^-1*tan(c+d*x)^4)
@test integrate(tan(c+d*x)^3*(a+im*a*tan(c+d*x)), x) == :(im*a*x+a*d^-1*log(cos(c+d*x))+(1/2)*a*d^-1*tan(c+d*x)^2+-1*im*a*d^-1*tan(c+d*x)+1//3*im*a*d^-1*tan(c+d*x)^3)
@test integrate(tan(c+d*x)^2*(a+im*a*tan(c+d*x)), x) == :(-1*a*x+a*d^-1*tan(c+d*x)+im*a*d^-1*log(cos(c+d*x))+(1/2)*im*a*d^-1*tan(c+d*x)^2)
@test integrate((a+im*a*tan(c+d*x))*tan(c+d*x), x) == :(-1*im*a*x+-1*a*d^-1*log(cos(c+d*x))+im*a*d^-1*tan(c+d*x))
@test integrate(a+im*a*tan(c+d*x), x) == :(a*x+-1*im*a*d^-1*log(cos(c+d*x)))
@test integrate((a+im*a*tan(c+d*x))*cot(c+d*x), x) == :(im*a*x+a*d^-1*log(sin(c+d*x)))
@test integrate(cot(c+d*x)^2*(a+im*a*tan(c+d*x)), x) == :(-1*a*x+-1*a*d^-1*cot(c+d*x)+im*a*d^-1*log(sin(c+d*x)))
@test integrate(cot(c+d*x)^3*(a+im*a*tan(c+d*x)), x) == :(-1*im*a*x+-1*a*d^-1*log(sin(c+d*x))+-1//2*a*d^-1*cot(c+d*x)^2+-1*im*a*d^-1*cot(c+d*x))
@test integrate(cot(c+d*x)^4*(a+im*a*tan(c+d*x)), x) == :(a*x+a*d^-1*cot(c+d*x)+-1//3*a*d^-1*cot(c+d*x)^3+-1*im*a*d^-1*log(sin(c+d*x))+-1//2*im*a*d^-1*cot(c+d*x)^2)
@test integrate(cot(c+d*x)^5*(a+im*a*tan(c+d*x)), x) == :(im*a*x+a*d^-1*log(sin(c+d*x))+(1/2)*a*d^-1*cot(c+d*x)^2+-1//4*a*d^-1*cot(c+d*x)^4+im*a*d^-1*cot(c+d*x)+-1//3*im*a*d^-1*cot(c+d*x)^3)
@test integrate(cot(c+d*x)^6*(a+im*a*tan(c+d*x)), x) == :(-1*a*x+-1*a*d^-1*cot(c+d*x)+-1//5*a*d^-1*cot(c+d*x)^5+1//3*a*d^-1*cot(c+d*x)^3+im*a*d^-1*log(sin(c+d*x))+(1/2)*im*a*d^-1*cot(c+d*x)^2+-1//4*im*a*d^-1*cot(c+d*x)^4)
@test integrate((a+im*a*tan(c+d*x))^2*tan(c+d*x)^4, x) == :(2*x*a^2+-2*a^2*d^-1*tan(c+d*x)+-1//5*a^2*d^-1*tan(c+d*x)^5+2//3*a^2*d^-1*tan(c+d*x)^3+(1/2)*im*a^2*d^-1*tan(c+d*x)^4+-1*im*a^2*d^-1*tan(c+d*x)^2+-2*im*a^2*d^-1*log(cos(c+d*x)))
@test integrate((a+im*a*tan(c+d*x))^2*tan(c+d*x)^3, x) == :(a^2*d^-1*tan(c+d*x)^2+2*im*x*a^2+2*a^2*d^-1*log(cos(c+d*x))+-1//4*a^2*d^-1*tan(c+d*x)^4+-2*im*a^2*d^-1*tan(c+d*x)+2//3*im*a^2*d^-1*tan(c+d*x)^3)
@test integrate((a+im*a*tan(c+d*x))^2*tan(c+d*x)^2, x) == :(-2*x*a^2+a^2*d^-1*tan(c+d*x)+2*im*a^2*d^-1*log(cos(c+d*x))+-1//3*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^3)
@test integrate((a+im*a*tan(c+d*x))^2*tan(c+d*x), x) == :((1/2)*d^-1*(a+im*a*tan(c+d*x))^2+-2*im*x*a^2+-2*a^2*d^-1*log(cos(c+d*x))+im*a^2*d^-1*tan(c+d*x))
@test integrate((a+im*a*tan(c+d*x))^2, x) == :(2*x*a^2+-1*a^2*d^-1*tan(c+d*x)+-2*im*a^2*d^-1*log(cos(c+d*x)))
@test integrate((a+im*a*tan(c+d*x))^2*cot(c+d*x), x) == :(a^2*d^-1*log(cos(c+d*x))+a^2*d^-1*log(sin(c+d*x))+2*im*x*a^2)
@test integrate((a+im*a*tan(c+d*x))^2*cot(c+d*x)^2, x) == :(-2*x*a^2+-1*a^2*d^-1*cot(c+d*x)+2*im*a^2*d^-1*log(sin(c+d*x)))
@test integrate((a+im*a*tan(c+d*x))^2*cot(c+d*x)^3, x) == :(-2*im*x*a^2+-2*a^2*d^-1*log(sin(c+d*x))+-1//2*a^2*d^-1*cot(c+d*x)^2+-2*im*a^2*d^-1*cot(c+d*x))
@test integrate((a+im*a*tan(c+d*x))^2*cot(c+d*x)^4, x) == :(2*x*a^2+2*a^2*d^-1*cot(c+d*x)+-1//3*a^2*d^-1*cot(c+d*x)^3+-1*im*a^2*d^-1*cot(c+d*x)^2+-2*im*a^2*d^-1*log(sin(c+d*x)))
@test integrate((a+im*a*tan(c+d*x))^2*cot(c+d*x)^5, x) == :(a^2*d^-1*cot(c+d*x)^2+2*im*x*a^2+2*a^2*d^-1*log(sin(c+d*x))+-1//4*a^2*d^-1*cot(c+d*x)^4+2*im*a^2*d^-1*cot(c+d*x)+-2//3*im*a^2*d^-1*cot(c+d*x)^3)
@test integrate((a+im*a*tan(c+d*x))^2*cot(c+d*x)^6, x) == :(-2*x*a^2+-2*a^2*d^-1*cot(c+d*x)+-1//5*a^2*d^-1*cot(c+d*x)^5+2//3*a^2*d^-1*cot(c+d*x)^3+im*a^2*d^-1*cot(c+d*x)^2+2*im*a^2*d^-1*log(sin(c+d*x))+-1//2*im*a^2*d^-1*cot(c+d*x)^4)
@test integrate((a+im*a*tan(c+d*x))^3*tan(c+d*x)^3, x) == :(2*a^3*d^-1*tan(c+d*x)^2+4*im*x*a^3+4*a^3*d^-1*log(cos(c+d*x))+-11//20*a^3*d^-1*tan(c+d*x)^4+-1//5*d^-1*tan(c+d*x)^4*(a^3+im*a^3*tan(c+d*x))+-4*im*a^3*d^-1*tan(c+d*x)+4//3*im*a^3*d^-1*tan(c+d*x)^3)
@test integrate((a+im*a*tan(c+d*x))^3*tan(c+d*x)^2, x) == :(-4*x*a^3+2*a^3*d^-1*tan(c+d*x)+4*im*a^3*d^-1*log(cos(c+d*x))+-1//2*im*a*d^-1*(a+im*a*tan(c+d*x))^2+-1//4*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^4)
@test integrate((a+im*a*tan(c+d*x))^3*tan(c+d*x), x) == :(1//3*d^-1*(a+im*a*tan(c+d*x))^3+(1/2)*a*d^-1*(a+im*a*tan(c+d*x))^2+-4*im*x*a^3+-4*a^3*d^-1*log(cos(c+d*x))+2*im*a^3*d^-1*tan(c+d*x))
@test integrate((a+im*a*tan(c+d*x))^3, x) == :(4*x*a^3+-2*a^3*d^-1*tan(c+d*x)+(1/2)*im*a*d^-1*(a+im*a*tan(c+d*x))^2+-4*im*a^3*d^-1*log(cos(c+d*x)))
@test integrate((a+im*a*tan(c+d*x))^3*cot(c+d*x), x) == :(-1*d^-1*(a^3+im*a^3*tan(c+d*x))+a^3*d^-1*log(sin(c+d*x))+3*a^3*d^-1*log(cos(c+d*x))+4*im*x*a^3)
@test integrate((a+im*a*tan(c+d*x))^3*cot(c+d*x)^2, x) == :(-4*x*a^3+-1*d^-1*(a^3+im*a^3*tan(c+d*x))*cot(c+d*x)+im*a^3*d^-1*log(cos(c+d*x))+3*im*a^3*d^-1*log(sin(c+d*x)))
@test integrate((a+im*a*tan(c+d*x))^3*cot(c+d*x)^3, x) == :(-4*im*x*a^3+-4*a^3*d^-1*log(sin(c+d*x))+-2*im*a^3*d^-1*cot(c+d*x)+-1//2*a*d^-1*(a+im*a*tan(c+d*x))^2*cot(c+d*x)^2)
@test integrate((a+im*a*tan(c+d*x))^3*cot(c+d*x)^4, x) == :(4*x*a^3+2*a^3*d^-1*cot(c+d*x)+-1//3*d^-1*(a+im*a*tan(c+d*x))^3*cot(c+d*x)^3+-4*im*a^3*d^-1*log(sin(c+d*x))+-1//2*im*a*d^-1*(a+im*a*tan(c+d*x))^2*cot(c+d*x)^2)
@test integrate((a+im*a*tan(c+d*x))^3*cot(c+d*x)^5, x) == :(2*a^3*d^-1*cot(c+d*x)^2+4*im*x*a^3+4*a^3*d^-1*log(sin(c+d*x))+-1//4*d^-1*cot(c+d*x)^4*(a^3+im*a^3*tan(c+d*x))+4*im*a^3*d^-1*cot(c+d*x)+-3//4*im*a^3*d^-1*cot(c+d*x)^3)
@test integrate((a+im*a*tan(c+d*x))^3*cot(c+d*x)^6, x) == :(-4*x*a^3+-4*a^3*d^-1*cot(c+d*x)+-1//5*d^-1*cot(c+d*x)^5*(a^3+im*a^3*tan(c+d*x))+4//3*a^3*d^-1*cot(c+d*x)^3+2*im*a^3*d^-1*cot(c+d*x)^2+4*im*a^3*d^-1*log(sin(c+d*x))+-11//20*im*a^3*d^-1*cot(c+d*x)^4)
@test integrate((a+im*a*tan(c+d*x))^4*tan(c+d*x)^3, x) == :(4*a^4*d^-1*tan(c+d*x)^2+8*im*x*a^4+8*a^4*d^-1*log(cos(c+d*x))+-67//60*a^4*d^-1*tan(c+d*x)^4+-7//15*d^-1*tan(c+d*x)^4*(a^4+im*a^4*tan(c+d*x))+-1//6*d^-1*(a^2+im*a^2*tan(c+d*x))^2*tan(c+d*x)^4+-8*im*a^4*d^-1*tan(c+d*x)+8//3*im*a^4*d^-1*tan(c+d*x)^3)
@test integrate((a+im*a*tan(c+d*x))^4*tan(c+d*x)^2, x) == :(-8*x*a^4+-1*im*d^-1*(a^2+im*a^2*tan(c+d*x))^2+4*a^4*d^-1*tan(c+d*x)+8*im*a^4*d^-1*log(cos(c+d*x))+-1//3*im*a*d^-1*(a+im*a*tan(c+d*x))^3+-1//5*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^5)
@test integrate((a+im*a*tan(c+d*x))^4*tan(c+d*x), x) == :(d^-1*(a^2+im*a^2*tan(c+d*x))^2+1//4*d^-1*(a+im*a*tan(c+d*x))^4+-8*im*x*a^4+-8*a^4*d^-1*log(cos(c+d*x))+1//3*a*d^-1*(a+im*a*tan(c+d*x))^3+4*im*a^4*d^-1*tan(c+d*x))
@test integrate((a+im*a*tan(c+d*x))^4, x) == :(8*x*a^4+im*d^-1*(a^2+im*a^2*tan(c+d*x))^2+-4*a^4*d^-1*tan(c+d*x)+-8*im*a^4*d^-1*log(cos(c+d*x))+1//3*im*a*d^-1*(a+im*a*tan(c+d*x))^3)
@test integrate((a+im*a*tan(c+d*x))^4*cot(c+d*x), x) == :(-1*d^-1*(3*a^4+3*im*a^4*tan(c+d*x))+-1//2*d^-1*(a^2+im*a^2*tan(c+d*x))^2+a^4*d^-1*log(sin(c+d*x))+7*a^4*d^-1*log(cos(c+d*x))+8*im*x*a^4)
@test integrate((a+im*a*tan(c+d*x))^4*cot(c+d*x)^2, x) == :(-8*x*a^4+-1*d^-1*(a^2+im*a^2*tan(c+d*x))^2*cot(c+d*x)+4*im*a^4*d^-1*log(cos(c+d*x))+4*im*a^4*d^-1*log(sin(c+d*x)))
@test integrate((a+im*a*tan(c+d*x))^4*cot(c+d*x)^3, x) == :(-1*a^4*d^-1*log(cos(c+d*x))+-8*im*x*a^4+-7*a^4*d^-1*log(sin(c+d*x))+-1//2*d^-1*(a^2+im*a^2*tan(c+d*x))^2*cot(c+d*x)^2+-3*im*d^-1*(a^4+im*a^4*tan(c+d*x))*cot(c+d*x))
@test integrate((a+im*a*tan(c+d*x))^4*cot(c+d*x)^4, x) == :(8*x*a^4+4*a^4*d^-1*cot(c+d*x)+-1*im*d^-1*(a^2+im*a^2*tan(c+d*x))^2*cot(c+d*x)^2+-8*im*a^4*d^-1*log(sin(c+d*x))+-1//3*a*d^-1*(a+im*a*tan(c+d*x))^3*cot(c+d*x)^3)
@test integrate((a+im*a*tan(c+d*x))^4*cot(c+d*x)^5, x) == :(d^-1*(a^2+im*a^2*tan(c+d*x))^2*cot(c+d*x)^2+8*im*x*a^4+8*a^4*d^-1*log(sin(c+d*x))+-1//4*d^-1*(a+im*a*tan(c+d*x))^4*cot(c+d*x)^4+4*im*a^4*d^-1*cot(c+d*x)+-1//3*im*a*d^-1*(a+im*a*tan(c+d*x))^3*cot(c+d*x)^3)
@test integrate((a+im*a*tan(c+d*x))^4*cot(c+d*x)^6, x) == :(-8*x*a^4+-8*a^4*d^-1*cot(c+d*x)+-1//5*d^-1*(a^2+im*a^2*tan(c+d*x))^2*cot(c+d*x)^5+23//15*a^4*d^-1*cot(c+d*x)^3+4*im*a^4*d^-1*cot(c+d*x)^2+8*im*a^4*d^-1*log(sin(c+d*x))+-3//5*im*d^-1*cot(c+d*x)^4*(a^4+im*a^4*tan(c+d*x)))
@test integrate((a+im*a*tan(c+d*x))^4*cot(c+d*x)^7, x) == :(-8*im*x*a^4+-8*a^4*d^-1*log(sin(c+d*x))+-4*a^4*d^-1*cot(c+d*x)^2+-1//6*d^-1*(a^2+im*a^2*tan(c+d*x))^2*cot(c+d*x)^6+67//60*a^4*d^-1*cot(c+d*x)^4+-8*im*a^4*d^-1*cot(c+d*x)+-7//15*im*d^-1*cot(c+d*x)^5*(a^4+im*a^4*tan(c+d*x))+8//3*im*a^4*d^-1*cot(c+d*x)^3)
@test integrate((a+im*a*tan(c+d*x))^-1*tan(c+d*x)^6, x) == :(5//2*x*a^-1+-5//2*a^-1*d^-1*tan(c+d*x)+-1//2*d^-1*(a+im*a*tan(c+d*x))^-1*tan(c+d*x)^5+5//6*a^-1*d^-1*tan(c+d*x)^3+3*im*a^-1*d^-1*log(cos(c+d*x))+-3//4*im*a^-1*d^-1*tan(c+d*x)^4+3//2*im*a^-1*d^-1*tan(c+d*x)^2)
@test integrate((a+im*a*tan(c+d*x))^-1*tan(c+d*x)^5, x) == :(a^-1*d^-1*tan(c+d*x)^2+2*a^-1*d^-1*log(cos(c+d*x))+-5//2*im*x*a^-1+-1//2*d^-1*(a+im*a*tan(c+d*x))^-1*tan(c+d*x)^4+-5//6*im*a^-1*d^-1*tan(c+d*x)^3+5//2*im*a^-1*d^-1*tan(c+d*x))
@test integrate((a+im*a*tan(c+d*x))^-1*tan(c+d*x)^4, x) == :(-3//2*x*a^-1+-1//2*d^-1*(a+im*a*tan(c+d*x))^-1*tan(c+d*x)^3+3//2*a^-1*d^-1*tan(c+d*x)+-1*im*a^-1*d^-1*tan(c+d*x)^2+-2*im*a^-1*d^-1*log(cos(c+d*x)))
@test integrate((a+im*a*tan(c+d*x))^-1*tan(c+d*x)^3, x) == :(-1*a^-1*d^-1*log(cos(c+d*x))+-1//2*d^-1*(a+im*a*tan(c+d*x))^-1*tan(c+d*x)^2+3//2*im*x*a^-1+-3//2*im*a^-1*d^-1*tan(c+d*x))
@test integrate((a+im*a*tan(c+d*x))^-1*tan(c+d*x)^2, x) == :((1/2)*x*a^-1+-1//2*im*d^-1*(a+im*a*tan(c+d*x))^-1+im*a^-1*d^-1*log(cos(c+d*x)))
@test integrate((a+im*a*tan(c+d*x))^-1*tan(c+d*x), x) == :(-1//2*d^-1*(a+im*a*tan(c+d*x))^-1+-1//2*im*x*a^-1)
@test integrate((a+im*a*tan(c+d*x))^-1, x) == :((1/2)*x*a^-1+(1/2)*im*d^-1*(a+im*a*tan(c+d*x))^-1)
@test integrate((a+im*a*tan(c+d*x))^-1*cot(c+d*x), x) == :((1/2)*d^-1*(a+im*a*tan(c+d*x))^-1+a^-1*d^-1*log(sin(c+d*x))+-1//2*im*x*a^-1)
@test integrate((a+im*a*tan(c+d*x))^-1*cot(c+d*x)^2, x) == :(-3//2*x*a^-1+(1/2)*d^-1*(a+im*a*tan(c+d*x))^-1*cot(c+d*x)+-3//2*a^-1*d^-1*cot(c+d*x)+-1*im*a^-1*d^-1*log(sin(c+d*x)))
@test integrate((a+im*a*tan(c+d*x))^-1*cot(c+d*x)^3, x) == :((1/2)*d^-1*(a+im*a*tan(c+d*x))^-1*cot(c+d*x)^2+-1*a^-1*d^-1*cot(c+d*x)^2+-2*a^-1*d^-1*log(sin(c+d*x))+3//2*im*x*a^-1+3//2*im*a^-1*d^-1*cot(c+d*x))
@test integrate((a+im*a*tan(c+d*x))^-1*cot(c+d*x)^4, x) == :(5//2*x*a^-1+(1/2)*d^-1*(a+im*a*tan(c+d*x))^-1*cot(c+d*x)^3+-5//6*a^-1*d^-1*cot(c+d*x)^3+5//2*a^-1*d^-1*cot(c+d*x)+im*a^-1*d^-1*cot(c+d*x)^2+2*im*a^-1*d^-1*log(sin(c+d*x)))
@test integrate((a+im*a*tan(c+d*x))^-2*tan(c+d*x)^6, x) == :(-25//4*x*a^-2+-25//12*a^-2*d^-1*tan(c+d*x)^3+-1//4*d^-1*(a+im*a*tan(c+d*x))^-2*tan(c+d*x)^5+25//4*a^-2*d^-1*tan(c+d*x)+-6*im*a^-2*d^-1*log(cos(c+d*x))+-3*im*a^-2*d^-1*tan(c+d*x)^2+3//2*im*a^-2*d^-1*(1+im*tan(c+d*x))^-1*tan(c+d*x)^4)
@test integrate((a+im*a*tan(c+d*x))^-2*tan(c+d*x)^5, x) == :(-4*a^-2*d^-1*log(cos(c+d*x))+-2*a^-2*d^-1*tan(c+d*x)^2+-1//4*d^-1*(a+im*a*tan(c+d*x))^-2*tan(c+d*x)^4+15//4*im*x*a^-2+-15//4*im*a^-2*d^-1*tan(c+d*x)+5//4*im*a^-2*d^-1*(1+im*tan(c+d*x))^-1*tan(c+d*x)^3)
@test integrate((a+im*a*tan(c+d*x))^-2*tan(c+d*x)^4, x) == :(9//4*x*a^-2+-9//4*a^-2*d^-1*tan(c+d*x)+-1//4*d^-1*(a+im*a*tan(c+d*x))^-2*tan(c+d*x)^3+2*im*a^-2*d^-1*log(cos(c+d*x))+im*a^-2*d^-1*(1+im*tan(c+d*x))^-1*tan(c+d*x)^2)
@test integrate((a+im*a*tan(c+d*x))^-2*tan(c+d*x)^3, x) == :(a^-2*d^-1*log(cos(c+d*x))+-3//4*im*x*a^-2+-3//4*a^-2*d^-1*(1+im*tan(c+d*x))^-1+-1//4*d^-1*(a+im*a*tan(c+d*x))^-2*tan(c+d*x)^2)
@test integrate((a+im*a*tan(c+d*x))^-2*tan(c+d*x)^2, x) == :(-1//4*x*a^-2+-1//4*im*d^-1*(a+im*a*tan(c+d*x))^-2+3//4*im*a^-2*d^-1*(1+im*tan(c+d*x))^-1)
@test integrate((a+im*a*tan(c+d*x))^-2*tan(c+d*x), x) == :(-1//4*d^-1*(a+im*a*tan(c+d*x))^-2+1//4*d^-1*(a^2+im*a^2*tan(c+d*x))^-1+-1//4*im*x*a^-2)
@test integrate((a+im*a*tan(c+d*x))^-2, x) == :(1//4*x*a^-2+1//4*im*d^-1*(a+im*a*tan(c+d*x))^-2+1//4*im*d^-1*(a^2+im*a^2*tan(c+d*x))^-1)
@test integrate((a+im*a*tan(c+d*x))^-2*cot(c+d*x), x) == :(1//4*d^-1*(a+im*a*tan(c+d*x))^-2+a^-2*d^-1*log(sin(c+d*x))+-3//4*im*x*a^-2+3//4*a^-2*d^-1*(1+im*tan(c+d*x))^-1)
@test integrate((a+im*a*tan(c+d*x))^-2*cot(c+d*x)^2, x) == :(-9//4*x*a^-2+-9//4*a^-2*d^-1*cot(c+d*x)+1//4*d^-1*(a+im*a*tan(c+d*x))^-2*cot(c+d*x)+a^-2*d^-1*(1+im*tan(c+d*x))^-1*cot(c+d*x)+-2*im*a^-2*d^-1*log(sin(c+d*x)))
@test integrate((a+im*a*tan(c+d*x))^-2*cot(c+d*x)^3, x) == :(-4*a^-2*d^-1*log(sin(c+d*x))+-2*a^-2*d^-1*cot(c+d*x)^2+1//4*d^-1*(a+im*a*tan(c+d*x))^-2*cot(c+d*x)^2+15//4*im*x*a^-2+5//4*a^-2*d^-1*(1+im*tan(c+d*x))^-1*cot(c+d*x)^2+15//4*im*a^-2*d^-1*cot(c+d*x))
@test integrate((a+im*a*tan(c+d*x))^-3*tan(c+d*x)^6, x) == :(55//8*x*a^-3+-55//8*a^-3*d^-1*tan(c+d*x)+-1//6*d^-1*(a+im*a*tan(c+d*x))^-3*tan(c+d*x)^5+55//24*d^-1*(a^3+im*a^3*tan(c+d*x))^-1*tan(c+d*x)^3+7*im*a^-3*d^-1*log(cos(c+d*x))+7//2*im*a^-3*d^-1*tan(c+d*x)^2+13//24*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-2*tan(c+d*x)^4)
@test integrate((a+im*a*tan(c+d*x))^-3*tan(c+d*x)^5, x) == :(3*a^-3*d^-1*log(cos(c+d*x))+-25//8*im*x*a^-3+-1//6*d^-1*(a+im*a*tan(c+d*x))^-3*tan(c+d*x)^4+3//2*d^-1*(a^3+im*a^3*tan(c+d*x))^-1*tan(c+d*x)^2+25//8*im*a^-3*d^-1*tan(c+d*x)+11//24*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-2*tan(c+d*x)^3)
@test integrate((a+im*a*tan(c+d*x))^-3*tan(c+d*x)^4, x) == :(-7//8*x*a^-3+-1//6*d^-1*(a+im*a*tan(c+d*x))^-3*tan(c+d*x)^3+7//8*im*d^-1*(a^3+im*a^3*tan(c+d*x))^-1+-1*im*a^-3*d^-1*log(cos(c+d*x))+3//8*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-2*tan(c+d*x)^2)
@test integrate((a+im*a*tan(c+d*x))^-3*tan(c+d*x)^3, x) == :(-1//8*a^-1*d^-1*(a+im*a*tan(c+d*x))^-2+1//8*im*x*a^-3+3//8*a^-3*d^-1*(1+im*tan(c+d*x))^-1+1//6*im*d^-1*(a+im*a*tan(c+d*x))^-3*tan(c+d*x)^3)
@test integrate((a+im*a*tan(c+d*x))^-3*tan(c+d*x)^2, x) == :(-1//8*x*a^-3+-1//6*im*d^-1*(a+im*a*tan(c+d*x))^-3+-1//8*im*d^-1*(a^3+im*a^3*tan(c+d*x))^-1+3//8*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-2)
@test integrate((a+im*a*tan(c+d*x))^-3*tan(c+d*x), x) == :(-1//6*d^-1*(a+im*a*tan(c+d*x))^-3+1//8*d^-1*(a^3+im*a^3*tan(c+d*x))^-1+-1//8*im*x*a^-3+1//8*a^-1*d^-1*(a+im*a*tan(c+d*x))^-2)
@test integrate((a+im*a*tan(c+d*x))^-3, x) == :(1//8*x*a^-3+1//6*im*d^-1*(a+im*a*tan(c+d*x))^-3+1//8*im*d^-1*(a^3+im*a^3*tan(c+d*x))^-1+1//8*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-2)
@test integrate((a+im*a*tan(c+d*x))^-3*cot(c+d*x), x) == :(1//6*d^-1*(a+im*a*tan(c+d*x))^-3+7//8*d^-1*(a^3+im*a^3*tan(c+d*x))^-1+a^-3*d^-1*log(sin(c+d*x))+-7//8*im*x*a^-3+3//8*a^-1*d^-1*(a+im*a*tan(c+d*x))^-2)
@test integrate((a+im*a*tan(c+d*x))^-3*cot(c+d*x)^2, x) == :(-25//8*x*a^-3+-25//8*a^-3*d^-1*cot(c+d*x)+1//6*d^-1*(a+im*a*tan(c+d*x))^-3*cot(c+d*x)+3//2*d^-1*(a^3+im*a^3*tan(c+d*x))^-1*cot(c+d*x)+-3*im*a^-3*d^-1*log(sin(c+d*x))+11//24*a^-1*d^-1*(a+im*a*tan(c+d*x))^-2*cot(c+d*x))
@test integrate((a+im*a*tan(c+d*x))^-4*tan(c+d*x)^6, x) == :(-65//16*x*a^-4+-1//8*d^-1*(a+im*a*tan(c+d*x))^-4*tan(c+d*x)^5+65//16*a^-4*d^-1*tan(c+d*x)+-4*im*a^-4*d^-1*log(cos(c+d*x))+31//48*a^-4*d^-1*(1+im*tan(c+d*x))^-2*tan(c+d*x)^3+-2*im*a^-4*d^-1*(1+im*tan(c+d*x))^-1*tan(c+d*x)^2+7//24*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3*tan(c+d*x)^4)
@test integrate((a+im*a*tan(c+d*x))^-4*tan(c+d*x)^5, x) == :(-1*a^-4*d^-1*log(cos(c+d*x))+-1//8*d^-1*(a+im*a*tan(c+d*x))^-4*tan(c+d*x)^4+15//16*im*x*a^-4+15//16*a^-4*d^-1*(1+im*tan(c+d*x))^-1+7//16*a^-4*d^-1*(1+im*tan(c+d*x))^-2*tan(c+d*x)^2+1//4*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3*tan(c+d*x)^3)
@test integrate((a+im*a*tan(c+d*x))^-4*tan(c+d*x)^4, x) == :(1//16*x*a^-4+1//16*im*d^-1*(a^2+im*a^2*tan(c+d*x))^-2+-3//16*im*a^-4*d^-1*(1+im*tan(c+d*x))^-1+1//8*im*d^-1*(a+im*a*tan(c+d*x))^-4*tan(c+d*x)^4+1//12*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3*tan(c+d*x)^3)
@test integrate((a+im*a*tan(c+d*x))^-4*tan(c+d*x)^3, x) == :(-1//16*d^-1*(a^2+im*a^2*tan(c+d*x))^-2+1//8*d^-1*(a+im*a*tan(c+d*x))^-4*tan(c+d*x)^4+1//16*im*x*a^-4+3//16*a^-4*d^-1*(1+im*tan(c+d*x))^-1+1//12*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3*tan(c+d*x)^3)
@test integrate((a+im*a*tan(c+d*x))^-4*tan(c+d*x)^2, x) == :(-1//16*x*a^-4+-1//8*im*d^-1*(a+im*a*tan(c+d*x))^-4+-1//16*im*d^-1*(a^2+im*a^2*tan(c+d*x))^-2+-1//16*im*d^-1*(a^4+im*a^4*tan(c+d*x))^-1+1//4*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3)
@test integrate((a+im*a*tan(c+d*x))^-4*tan(c+d*x), x) == :(-1//8*d^-1*(a+im*a*tan(c+d*x))^-4+1//16*d^-1*(a^2+im*a^2*tan(c+d*x))^-2+1//16*d^-1*(a^4+im*a^4*tan(c+d*x))^-1+-1//16*im*x*a^-4+1//12*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3)
@test integrate((a+im*a*tan(c+d*x))^-4, x) == :(1//16*x*a^-4+1//8*im*d^-1*(a+im*a*tan(c+d*x))^-4+1//16*im*d^-1*(a^2+im*a^2*tan(c+d*x))^-2+1//16*im*d^-1*(a^4+im*a^4*tan(c+d*x))^-1+1//12*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3)
@test integrate((a+im*a*tan(c+d*x))^-4*cot(c+d*x), x) == :(1//8*d^-1*(a+im*a*tan(c+d*x))^-4+a^-4*d^-1*log(sin(c+d*x))+-15//16*im*x*a^-4+1//4*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3+7//16*a^-4*d^-1*(1+im*tan(c+d*x))^-2+15//16*a^-4*d^-1*(1+im*tan(c+d*x))^-1)
@test integrate((a+im*a*tan(c+d*x))^-4*cot(c+d*x)^2, x) == :(-65//16*x*a^-4+-65//16*a^-4*d^-1*cot(c+d*x)+1//8*d^-1*(a+im*a*tan(c+d*x))^-4*cot(c+d*x)+-4*im*a^-4*d^-1*log(sin(c+d*x))+2*a^-4*d^-1*(1+im*tan(c+d*x))^-1*cot(c+d*x)+7//24*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3*cot(c+d*x)+31//48*a^-4*d^-1*(1+im*tan(c+d*x))^-2*cot(c+d*x))
@test integrate((a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^4, x) == :(2//7*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^3+8//35*im*d^-1*(a+im*a*tan(c+d*x))^(1/2)+-2//35*im*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^2+62//105*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^3//2+-1*im*2^(1/2)*a^(1/2)*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^3, x) == :(-8//5*d^-1*(a+im*a*tan(c+d*x))^(1/2)+-2//15*a^-1*d^-1*(a+im*a*tan(c+d*x))^3//2+2//5*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^2+2^(1/2)*a^(1/2)*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^2, x) == :(-2//3*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^3//2+im*2^(1/2)*a^(1/2)*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x), x) == :(2*d^-1*(a+im*a*tan(c+d*x))^(1/2)+-1*2^(1/2)*a^(1/2)*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^(1/2), x) == :(-1*im*2^(1/2)*a^(1/2)*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x), x) == :(-2*a^(1/2)*d^-1*arctanh(a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+2^(1/2)*a^(1/2)*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^2, x) == :(-1*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)+-1*im*a^(1/2)*d^-1*arctanh(a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+im*2^(1/2)*a^(1/2)*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^3, x) == :(-1//2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^2+7//4*a^(1/2)*d^-1*arctanh(a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+-1*2^(1/2)*a^(1/2)*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+-1//4*im*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x))
@test integrate((a+im*a*tan(c+d*x))^3//2*tan(c+d*x)^3, x) == :(-76//105*d^-1*(a+im*a*tan(c+d*x))^3//2+-64//35*a*d^-1*(a+im*a*tan(c+d*x))^(1/2)+2*2^(1/2)*a^3//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+-2//7*a^2*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^4+16//35*a*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^2+2//7*im*a^2*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^3)
@test integrate((a+im*a*tan(c+d*x))^3//2*tan(c+d*x)^2, x) == :(-2*im*a*d^-1*(a+im*a*tan(c+d*x))^(1/2)+-2//5*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^5//2+2*im*2^(1/2)*a^3//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^3//2*tan(c+d*x), x) == :(2//3*d^-1*(a+im*a*tan(c+d*x))^3//2+2*a*d^-1*(a+im*a*tan(c+d*x))^(1/2)+-2*2^(1/2)*a^3//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^3//2, x) == :(2*im*a*d^-1*(a+im*a*tan(c+d*x))^(1/2)+-2*im*2^(1/2)*a^3//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^3//2*cot(c+d*x), x) == :(-2*a^3//2*d^-1*arctanh(a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+2*2^(1/2)*a^3//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^3//2*cot(c+d*x)^2, x) == :(-1*im*a^2*d^-1*(a+im*a*tan(c+d*x))^-1//2+-1*a^2*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)+-3*im*a^3//2*d^-1*arctanh(a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+2*im*2^(1/2)*a^3//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^3//2*cot(c+d*x)^3, x) == :(11//4*a^3//2*d^-1*arctanh(a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+-2*2^(1/2)*a^3//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+-1//2*a^2*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^2+-5//4*im*a*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)+-1//2*im*a^2*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x))
@test integrate((a+im*a*tan(c+d*x))^5//2*tan(c+d*x)^3, x) == :(-472//315*a*d^-1*(a+im*a*tan(c+d*x))^3//2+-368//105*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)+4*2^(1/2)*a^5//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+-2//9*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^4+92//105*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^2+38//63*im*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^3)
@test integrate((a+im*a*tan(c+d*x))^5//2*tan(c+d*x)^2, x) == :(-4*im*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)+-2//3*im*a*d^-1*(a+im*a*tan(c+d*x))^3//2+-2//7*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^7//2+4*im*2^(1/2)*a^5//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^5//2*tan(c+d*x), x) == :(2//5*d^-1*(a+im*a*tan(c+d*x))^5//2+4*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)+2//3*a*d^-1*(a+im*a*tan(c+d*x))^3//2+-4*2^(1/2)*a^5//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^5//2, x) == :(4*im*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)+2//3*im*a*d^-1*(a+im*a*tan(c+d*x))^3//2+-4*im*2^(1/2)*a^5//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^5//2*cot(c+d*x), x) == :(-2*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)+-2*a^5//2*d^-1*arctanh(a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+4*2^(1/2)*a^5//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^5//2*cot(c+d*x)^2, x) == :(-1*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)+-5*im*a^5//2*d^-1*arctanh(a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+4*im*2^(1/2)*a^5//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^5//2*cot(c+d*x)^3, x) == :(23//4*a^5//2*d^-1*arctanh(a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+-4*2^(1/2)*a^5//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+-1//2*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^2+-9//4*im*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x))
@test integrate((a+im*a*tan(c+d*x))^5//2*cot(c+d*x)^4, x) == :(-1//3*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^3+19//8*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)+45//8*im*a^5//2*d^-1*arctanh(a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+-4*im*2^(1/2)*a^5//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+-13//12*im*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^2)
@test integrate((a+im*a*tan(c+d*x))^7//2, x) == :(8*im*a^3*d^-1*(a+im*a*tan(c+d*x))^(1/2)+2//5*im*a*d^-1*(a+im*a*tan(c+d*x))^5//2+4//3*im*a^2*d^-1*(a+im*a*tan(c+d*x))^3//2+-8*im*2^(1/2)*a^7//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^5, x) == :(-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^4+-188//35*a^-1*d^-1*(a+im*a*tan(c+d*x))^(1/2)+223//105*a^-2*d^-1*(a+im*a*tan(c+d*x))^3//2+-1//2*2^(1/2)*a^-1//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+47//35*a^-1*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^2+-9//7*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^3)
@test integrate((a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^4, x) == :(-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^3+-23//15*im*a^-2*d^-1*(a+im*a*tan(c+d*x))^3//2+28//5*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^(1/2)+-7//5*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^2+-1//2*im*2^(1/2)*a^-1//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^3, x) == :(-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^2+4*a^-1*d^-1*(a+im*a*tan(c+d*x))^(1/2)+-5//3*a^-2*d^-1*(a+im*a*tan(c+d*x))^3//2+(1/2)*2^(1/2)*a^-1//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^2, x) == :(-1*im*d^-1*(a+im*a*tan(c+d*x))^-1//2+-2*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^(1/2)+(1/2)*im*2^(1/2)*a^-1//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-1//2*tan(c+d*x), x) == :(-1*d^-1*(a+im*a*tan(c+d*x))^-1//2+-1//2*2^(1/2)*a^-1//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-1//2, x) == :(im*d^-1*(a+im*a*tan(c+d*x))^-1//2+-1//2*im*2^(1/2)*a^-1//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-1//2*cot(c+d*x), x) == :(d^-1*(a+im*a*tan(c+d*x))^-1//2+-2*a^-1//2*d^-1*arctanh(a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+(1/2)*2^(1/2)*a^-1//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^2, x) == :(d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)+im*a^-1//2*d^-1*arctanh(a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+-2*a^-1*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)+(1/2)*im*2^(1/2)*a^-1//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^3, x) == :(d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^2+11//4*a^-1//2*d^-1*arctanh(a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+-3//2*a^-1*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^2+-1//2*2^(1/2)*a^-1//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+7//4*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x))
@test integrate((a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^5, x) == :(-151//30*a^-3*d^-1*(a+im*a*tan(c+d*x))^3//2+-1//3*d^-1*(a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^4+78//5*a^-2*d^-1*(a+im*a*tan(c+d*x))^(1/2)+-39//10*a^-2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^2+-1//4*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+19//6*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^3)
@test integrate((a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^4, x) == :(-1//3*d^-1*(a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^3+-10*im*a^-2*d^-1*(a+im*a*tan(c+d*x))^(1/2)+7//2*im*a^-3*d^-1*(a+im*a*tan(c+d*x))^3//2+-1//4*im*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+5//2*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^2)
@test integrate((a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^3, x) == :(-11//6*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//2+-7//3*a^-2*d^-1*(a+im*a*tan(c+d*x))^(1/2)+-1//3*d^-1*(a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^2+1//4*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^2, x) == :(-1//3*im*d^-1*(a+im*a*tan(c+d*x))^-3//2+3//2*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//2+1//4*im*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-3//2*tan(c+d*x), x) == :(-1//3*d^-1*(a+im*a*tan(c+d*x))^-3//2+(1/2)*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//2+-1//4*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-3//2, x) == :(1//3*im*d^-1*(a+im*a*tan(c+d*x))^-3//2+(1/2)*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//2+-1//4*im*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-3//2*cot(c+d*x), x) == :(1//3*d^-1*(a+im*a*tan(c+d*x))^-3//2+-2*a^-3//2*d^-1*arctanh(a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+3//2*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//2+1//4*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)^2, x) == :(1//3*d^-1*(a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)+3*im*a^-3//2*d^-1*arctanh(a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+-7//2*a^-2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)+13//6*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)+1//4*im*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)^3, x) == :(1//3*d^-1*(a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)^2+23//4*a^-3//2*d^-1*arctanh(a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+-11//3*a^-2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^2+-1//4*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+17//6*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^2+21//4*im*a^-2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x))
@test integrate((a+im*a*tan(c+d*x))^-5//2*tan(c+d*x)^5, x) == :(-89//5*a^-3*d^-1*(a+im*a*tan(c+d*x))^(1/2)+-1//5*d^-1*(a+im*a*tan(c+d*x))^-5//2*tan(c+d*x)^4+361//60*a^-4*d^-1*(a+im*a*tan(c+d*x))^3//2+-1//8*2^(1/2)*a^-5//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+89//20*a^-2*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^2+7//10*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^3)
@test integrate((a+im*a*tan(c+d*x))^-5//2*tan(c+d*x)^4, x) == :(-1//5*d^-1*(a+im*a*tan(c+d*x))^-5//2*tan(c+d*x)^3+83//30*im*a^-3*d^-1*(a+im*a*tan(c+d*x))^(1/2)+151//60*im*a^-2*d^-1*(a+im*a*tan(c+d*x))^-1//2+-1//8*im*2^(1/2)*a^-5//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+17//30*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^2)
@test integrate((a+im*a*tan(c+d*x))^-5//2*tan(c+d*x)^3, x) == :(-13//30*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3//2+-1//5*d^-1*(a+im*a*tan(c+d*x))^-5//2*tan(c+d*x)^2+31//20*a^-2*d^-1*(a+im*a*tan(c+d*x))^-1//2+1//8*2^(1/2)*a^-5//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-5//2*tan(c+d*x)^2, x) == :(-1//5*im*d^-1*(a+im*a*tan(c+d*x))^-5//2+(1/2)*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3//2+-1//4*im*a^-2*d^-1*(a+im*a*tan(c+d*x))^-1//2+1//8*im*2^(1/2)*a^-5//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-5//2*tan(c+d*x), x) == :(-1//5*d^-1*(a+im*a*tan(c+d*x))^-5//2+1//4*a^-2*d^-1*(a+im*a*tan(c+d*x))^-1//2+1//6*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3//2+-1//8*2^(1/2)*a^-5//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-5//2, x) == :(1//5*im*d^-1*(a+im*a*tan(c+d*x))^-5//2+1//4*im*a^-2*d^-1*(a+im*a*tan(c+d*x))^-1//2+1//6*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3//2+-1//8*im*2^(1/2)*a^-5//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-5//2*cot(c+d*x), x) == :(1//5*d^-1*(a+im*a*tan(c+d*x))^-5//2+(1/2)*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3//2+-2*a^-5//2*d^-1*arctanh(a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+7//4*a^-2*d^-1*(a+im*a*tan(c+d*x))^-1//2+1//8*2^(1/2)*a^-5//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-5//2*cot(c+d*x)^2, x) == :(1//5*d^-1*(a+im*a*tan(c+d*x))^-5//2*cot(c+d*x)+5*im*a^-5//2*d^-1*arctanh(a^-1//2*(a+im*a*tan(c+d*x))^(1/2))+-21//4*a^-3*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)+19//30*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)+41//12*a^-2*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)+1//8*im*2^(1/2)*a^-5//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-7//2, x) == :(1//7*im*d^-1*(a+im*a*tan(c+d*x))^-7//2+1//8*im*a^-3*d^-1*(a+im*a*tan(c+d*x))^-1//2+1//10*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-5//2+1//12*im*a^-2*d^-1*(a+im*a*tan(c+d*x))^-3//2+-1//16*im*2^(1/2)*a^-7//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+im*a*tan(c+d*x))^(1/2)))
@test integrate((d*tan(e+f*x))^5//2*(a+im*a*tan(e+f*x)), x) == :(2//3*a*d*f^-1*(d*tan(e+f*x))^3//2+2//5*im*a*f^-1*(d*tan(e+f*x))^5//2+-2*im*a*d^2*f^-1*(d*tan(e+f*x))^(1/2)+-2*a*(-1)^3//4*d^5//2*f^-1*arctan((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^3//2*(a+im*a*tan(e+f*x)), x) == :(2*a*d*f^-1*(d*tan(e+f*x))^(1/2)+2//3*im*a*f^-1*(d*tan(e+f*x))^3//2+2*a*(-1)^1//4*d^3//2*f^-1*arctan((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^(1/2)*(a+im*a*tan(e+f*x)), x) == :(2*im*a*f^-1*(d*tan(e+f*x))^(1/2)+2*a*(-1)^3//4*d^(1/2)*f^-1*arctan((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^-1//2*(a+im*a*tan(e+f*x)), x) == :(-2*a*(-1)^1//4*d^-1//2*f^-1*arctan((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^-3//2*(a+im*a*tan(e+f*x)), x) == :(-2*a*d^-1*f^-1*(d*tan(e+f*x))^-1//2+-2*a*(-1)^3//4*d^-3//2*f^-1*arctan((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^-5//2*(a+im*a*tan(e+f*x)), x) == :(-2//3*a*d^-1*f^-1*(d*tan(e+f*x))^-3//2+-2*im*a*d^-2*f^-1*(d*tan(e+f*x))^-1//2+2*a*(-1)^1//4*d^-5//2*f^-1*arctan((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^-7//2*(a+im*a*tan(e+f*x)), x) == :(2*a*d^-3*f^-1*(d*tan(e+f*x))^-1//2+-2//5*a*d^-1*f^-1*(d*tan(e+f*x))^-5//2+2*a*(-1)^3//4*d^-7//2*f^-1*arctan((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2))+-2//3*im*a*d^-2*f^-1*(d*tan(e+f*x))^-3//2)
@test integrate((d*tan(e+f*x))^5//2*(a+-1*im*a*tan(e+f*x)), x) == :(-2//5*im*a*f^-1*(d*tan(e+f*x))^5//2+2//3*a*d*f^-1*(d*tan(e+f*x))^3//2+2*im*a*d^2*f^-1*(d*tan(e+f*x))^(1/2)+2*a*(-1)^3//4*d^5//2*f^-1*arctanh((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^3//2*(a+-1*im*a*tan(e+f*x)), x) == :(2*a*d*f^-1*(d*tan(e+f*x))^(1/2)+-2//3*im*a*f^-1*(d*tan(e+f*x))^3//2+2*a*(-1)^1//4*d^3//2*f^-1*arctanh((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^(1/2)*(a+-1*im*a*tan(e+f*x)), x) == :(-2*im*a*f^-1*(d*tan(e+f*x))^(1/2)+-2*a*(-1)^3//4*d^(1/2)*f^-1*arctanh((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^-1//2*(a+-1*im*a*tan(e+f*x)), x) == :(-2*a*(-1)^1//4*d^-1//2*f^-1*arctanh((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^-3//2*(a+-1*im*a*tan(e+f*x)), x) == :(-2*a*d^-1*f^-1*(d*tan(e+f*x))^-1//2+2*a*(-1)^3//4*d^-3//2*f^-1*arctanh((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^-5//2*(a+-1*im*a*tan(e+f*x)), x) == :(-2//3*a*d^-1*f^-1*(d*tan(e+f*x))^-3//2+2*im*a*d^-2*f^-1*(d*tan(e+f*x))^-1//2+2*a*(-1)^1//4*d^-5//2*f^-1*arctanh((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^-7//2*(a+-1*im*a*tan(e+f*x)), x) == :(2*a*d^-3*f^-1*(d*tan(e+f*x))^-1//2+-2//5*a*d^-1*f^-1*(d*tan(e+f*x))^-5//2+-2*a*(-1)^3//4*d^-7//2*f^-1*arctanh((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2))+2//3*im*a*d^-2*f^-1*(d*tan(e+f*x))^-3//2)
@test integrate((d*tan(e+f*x))^5//2*(a+im*a*tan(e+f*x))^2, x) == :(-2//7*a^2*d^-1*f^-1*(d*tan(e+f*x))^7//2+4//3*d*a^2*f^-1*(d*tan(e+f*x))^3//2+4//5*im*a^2*f^-1*(d*tan(e+f*x))^5//2+-4*im*a^2*d^2*f^-1*(d*tan(e+f*x))^(1/2)+-4*(-1)^3//4*a^2*d^5//2*f^-1*arctan((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^3//2*(a+im*a*tan(e+f*x))^2, x) == :(4*d*a^2*f^-1*(d*tan(e+f*x))^(1/2)+-2//5*a^2*d^-1*f^-1*(d*tan(e+f*x))^5//2+4//3*im*a^2*f^-1*(d*tan(e+f*x))^3//2+4*(-1)^1//4*a^2*d^3//2*f^-1*arctan((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^(1/2)*(a+im*a*tan(e+f*x))^2, x) == :(4*im*a^2*f^-1*(d*tan(e+f*x))^(1/2)+-2//3*a^2*d^-1*f^-1*(d*tan(e+f*x))^3//2+4*(-1)^3//4*a^2*d^(1/2)*f^-1*arctan((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^-1//2*(a+im*a*tan(e+f*x))^2, x) == :(-2*a^2*d^-1*f^-1*(d*tan(e+f*x))^(1/2)+-4*(-1)^1//4*a^2*d^-1//2*f^-1*arctan((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^-3//2*(a+im*a*tan(e+f*x))^2, x) == :(-2*a^2*d^-1*f^-1*(d*tan(e+f*x))^-1//2+-4*(-1)^3//4*a^2*d^-3//2*f^-1*arctan((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^-5//2*(a+im*a*tan(e+f*x))^2, x) == :(-2//3*a^2*d^-1*f^-1*(d*tan(e+f*x))^-3//2+-4*im*a^2*d^-2*f^-1*(d*tan(e+f*x))^-1//2+4*(-1)^1//4*a^2*d^-5//2*f^-1*arctan((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^-7//2*(a+im*a*tan(e+f*x))^2, x) == :(4*a^2*d^-3*f^-1*(d*tan(e+f*x))^-1//2+-2//5*a^2*d^-1*f^-1*(d*tan(e+f*x))^-5//2+4*(-1)^3//4*a^2*d^-7//2*f^-1*arctan((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2))+-4//3*im*a^2*d^-2*f^-1*(d*tan(e+f*x))^-3//2)
@test integrate((d*tan(e+f*x))^5//2*(a+im*a*tan(e+f*x))^3, x) == :(-40//63*a^3*d^-1*f^-1*(d*tan(e+f*x))^7//2+-2//9*d^-1*f^-1*(d*tan(e+f*x))^7//2*(a^3+im*a^3*tan(e+f*x))+8//3*d*a^3*f^-1*(d*tan(e+f*x))^3//2+8//5*im*a^3*f^-1*(d*tan(e+f*x))^5//2+-8*im*a^3*d^2*f^-1*(d*tan(e+f*x))^(1/2)+-8*(-1)^3//4*a^3*d^5//2*f^-1*arctan((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^3//2*(a+im*a*tan(e+f*x))^3, x) == :(8*d*a^3*f^-1*(d*tan(e+f*x))^(1/2)+-32//35*a^3*d^-1*f^-1*(d*tan(e+f*x))^5//2+-2//7*d^-1*f^-1*(d*tan(e+f*x))^5//2*(a^3+im*a^3*tan(e+f*x))+8//3*im*a^3*f^-1*(d*tan(e+f*x))^3//2+8*(-1)^1//4*a^3*d^3//2*f^-1*arctan((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^(1/2)*(a+im*a*tan(e+f*x))^3, x) == :(8*im*a^3*f^-1*(d*tan(e+f*x))^(1/2)+-8//5*a^3*d^-1*f^-1*(d*tan(e+f*x))^3//2+-2//5*d^-1*f^-1*(d*tan(e+f*x))^3//2*(a^3+im*a^3*tan(e+f*x))+8*(-1)^3//4*a^3*d^(1/2)*f^-1*arctan((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^-1//2*(a+im*a*tan(e+f*x))^3, x) == :(-16//3*a^3*d^-1*f^-1*(d*tan(e+f*x))^(1/2)+-2//3*d^-1*f^-1*(d*tan(e+f*x))^(1/2)*(a^3+im*a^3*tan(e+f*x))+-8*(-1)^1//4*a^3*d^-1//2*f^-1*arctan((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^-3//2*(a+im*a*tan(e+f*x))^3, x) == :(-1*d^-1*f^-1*(d*tan(e+f*x))^-1//2*(2*a^3+2*im*a^3*tan(e+f*x))+-8*(-1)^3//4*a^3*d^-3//2*f^-1*arctan((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^-5//2*(a+im*a*tan(e+f*x))^3, x) == :(-1//3*d^-1*f^-1*(d*tan(e+f*x))^-3//2*(2*a^3+2*im*a^3*tan(e+f*x))+8*(-1)^1//4*a^3*d^-5//2*f^-1*arctan((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2))+-16//3*im*a^3*d^-2*f^-1*(d*tan(e+f*x))^-1//2)
@test integrate((d*tan(e+f*x))^-7//2*(a+im*a*tan(e+f*x))^3, x) == :(8*a^3*d^-3*f^-1*(d*tan(e+f*x))^-1//2+-1//5*d^-1*f^-1*(d*tan(e+f*x))^-5//2*(2*a^3+2*im*a^3*tan(e+f*x))+8*(-1)^3//4*a^3*d^-7//2*f^-1*arctan((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2))+-8//5*im*a^3*d^-2*f^-1*(d*tan(e+f*x))^-3//2)
@test integrate((d*tan(e+f*x))^-9//2*(a+im*a*tan(e+f*x))^3, x) == :(-1//7*d^-1*f^-1*(d*tan(e+f*x))^-7//2*(2*a^3+2*im*a^3*tan(e+f*x))+8//3*a^3*d^-3*f^-1*(d*tan(e+f*x))^-3//2+-8*(-1)^1//4*a^3*d^-9//2*f^-1*arctan((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2))+8*im*a^3*d^-4*f^-1*(d*tan(e+f*x))^-1//2+-32//35*im*a^3*d^-2*f^-1*(d*tan(e+f*x))^-5//2)
@test integrate((d*tan(e+f*x))^7//2*(a+im*a*tan(e+f*x))^-1, x) == :(-1//2*d*f^-1*(d*tan(e+f*x))^5//2*(a+im*a*tan(e+f*x))^-1+5//2*a^-1*d^3*f^-1*(d*tan(e+f*x))^(1/2)+-7//6*im*a^-1*d^2*f^-1*(d*tan(e+f*x))^3//2+(1/2)*2^(1/2)*a^-1*d^7//2*f^-1*(5//4+-7//4*im)*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+(1/2)*2^(1/2)*a^-1*d^7//2*f^-1*(5//8+7//8*im)*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-1*d^7//2*f^-1*(5//4+-7//4*im)*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-1*d^7//2*f^-1*(5//8+7//8*im)*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x)))
@test integrate((d*tan(e+f*x))^5//2*(a+im*a*tan(e+f*x))^-1, x) == :(-1//2*d*f^-1*(d*tan(e+f*x))^3//2*(a+im*a*tan(e+f*x))^-1+-5//2*im*a^-1*d^2*f^-1*(d*tan(e+f*x))^(1/2)+(1/2)*2^(1/2)*a^-1*d^5//2*f^-1*(3//4+5//4*im)*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+(1/2)*2^(1/2)*a^-1*d^5//2*f^-1*(3//8+-5//8*im)*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-1*d^5//2*f^-1*(3//4+5//4*im)*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-1*d^5//2*f^-1*(3//8+-5//8*im)*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x)))
@test integrate((d*tan(e+f*x))^3//2*(a+im*a*tan(e+f*x))^-1, x) == :(-1//2*d*f^-1*(d*tan(e+f*x))^(1/2)*(a+im*a*tan(e+f*x))^-1+(1/2)*2^(1/2)*a^-1*d^3//2*f^-1*(1//4+-3//4*im)*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+(1/2)*2^(1/2)*a^-1*d^3//2*f^-1*(1//8+3//8*im)*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x))+-1//2*2^(1/2)*a^-1*d^3//2*f^-1*(1//4+-3//4*im)*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-1*d^3//2*f^-1*(1//8+3//8*im)*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^(1/2)*(a+im*a*tan(e+f*x))^-1, x) == :((1/2)*im*f^-1*(d*tan(e+f*x))^(1/2)*(a+im*a*tan(e+f*x))^-1+(1/2)*(-1)^3//4*a^-1*d^(1/2)*f^-1*arctan((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^-1//2*(a+im*a*tan(e+f*x))^-1, x) == :((1/2)*d^-1*f^-1*(d*tan(e+f*x))^(1/2)*(a+im*a*tan(e+f*x))^-1+(1/2)*2^(1/2)*a^-1*d^-1//2*f^-1*(3//4+-1//4*im)*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+(1/2)*2^(1/2)*a^-1*d^-1//2*f^-1*(3//8+1//8*im)*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x))+-1//2*2^(1/2)*a^-1*d^-1//2*f^-1*(3//4+-1//4*im)*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-1*d^-1//2*f^-1*(3//8+1//8*im)*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^-3//2*(a+im*a*tan(e+f*x))^-1, x) == :((1/2)*d^-1*f^-1*(d*tan(e+f*x))^-1//2*(a+im*a*tan(e+f*x))^-1+-5//2*a^-1*d^-1*f^-1*(d*tan(e+f*x))^-1//2+(1/2)*2^(1/2)*a^-1*d^-3//2*f^-1*(5//4+3//4*im)*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+(1/2)*2^(1/2)*a^-1*d^-3//2*f^-1*(5//8+-3//8*im)*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x))+-1//2*2^(1/2)*a^-1*d^-3//2*f^-1*(5//4+3//4*im)*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-1*d^-3//2*f^-1*(5//8+-3//8*im)*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^-5//2*(a+im*a*tan(e+f*x))^-1, x) == :((1/2)*d^-1*f^-1*(d*tan(e+f*x))^-3//2*(a+im*a*tan(e+f*x))^-1+-7//6*a^-1*d^-1*f^-1*(d*tan(e+f*x))^-3//2+5//2*im*a^-1*d^-2*f^-1*(d*tan(e+f*x))^-1//2+(1/2)*2^(1/2)*a^-1*d^-5//2*f^-1*(7//4+-5//4*im)*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+(1/2)*2^(1/2)*a^-1*d^-5//2*f^-1*(7//8+5//8*im)*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-1*d^-5//2*f^-1*(7//4+-5//4*im)*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-1*d^-5//2*f^-1*(7//8+5//8*im)*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x)))
@test integrate((d*tan(e+f*x))^9//2*(a+im*a*tan(e+f*x))^-2, x) == :(-49//24*a^-2*d^3*f^-1*(d*tan(e+f*x))^3//2+-1//4*d*f^-1*(d*tan(e+f*x))^7//2*(a+im*a*tan(e+f*x))^-2+-45//8*im*a^-2*d^4*f^-1*(d*tan(e+f*x))^(1/2)+(1/2)*2^(1/2)*a^-2*d^9//2*f^-1*(49//16+45//16*im)*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+(1/2)*2^(1/2)*a^-2*d^9//2*f^-1*(49//32+-45//32*im)*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-2*d^9//2*f^-1*(49//16+45//16*im)*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-2*d^9//2*f^-1*(49//32+-45//32*im)*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x))+9//8*im*a^-2*d^2*f^-1*(d*tan(e+f*x))^5//2*(1+im*tan(e+f*x))^-1)
@test integrate((d*tan(e+f*x))^7//2*(a+im*a*tan(e+f*x))^-2, x) == :(-25//8*a^-2*d^3*f^-1*(d*tan(e+f*x))^(1/2)+-1//4*d*f^-1*(d*tan(e+f*x))^5//2*(a+im*a*tan(e+f*x))^-2+(1/2)*2^(1/2)*a^-2*d^7//2*f^-1*(25//16+-21//16*im)*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+(1/2)*2^(1/2)*a^-2*d^7//2*f^-1*(25//32+21//32*im)*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x))+-1//2*2^(1/2)*a^-2*d^7//2*f^-1*(25//16+-21//16*im)*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-2*d^7//2*f^-1*(25//32+21//32*im)*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2))+7//8*im*a^-2*d^2*f^-1*(d*tan(e+f*x))^3//2*(1+im*tan(e+f*x))^-1)
@test integrate((d*tan(e+f*x))^5//2*(a+im*a*tan(e+f*x))^-2, x) == :(-1//4*d*f^-1*(d*tan(e+f*x))^3//2*(a+im*a*tan(e+f*x))^-2+(1/2)*2^(1/2)*a^-2*d^5//2*f^-1*(9//16+5//16*im)*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+(1/2)*2^(1/2)*a^-2*d^5//2*f^-1*(9//32+-5//32*im)*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x))+-1//2*2^(1/2)*a^-2*d^5//2*f^-1*(9//16+5//16*im)*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-2*d^5//2*f^-1*(9//32+-5//32*im)*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2))+5//8*im*a^-2*d^2*f^-1*(d*tan(e+f*x))^(1/2)*(1+im*tan(e+f*x))^-1)
@test integrate((d*tan(e+f*x))^3//2*(a+im*a*tan(e+f*x))^-2, x) == :(-1//4*d*f^-1*(d*tan(e+f*x))^(1/2)*(a+im*a*tan(e+f*x))^-2+3//8*d*a^-2*f^-1*(d*tan(e+f*x))^(1/2)*(1+im*tan(e+f*x))^-1+(1/2)*2^(1/2)*a^-2*d^3//2*f^-1*(1//16+3//16*im)*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+(1/2)*2^(1/2)*a^-2*d^3//2*f^-1*(1//32+-3//32*im)*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-2*d^3//2*f^-1*(1//16+3//16*im)*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-2*d^3//2*f^-1*(1//32+-3//32*im)*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x)))
@test integrate((d*tan(e+f*x))^(1/2)*(a+im*a*tan(e+f*x))^-2, x) == :(1//4*im*f^-1*(d*tan(e+f*x))^(1/2)*(a+im*a*tan(e+f*x))^-2+1//8*im*a^-2*f^-1*(d*tan(e+f*x))^(1/2)*(1+im*tan(e+f*x))^-1+(1/2)*2^(1/2)*a^-2*d^(1/2)*f^-1*(1//16+-3//16*im)*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+(1/2)*2^(1/2)*a^-2*d^(1/2)*f^-1*(1//32+3//32*im)*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-2*d^(1/2)*f^-1*(1//16+-3//16*im)*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-2*d^(1/2)*f^-1*(1//32+3//32*im)*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x)))
@test integrate((d*tan(e+f*x))^-1//2*(a+im*a*tan(e+f*x))^-2, x) == :(1//4*d^-1*f^-1*(d*tan(e+f*x))^(1/2)*(a+im*a*tan(e+f*x))^-2+5//8*a^-2*d^-1*f^-1*(d*tan(e+f*x))^(1/2)*(1+im*tan(e+f*x))^-1+(1/2)*2^(1/2)*a^-2*d^-1//2*f^-1*(9//16+-5//16*im)*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+(1/2)*2^(1/2)*a^-2*d^-1//2*f^-1*(9//32+5//32*im)*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x))+-1//2*2^(1/2)*a^-2*d^-1//2*f^-1*(9//16+-5//16*im)*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-2*d^-1//2*f^-1*(9//32+5//32*im)*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^-3//2*(a+im*a*tan(e+f*x))^-2, x) == :(-25//8*a^-2*d^-1*f^-1*(d*tan(e+f*x))^-1//2+1//4*d^-1*f^-1*(d*tan(e+f*x))^-1//2*(a+im*a*tan(e+f*x))^-2+7//8*a^-2*d^-1*f^-1*(d*tan(e+f*x))^-1//2*(1+im*tan(e+f*x))^-1+(1/2)*2^(1/2)*a^-2*d^-3//2*f^-1*(25//16+21//16*im)*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+(1/2)*2^(1/2)*a^-2*d^-3//2*f^-1*(25//32+-21//32*im)*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x))+-1//2*2^(1/2)*a^-2*d^-3//2*f^-1*(25//16+21//16*im)*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-2*d^-3//2*f^-1*(25//32+-21//32*im)*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^-5//2*(a+im*a*tan(e+f*x))^-2, x) == :(-49//24*a^-2*d^-1*f^-1*(d*tan(e+f*x))^-3//2+1//4*d^-1*f^-1*(d*tan(e+f*x))^-3//2*(a+im*a*tan(e+f*x))^-2+9//8*a^-2*d^-1*f^-1*(d*tan(e+f*x))^-3//2*(1+im*tan(e+f*x))^-1+45//8*im*a^-2*d^-2*f^-1*(d*tan(e+f*x))^-1//2+(1/2)*2^(1/2)*a^-2*d^-5//2*f^-1*(49//16+-45//16*im)*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+(1/2)*2^(1/2)*a^-2*d^-5//2*f^-1*(49//32+45//32*im)*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-2*d^-5//2*f^-1*(49//16+-45//16*im)*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-2*d^-5//2*f^-1*(49//32+45//32*im)*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x)))
@test integrate((d*tan(e+f*x))^9//2*(a+im*a*tan(e+f*x))^-3, x) == :(-1//6*d*f^-1*(d*tan(e+f*x))^7//2*(a+im*a*tan(e+f*x))^-3+7//6*d^3*f^-1*(d*tan(e+f*x))^3//2*(a^3+im*a^3*tan(e+f*x))^-1+15//4*im*a^-3*d^4*f^-1*(d*tan(e+f*x))^(1/2)+(1/2)*2^(1/2)*a^-3*d^9//2*f^-1*(7//4+15//8*im)*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+(1/2)*2^(1/2)*a^-3*d^9//2*f^-1*(7//8+-15//16*im)*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x))+-1//2*2^(1/2)*a^-3*d^9//2*f^-1*(7//4+15//8*im)*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-3*d^9//2*f^-1*(7//8+-15//16*im)*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2))+5//12*im*a^-1*d^2*f^-1*(d*tan(e+f*x))^5//2*(a+im*a*tan(e+f*x))^-2)
@test integrate((d*tan(e+f*x))^7//2*(a+im*a*tan(e+f*x))^-3, x) == :(-1//6*d*f^-1*(d*tan(e+f*x))^5//2*(a+im*a*tan(e+f*x))^-3+5//8*d^3*f^-1*(d*tan(e+f*x))^(1/2)*(a^3+im*a^3*tan(e+f*x))^-1+(1/2)*2^(1/2)*a^-3*d^7//2*f^-1*(5//16+-7//16*im)*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+(1/2)*2^(1/2)*a^-3*d^7//2*f^-1*(5//32+7//32*im)*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-3*d^7//2*f^-1*(5//16+-7//16*im)*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-3*d^7//2*f^-1*(5//32+7//32*im)*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x))+1//3*im*a^-1*d^2*f^-1*(d*tan(e+f*x))^3//2*(a+im*a*tan(e+f*x))^-2)
@test integrate((d*tan(e+f*x))^5//2*(a+im*a*tan(e+f*x))^-3, x) == :(-1//6*d*f^-1*(d*tan(e+f*x))^3//2*(a+im*a*tan(e+f*x))^-3+-1//4*im*d^2*f^-1*(d*tan(e+f*x))^(1/2)*(a^3+im*a^3*tan(e+f*x))^-1+-1//16*2^(1/2)*a^-3*d^5//2*f^-1*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//32*2^(1/2)*a^-3*d^5//2*f^-1*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2))+1//16*2^(1/2)*a^-3*d^5//2*f^-1*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+1//32*2^(1/2)*a^-3*d^5//2*f^-1*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x))+1//4*im*a^-1*d^2*f^-1*(d*tan(e+f*x))^(1/2)*(a+im*a*tan(e+f*x))^-2)
@test integrate((d*tan(e+f*x))^3//2*(a+im*a*tan(e+f*x))^-3, x) == :(-1//6*d*f^-1*(d*tan(e+f*x))^(1/2)*(a+im*a*tan(e+f*x))^-3+1//8*d*f^-1*(d*tan(e+f*x))^(1/2)*(a^3+im*a^3*tan(e+f*x))^-1+1//6*d*a^-1*f^-1*(d*tan(e+f*x))^(1/2)*(a+im*a*tan(e+f*x))^-2+1//8*(-1)^1//4*a^-3*d^3//2*f^-1*arctan((-1)^3//4*d^-1//2*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^(1/2)*(a+im*a*tan(e+f*x))^-3, x) == :(1//6*im*f^-1*(d*tan(e+f*x))^(1/2)*(a+im*a*tan(e+f*x))^-3+1//12*im*a^-1*f^-1*(d*tan(e+f*x))^(1/2)*(a+im*a*tan(e+f*x))^-2+-1//16*im*2^(1/2)*a^-3*d^(1/2)*f^-1*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//32*im*2^(1/2)*a^-3*d^(1/2)*f^-1*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x))+1//16*im*2^(1/2)*a^-3*d^(1/2)*f^-1*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+1//32*im*2^(1/2)*a^-3*d^(1/2)*f^-1*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^-1//2*(a+im*a*tan(e+f*x))^-3, x) == :(1//6*d^-1*f^-1*(d*tan(e+f*x))^(1/2)*(a+im*a*tan(e+f*x))^-3+5//8*d^-1*f^-1*(d*tan(e+f*x))^(1/2)*(a^3+im*a^3*tan(e+f*x))^-1+1//3*a^-1*d^-1*f^-1*(d*tan(e+f*x))^(1/2)*(a+im*a*tan(e+f*x))^-2+(1/2)*2^(1/2)*a^-3*d^-1//2*f^-1*(7//16+-5//16*im)*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+(1/2)*2^(1/2)*a^-3*d^-1//2*f^-1*(7//32+5//32*im)*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x))+-1//2*2^(1/2)*a^-3*d^-1//2*f^-1*(7//16+-5//16*im)*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-3*d^-1//2*f^-1*(7//32+5//32*im)*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^-3//2*(a+im*a*tan(e+f*x))^-3, x) == :(-15//4*a^-3*d^-1*f^-1*(d*tan(e+f*x))^-1//2+1//6*d^-1*f^-1*(d*tan(e+f*x))^-1//2*(a+im*a*tan(e+f*x))^-3+7//6*d^-1*f^-1*(d*tan(e+f*x))^-1//2*(a^3+im*a^3*tan(e+f*x))^-1+5//12*a^-1*d^-1*f^-1*(d*tan(e+f*x))^-1//2*(a+im*a*tan(e+f*x))^-2+(1/2)*2^(1/2)*a^-3*d^-3//2*f^-1*(15//8+7//4*im)*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+(1/2)*2^(1/2)*a^-3*d^-3//2*f^-1*(15//16+-7//8*im)*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x))+-1//2*2^(1/2)*a^-3*d^-3//2*f^-1*(15//8+7//4*im)*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-3*d^-3//2*f^-1*(15//16+-7//8*im)*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^5//2, x) == :((1/2)*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^3//2+a^(1/2)*d^-1*(1+im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-1//4*im*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^(1/2)+7//4*(-1)^3//4*a^(1/2)*d^-1*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^3//2, x) == :(d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^(1/2)+-1*(-1)^1//4*a^(1/2)*d^-1*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+-1*a^(1/2)*d^-1*(1+-1im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^(1/2), x) == :(-1*a^(1/2)*d^-1*(1+im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-2*(-1)^3//4*a^(1/2)*d^-1*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2, x) == :(a^(1/2)*d^-1*(1+-1im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-3//2, x) == :(-2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2+a^(1/2)*d^-1*(1+im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-5//2, x) == :(-2//3*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-3//2+a^(1/2)*d^-1*(-1+im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-2//3*im*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2)
@test integrate((a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-7//2, x) == :(-2//5*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-5//2+26//15*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2+a^(1/2)*d^-1*(-1+-1im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-2//15*im*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-3//2)
@test integrate((a+im*a*tan(c+d*x))^3//2*tan(c+d*x)^5//2, x) == :(a^3//2*d^-1*(2+2im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-1//3*a^2*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^7//2+7//12*a*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^3//2+23//8*(-1)^3//4*a^3//2*d^-1*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+-9//8*im*a*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^(1/2)+1//3*im*a^2*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^5//2)
@test integrate((a+im*a*tan(c+d*x))^3//2*tan(c+d*x)^3//2, x) == :(-1*a^3//2*d^-1*(2+-2im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-11//4*(-1)^1//4*a^3//2*d^-1*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+-1//2*a^2*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^5//2+5//4*a*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^(1/2)+(1/2)*im*a^2*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^3//2)
@test integrate((a+im*a*tan(c+d*x))^3//2*tan(c+d*x)^(1/2), x) == :(-1*a^2*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^3//2+-1*a^3//2*d^-1*(2+2im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-3*(-1)^3//4*a^3//2*d^-1*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+im*a^2*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))
@test integrate((a+im*a*tan(c+d*x))^3//2*tan(c+d*x)^-1//2, x) == :(a^3//2*d^-1*(2+-2im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+2*(-1)^1//4*a^3//2*d^-1*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^3//2*tan(c+d*x)^-3//2, x) == :(a^3//2*d^-1*(2+2im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-2*a*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2)
@test integrate((a+im*a*tan(c+d*x))^3//2*tan(c+d*x)^-5//2, x) == :(-2//3*d^-1*(a+im*a*tan(c+d*x))^3//2*tan(c+d*x)^-3//2+a^3//2*d^-1*(-2+2im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-2*im*a*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2)
@test integrate((a+im*a*tan(c+d*x))^3//2*tan(c+d*x)^-7//2, x) == :(a^3//2*d^-1*(-2+-2im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-2//5*a^2*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^-5//2+12//5*a*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2+-4//5*im*a*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-3//2+-2//5*im*a^2*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^-3//2)
@test integrate((a+im*a*tan(c+d*x))^3//2*tan(c+d*x)^-9//2, x) == :(a^3//2*d^-1*(2+-2im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-2//7*a^2*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^-7//2+76//105*a*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-3//2+-16//35*im*a*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-5//2+-2//7*im*a^2*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^-5//2+268//105*im*a*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2)
@test integrate((a+im*a*tan(c+d*x))^5//2*tan(c+d*x)^5//2, x) == :(a^5//2*d^-1*(4+4im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-1//4*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^7//2+107//96*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^3//2+363//64*(-1)^3//4*a^5//2*d^-1*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+-149//64*im*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^(1/2)+17//24*im*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^5//2)
@test integrate((a+im*a*tan(c+d*x))^5//2*tan(c+d*x)^3//2, x) == :(-1*a^5//2*d^-1*(4+-4im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-45//8*(-1)^1//4*a^5//2*d^-1*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+-1//3*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^5//2+19//8*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^(1/2)+13//12*im*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^3//2)
@test integrate((a+im*a*tan(c+d*x))^5//2*tan(c+d*x)^(1/2), x) == :(-1*a^5//2*d^-1*(4+4im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-23//4*(-1)^3//4*a^5//2*d^-1*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+-1//2*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^3//2+9//4*im*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^(1/2))
@test integrate((a+im*a*tan(c+d*x))^5//2*tan(c+d*x)^-1//2, x) == :(a^5//2*d^-1*(4+-4im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-1*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^(1/2)+5*(-1)^1//4*a^5//2*d^-1*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^5//2*tan(c+d*x)^-3//2, x) == :(a^5//2*d^-1*(4+4im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-2*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2+2*(-1)^3//4*a^5//2*d^-1*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^5//2*tan(c+d*x)^-5//2, x) == :(a^5//2*d^-1*(-4+4im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-2//3*a*d^-1*(a+im*a*tan(c+d*x))^3//2*tan(c+d*x)^-3//2+-4*im*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2)
@test integrate((a+im*a*tan(c+d*x))^5//2*tan(c+d*x)^-7//2, x) == :(-2//5*d^-1*(a+im*a*tan(c+d*x))^5//2*tan(c+d*x)^-5//2+a^5//2*d^-1*(-4+-4im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+4*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2+-2//3*im*a*d^-1*(a+im*a*tan(c+d*x))^3//2*tan(c+d*x)^-3//2)
@test integrate((a+im*a*tan(c+d*x))^5//2*tan(c+d*x)^-9//2, x) == :(a^5//2*d^-1*(4+-4im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-2//7*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-7//2+32//21*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-3//2+-6//7*im*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-5//2+104//21*im*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2)
@test integrate((a+im*a*tan(c+d*x))^5//2*tan(c+d*x)^-11//2, x) == :(a^5//2*d^-1*(4+4im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-1576//315*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2+-2//9*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-9//2+92//105*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-5//2+-38//63*im*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-7//2+472//315*im*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-3//2)
@test integrate((a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^7//2, x) == :(-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^5//2+a^-1//2*d^-1*(1/2+-1//2*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+7//4*a^-1*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^(1/2)+11//4*(-1)^1//4*a^-1//2*d^-1*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+-3//2*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^3//2)
@test integrate((a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^5//2, x) == :(-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^3//2+a^-1//2*d^-1*(1/2+(1/2)*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-1*(-1)^3//4*a^-1//2*d^-1*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+-2*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^(1/2))
@test integrate((a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^3//2, x) == :(-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)+-1*a^-1//2*d^-1*(1/2+-1//2*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-2*(-1)^1//4*a^-1//2*d^-1*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2), x) == :(im*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)+a^-1//2*d^-1*(-1//2+-1//2*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^-1//2, x) == :(d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)+a^-1//2*d^-1*(1/2+-1//2*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^-3//2, x) == :(d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^-1//2+a^-1//2*d^-1*(1/2+(1/2)*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-3*a^-1*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2)
@test integrate((a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^-5//2, x) == :(d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^-3//2+-1*a^-1//2*d^-1*(1/2+-1//2*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-5//3*a^-1*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-3//2+7//3*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2)
@test integrate((a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^-7//2, x) == :(d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^-5//2+-1*a^-1//2*d^-1*(1/2+(1/2)*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-7//5*a^-1*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-5//2+61//15*a^-1*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2+23//15*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-3//2)
@test integrate((a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^7//2, x) == :(-1//3*d^-1*(a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^5//2+a^-3//2*d^-1*(1//4+-1//4*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-3*(-1)^1//4*a^-3//2*d^-1*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+-7//2*a^-2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^(1/2)+13//6*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^3//2)
@test integrate((a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^5//2, x) == :(-1//3*d^-1*(a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^3//2+a^-3//2*d^-1*(1//4+1//4*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+2*(-1)^3//4*a^-3//2*d^-1*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+3//2*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))
@test integrate((a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^3//2, x) == :(a^-3//2*d^-1*(-1//4+1//4*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+(1/2)*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)+1//3*im*d^-1*(a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^3//2)
@test integrate((a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^(1/2), x) == :(1//3*d^-1*(a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^3//2+-1*a^-3//2*d^-1*(1//4+1//4*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+(1/2)*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))
@test integrate((a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^-1//2, x) == :(1//3*d^-1*(a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^(1/2)+a^-3//2*d^-1*(1//4+-1//4*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+7//6*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))
@test integrate((a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^-3//2, x) == :(1//3*d^-1*(a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^-1//2+a^-3//2*d^-1*(1//4+1//4*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-25//6*a^-2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2+11//6*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^-1//2)
@test integrate((a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^-5//2, x) == :(1//3*d^-1*(a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^-3//2+a^-3//2*d^-1*(-1//4+1//4*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-7//2*a^-2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-3//2+5//2*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^-3//2+13//2*im*a^-2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2)
@test integrate((a+im*a*tan(c+d*x))^-5//2*tan(c+d*x)^9//2, x) == :(-1//5*d^-1*(a+im*a*tan(c+d*x))^-5//2*tan(c+d*x)^7//2+-1*a^-5//2*d^-1*(1//8+1//8*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+5*(-1)^3//4*a^-5//2*d^-1*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+41//12*a^-2*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^3//2+19//30*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^5//2+21//4*im*a^-3*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^(1/2))
@test integrate((a+im*a*tan(c+d*x))^-5//2*tan(c+d*x)^7//2, x) == :(-1//5*d^-1*(a+im*a*tan(c+d*x))^-5//2*tan(c+d*x)^5//2+a^-5//2*d^-1*(1//8+-1//8*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+2*(-1)^1//4*a^-5//2*d^-1*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+7//4*a^-2*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)+(1/2)*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^3//2)
@test integrate((a+im*a*tan(c+d*x))^-5//2*tan(c+d*x)^5//2, x) == :(a^-5//2*d^-1*(1//8+1//8*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+1//5*im*d^-1*(a+im*a*tan(c+d*x))^-5//2*tan(c+d*x)^5//2+1//6*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^3//2+-1//4*im*a^-2*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))
@test integrate((a+im*a*tan(c+d*x))^-5//2*tan(c+d*x)^3//2, x) == :(1//5*d^-1*(a+im*a*tan(c+d*x))^-5//2*tan(c+d*x)^5//2+a^-5//2*d^-1*(-1//8+1//8*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+1//4*a^-2*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)+1//6*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^3//2)
@test integrate((a+im*a*tan(c+d*x))^-5//2*tan(c+d*x)^(1/2), x) == :(a^-5//2*d^-1*(-1//8+-1//8*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+1//5*im*d^-1*(a+im*a*tan(c+d*x))^-5//2*tan(c+d*x)^(1/2)+-1//20*im*a^-2*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)+1//10*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^(1/2))
@test integrate((a+im*a*tan(c+d*x))^-5//2*tan(c+d*x)^-1//2, x) == :(1//5*d^-1*(a+im*a*tan(c+d*x))^-5//2*tan(c+d*x)^(1/2)+a^-5//2*d^-1*(1//8+-1//8*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+13//30*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^(1/2)+67//60*a^-2*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))
@test integrate((a+im*a*tan(c+d*x))^-5//2*tan(c+d*x)^-3//2, x) == :(1//5*d^-1*(a+im*a*tan(c+d*x))^-5//2*tan(c+d*x)^-1//2+a^-5//2*d^-1*(1//8+1//8*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-317//60*a^-3*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2+17//30*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^-1//2+151//60*a^-2*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^-1//2)
@test integrate((a+im*a*tan(c+d*x))^-5//2*tan(c+d*x)^-5//2, x) == :(1//5*d^-1*(a+im*a*tan(c+d*x))^-5//2*tan(c+d*x)^-3//2+a^-5//2*d^-1*(-1//8+1//8*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-361//60*a^-3*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-3//2+7//10*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3//2*tan(c+d*x)^-3//2+89//20*a^-2*d^-1*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^-3//2+707//60*im*a^-3*d^-1*(a+im*a*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2)
@test integrate((a+im*a*tan(c+d*x))^-1*tan(c+d*x)^10//3, x) == :(-7//6*a^-1*d^-1*arctan(tan(c+d*x)^1//3)+-7//12*a^-1*d^-1*arctan(3^(1/2)+2*tan(c+d*x)^1//3)+-1//2*d^-1*(a+im*a*tan(c+d*x))^-1*tan(c+d*x)^7//3+7//2*a^-1*d^-1*tan(c+d*x)^1//3+7//12*a^-1*d^-1*arctan(3^(1/2)+-2*tan(c+d*x)^1//3)+-7//24*3^(1/2)*a^-1*d^-1*log(1+tan(c+d*x)^2//3+3^(1/2)*tan(c+d*x)^1//3)+-5//4*im*a^-1*d^-1*tan(c+d*x)^4//3+-5//6*im*a^-1*d^-1*log(1+tan(c+d*x)^2//3)+5//12*im*a^-1*d^-1*log(1+tan(c+d*x)^4//3+-1*tan(c+d*x)^2//3)+7//24*3^(1/2)*a^-1*d^-1*log(1+tan(c+d*x)^2//3+-1*3^(1/2)*tan(c+d*x)^1//3)+-5//6*im*3^(1/2)*a^-1*d^-1*arctan(1//3*3^(1/2)*(1+-2*tan(c+d*x)^2//3)))
@test integrate((a+im*a*tan(c+d*x))^-1*tan(c+d*x)^8//3, x) == :(-5//12*a^-1*d^-1*arctan(3^(1/2)+-2*tan(c+d*x)^1//3)+-1//2*d^-1*(a+im*a*tan(c+d*x))^-1*tan(c+d*x)^5//3+5//6*a^-1*d^-1*arctan(tan(c+d*x)^1//3)+5//12*a^-1*d^-1*arctan(3^(1/2)+2*tan(c+d*x)^1//3)+-2*im*a^-1*d^-1*tan(c+d*x)^2//3+-5//24*3^(1/2)*a^-1*d^-1*log(1+tan(c+d*x)^2//3+3^(1/2)*tan(c+d*x)^1//3)+-1//3*im*a^-1*d^-1*log(1+tan(c+d*x)^4//3+-1*tan(c+d*x)^2//3)+2//3*im*a^-1*d^-1*log(1+tan(c+d*x)^2//3)+5//24*3^(1/2)*a^-1*d^-1*log(1+tan(c+d*x)^2//3+-1*3^(1/2)*tan(c+d*x)^1//3)+-2//3*im*3^(1/2)*a^-1*d^-1*arctan(1//3*3^(1/2)*(1+-2*tan(c+d*x)^2//3)))
@test integrate((a+im*a*tan(c+d*x))^-1*tan(c+d*x)^4//3, x) == :(-1//2*d^-1*(a+im*a*tan(c+d*x))^-1*tan(c+d*x)^1//3+-1//12*a^-1*d^-1*arctan(3^(1/2)+-2*tan(c+d*x)^1//3)+1//6*a^-1*d^-1*arctan(tan(c+d*x)^1//3)+1//12*a^-1*d^-1*arctan(3^(1/2)+2*tan(c+d*x)^1//3)+-1//6*im*a^-1*d^-1*log(1+tan(c+d*x)^4//3+-1*tan(c+d*x)^2//3)+-1//24*3^(1/2)*a^-1*d^-1*log(1+tan(c+d*x)^2//3+-1*3^(1/2)*tan(c+d*x)^1//3)+1//3*im*a^-1*d^-1*log(1+tan(c+d*x)^2//3)+1//24*3^(1/2)*a^-1*d^-1*log(1+tan(c+d*x)^2//3+3^(1/2)*tan(c+d*x)^1//3)+1//3*im*3^(1/2)*a^-1*d^-1*arctan(1//3*3^(1/2)*(1+-2*tan(c+d*x)^2//3)))
@test integrate((a+im*a*tan(c+d*x))^-1*tan(c+d*x)^2//3, x) == :(-1//12*a^-1*d^-1*arctan(3^(1/2)+-2*tan(c+d*x)^1//3)+1//6*a^-1*d^-1*arctan(tan(c+d*x)^1//3)+1//12*a^-1*d^-1*arctan(3^(1/2)+2*tan(c+d*x)^1//3)+(1/2)*im*d^-1*(a+im*a*tan(c+d*x))^-1*tan(c+d*x)^2//3+-1//6*im*a^-1*d^-1*log(1+tan(c+d*x)^2//3)+-1//24*3^(1/2)*a^-1*d^-1*log(1+tan(c+d*x)^2//3+3^(1/2)*tan(c+d*x)^1//3)+1//12*im*a^-1*d^-1*log(1+tan(c+d*x)^4//3+-1*tan(c+d*x)^2//3)+1//24*3^(1/2)*a^-1*d^-1*log(1+tan(c+d*x)^2//3+-1*3^(1/2)*tan(c+d*x)^1//3)+1//6*im*3^(1/2)*a^-1*d^-1*arctan(1//3*3^(1/2)*(1+-2*tan(c+d*x)^2//3)))
@test integrate((a+im*a*tan(c+d*x))^-1*tan(c+d*x)^-1//3, x) == :((1/2)*d^-1*(a+im*a*tan(c+d*x))^-1*tan(c+d*x)^2//3+-1//6*a^-1*d^-1*log(1+tan(c+d*x)^4//3+-1*tan(c+d*x)^2//3)+1//3*a^-1*d^-1*log(1+tan(c+d*x)^2//3)+-1//3*3^(1/2)*a^-1*d^-1*arctan(1//3*3^(1/2)*(1+-2*tan(c+d*x)^2//3))+-1//6*im*a^-1*d^-1*arctan(tan(c+d*x)^1//3)+-1//12*im*a^-1*d^-1*arctan(3^(1/2)+2*tan(c+d*x)^1//3)+1//12*im*a^-1*d^-1*arctan(3^(1/2)+-2*tan(c+d*x)^1//3)+-1//24*im*3^(1/2)*a^-1*d^-1*log(1+tan(c+d*x)^2//3+-1*3^(1/2)*tan(c+d*x)^1//3)+1//24*im*3^(1/2)*a^-1*d^-1*log(1+tan(c+d*x)^2//3+3^(1/2)*tan(c+d*x)^1//3))
@test integrate((a+im*a*tan(c+d*x))^-1*tan(c+d*x)^-5//3, x) == :((1/2)*d^-1*(a+im*a*tan(c+d*x))^-1*tan(c+d*x)^-2//3+-2*a^-1*d^-1*tan(c+d*x)^-2//3+-1//3*a^-1*d^-1*log(1+tan(c+d*x)^4//3+-1*tan(c+d*x)^2//3)+2//3*a^-1*d^-1*log(1+tan(c+d*x)^2//3)+-5//6*im*a^-1*d^-1*arctan(tan(c+d*x)^1//3)+-5//12*im*a^-1*d^-1*arctan(3^(1/2)+2*tan(c+d*x)^1//3)+2//3*3^(1/2)*a^-1*d^-1*arctan(1//3*3^(1/2)*(1+-2*tan(c+d*x)^2//3))+5//12*im*a^-1*d^-1*arctan(3^(1/2)+-2*tan(c+d*x)^1//3)+-5//24*im*3^(1/2)*a^-1*d^-1*log(1+tan(c+d*x)^2//3+3^(1/2)*tan(c+d*x)^1//3)+5//24*im*3^(1/2)*a^-1*d^-1*log(1+tan(c+d*x)^2//3+-1*3^(1/2)*tan(c+d*x)^1//3))
@test integrate((a+im*a*tan(c+d*x))^-1*tan(c+d*x)^-7//3, x) == :((1/2)*d^-1*(a+im*a*tan(c+d*x))^-1*tan(c+d*x)^-4//3+-5//4*a^-1*d^-1*tan(c+d*x)^-4//3+-5//6*a^-1*d^-1*log(1+tan(c+d*x)^2//3)+5//12*a^-1*d^-1*log(1+tan(c+d*x)^4//3+-1*tan(c+d*x)^2//3)+-7//12*im*a^-1*d^-1*arctan(3^(1/2)+-2*tan(c+d*x)^1//3)+5//6*3^(1/2)*a^-1*d^-1*arctan(1//3*3^(1/2)*(1+-2*tan(c+d*x)^2//3))+7//2*im*a^-1*d^-1*tan(c+d*x)^-1//3+7//6*im*a^-1*d^-1*arctan(tan(c+d*x)^1//3)+7//12*im*a^-1*d^-1*arctan(3^(1/2)+2*tan(c+d*x)^1//3)+-7//24*im*3^(1/2)*a^-1*d^-1*log(1+tan(c+d*x)^2//3+3^(1/2)*tan(c+d*x)^1//3)+7//24*im*3^(1/2)*a^-1*d^-1*log(1+tan(c+d*x)^2//3+-1*3^(1/2)*tan(c+d*x)^1//3))
@test integrate((a+im*a*tan(c+d*x))^-2*tan(c+d*x)^14//3, x) == :(-121//60*a^-2*d^-1*tan(c+d*x)^5//3+-121//72*a^-2*d^-1*arctan(3^(1/2)+-2*tan(c+d*x)^1//3)+-1//4*d^-1*(a+im*a*tan(c+d*x))^-2*tan(c+d*x)^11//3+121//36*a^-2*d^-1*arctan(tan(c+d*x)^1//3)+121//72*a^-2*d^-1*arctan(3^(1/2)+2*tan(c+d*x)^1//3)+-121//144*3^(1/2)*a^-2*d^-1*log(1+tan(c+d*x)^2//3+3^(1/2)*tan(c+d*x)^1//3)+-14//3*im*a^-2*d^-1*tan(c+d*x)^2//3+-7//9*im*a^-2*d^-1*log(1+tan(c+d*x)^4//3+-1*tan(c+d*x)^2//3)+14//9*im*a^-2*d^-1*log(1+tan(c+d*x)^2//3)+121//144*3^(1/2)*a^-2*d^-1*log(1+tan(c+d*x)^2//3+-1*3^(1/2)*tan(c+d*x)^1//3)+-14//9*im*3^(1/2)*a^-2*d^-1*arctan(1//3*3^(1/2)*(1+-2*tan(c+d*x)^2//3))+7//6*im*a^-2*d^-1*(1+im*tan(c+d*x))^-1*tan(c+d*x)^8//3)
@test integrate((a+im*a*tan(c+d*x))^-2*tan(c+d*x)^10//3, x) == :(-49//12*a^-2*d^-1*tan(c+d*x)^1//3+-49//72*a^-2*d^-1*arctan(3^(1/2)+-2*tan(c+d*x)^1//3)+-1//4*d^-1*(a+im*a*tan(c+d*x))^-2*tan(c+d*x)^7//3+49//36*a^-2*d^-1*arctan(tan(c+d*x)^1//3)+49//72*a^-2*d^-1*arctan(3^(1/2)+2*tan(c+d*x)^1//3)+-49//144*3^(1/2)*a^-2*d^-1*log(1+tan(c+d*x)^2//3+-1*3^(1/2)*tan(c+d*x)^1//3)+-5//18*im*a^-2*d^-1*log(1+tan(c+d*x)^4//3+-1*tan(c+d*x)^2//3)+5//9*im*a^-2*d^-1*log(1+tan(c+d*x)^2//3)+49//144*3^(1/2)*a^-2*d^-1*log(1+tan(c+d*x)^2//3+3^(1/2)*tan(c+d*x)^1//3)+5//6*im*a^-2*d^-1*(1+im*tan(c+d*x))^-1*tan(c+d*x)^4//3+5//9*im*3^(1/2)*a^-2*d^-1*arctan(1//3*3^(1/2)*(1+-2*tan(c+d*x)^2//3)))
@test integrate((a+im*a*tan(c+d*x))^-2*tan(c+d*x)^8//3, x) == :(-25//36*a^-2*d^-1*arctan(tan(c+d*x)^1//3)+-25//72*a^-2*d^-1*arctan(3^(1/2)+2*tan(c+d*x)^1//3)+-1//4*d^-1*(a+im*a*tan(c+d*x))^-2*tan(c+d*x)^5//3+25//72*a^-2*d^-1*arctan(3^(1/2)+-2*tan(c+d*x)^1//3)+-25//144*3^(1/2)*a^-2*d^-1*log(1+tan(c+d*x)^2//3+-1*3^(1/2)*tan(c+d*x)^1//3)+-2//9*im*a^-2*d^-1*log(1+tan(c+d*x)^2//3)+1//9*im*a^-2*d^-1*log(1+tan(c+d*x)^4//3+-1*tan(c+d*x)^2//3)+25//144*3^(1/2)*a^-2*d^-1*log(1+tan(c+d*x)^2//3+3^(1/2)*tan(c+d*x)^1//3)+2//3*im*a^-2*d^-1*(1+im*tan(c+d*x))^-1*tan(c+d*x)^2//3+2//9*im*3^(1/2)*a^-2*d^-1*arctan(1//3*3^(1/2)*(1+-2*tan(c+d*x)^2//3)))
@test integrate((a+im*a*tan(c+d*x))^-2*tan(c+d*x)^4//3, x) == :(-1//4*d^-1*(a+im*a*tan(c+d*x))^-2*tan(c+d*x)^1//3+-1//36*a^-2*d^-1*arctan(tan(c+d*x)^1//3)+-1//72*a^-2*d^-1*arctan(3^(1/2)+2*tan(c+d*x)^1//3)+1//72*a^-2*d^-1*arctan(3^(1/2)+-2*tan(c+d*x)^1//3)+-1//18*im*a^-2*d^-1*log(1+tan(c+d*x)^4//3+-1*tan(c+d*x)^2//3)+-1//144*3^(1/2)*a^-2*d^-1*log(1+tan(c+d*x)^2//3+3^(1/2)*tan(c+d*x)^1//3)+1//3*a^-2*d^-1*(1+im*tan(c+d*x))^-1*tan(c+d*x)^1//3+1//9*im*a^-2*d^-1*log(1+tan(c+d*x)^2//3)+1//144*3^(1/2)*a^-2*d^-1*log(1+tan(c+d*x)^2//3+-1*3^(1/2)*tan(c+d*x)^1//3)+1//9*im*3^(1/2)*a^-2*d^-1*arctan(1//3*3^(1/2)*(1+-2*tan(c+d*x)^2//3)))
@test integrate((a+im*a*tan(c+d*x))^-2*tan(c+d*x)^2//3, x) == :(-1//72*a^-2*d^-1*arctan(3^(1/2)+-2*tan(c+d*x)^1//3)+1//4*d^-1*(a+im*a*tan(c+d*x))^-2*tan(c+d*x)^5//3+1//36*a^-2*d^-1*arctan(tan(c+d*x)^1//3)+1//72*a^-2*d^-1*arctan(3^(1/2)+2*tan(c+d*x)^1//3)+-1//9*im*a^-2*d^-1*log(1+tan(c+d*x)^2//3)+-1//144*3^(1/2)*a^-2*d^-1*log(1+tan(c+d*x)^2//3+3^(1/2)*tan(c+d*x)^1//3)+1//18*im*a^-2*d^-1*log(1+tan(c+d*x)^4//3+-1*tan(c+d*x)^2//3)+1//144*3^(1/2)*a^-2*d^-1*log(1+tan(c+d*x)^2//3+-1*3^(1/2)*tan(c+d*x)^1//3)+1//3*im*a^-2*d^-1*(1+im*tan(c+d*x))^-1*tan(c+d*x)^2//3+1//9*im*3^(1/2)*a^-2*d^-1*arctan(1//3*3^(1/2)*(1+-2*tan(c+d*x)^2//3)))
@test integrate((a+im*a*tan(c+d*x))^-2*tan(c+d*x)^-1//3, x) == :(-1//9*a^-2*d^-1*log(1+tan(c+d*x)^4//3+-1*tan(c+d*x)^2//3)+1//4*d^-1*(a+im*a*tan(c+d*x))^-2*tan(c+d*x)^2//3+2//9*a^-2*d^-1*log(1+tan(c+d*x)^2//3)+-7//36*im*a^-2*d^-1*arctan(tan(c+d*x)^1//3)+-7//72*im*a^-2*d^-1*arctan(3^(1/2)+2*tan(c+d*x)^1//3)+-2//9*3^(1/2)*a^-2*d^-1*arctan(1//3*3^(1/2)*(1+-2*tan(c+d*x)^2//3))+7//12*a^-2*d^-1*(1+im*tan(c+d*x))^-1*tan(c+d*x)^2//3+7//72*im*a^-2*d^-1*arctan(3^(1/2)+-2*tan(c+d*x)^1//3)+-7//144*im*3^(1/2)*a^-2*d^-1*log(1+tan(c+d*x)^2//3+-1*3^(1/2)*tan(c+d*x)^1//3)+7//144*im*3^(1/2)*a^-2*d^-1*log(1+tan(c+d*x)^2//3+3^(1/2)*tan(c+d*x)^1//3))
@test integrate((a+im*a*tan(c+d*x))^-2*tan(c+d*x)^-5//3, x) == :(-8//3*a^-2*d^-1*tan(c+d*x)^-2//3+-4//9*a^-2*d^-1*log(1+tan(c+d*x)^4//3+-1*tan(c+d*x)^2//3)+1//4*d^-1*(a+im*a*tan(c+d*x))^-2*tan(c+d*x)^-2//3+8//9*a^-2*d^-1*log(1+tan(c+d*x)^2//3)+-55//36*im*a^-2*d^-1*arctan(tan(c+d*x)^1//3)+-55//72*im*a^-2*d^-1*arctan(3^(1/2)+2*tan(c+d*x)^1//3)+8//9*3^(1/2)*a^-2*d^-1*arctan(1//3*3^(1/2)*(1+-2*tan(c+d*x)^2//3))+11//12*a^-2*d^-1*(1+im*tan(c+d*x))^-1*tan(c+d*x)^-2//3+55//72*im*a^-2*d^-1*arctan(3^(1/2)+-2*tan(c+d*x)^1//3)+-55//144*im*3^(1/2)*a^-2*d^-1*log(1+tan(c+d*x)^2//3+3^(1/2)*tan(c+d*x)^1//3)+55//144*im*3^(1/2)*a^-2*d^-1*log(1+tan(c+d*x)^2//3+-1*3^(1/2)*tan(c+d*x)^1//3))
@test integrate((a+im*a*tan(c+d*x))^-2*tan(c+d*x)^-7//3, x) == :(-25//12*a^-2*d^-1*tan(c+d*x)^-4//3+-25//18*a^-2*d^-1*log(1+tan(c+d*x)^2//3)+1//4*d^-1*(a+im*a*tan(c+d*x))^-2*tan(c+d*x)^-4//3+25//36*a^-2*d^-1*log(1+tan(c+d*x)^4//3+-1*tan(c+d*x)^2//3)+-91//72*im*a^-2*d^-1*arctan(3^(1/2)+-2*tan(c+d*x)^1//3)+13//12*a^-2*d^-1*(1+im*tan(c+d*x))^-1*tan(c+d*x)^-4//3+25//18*3^(1/2)*a^-2*d^-1*arctan(1//3*3^(1/2)*(1+-2*tan(c+d*x)^2//3))+91//12*im*a^-2*d^-1*tan(c+d*x)^-1//3+91//36*im*a^-2*d^-1*arctan(tan(c+d*x)^1//3)+91//72*im*a^-2*d^-1*arctan(3^(1/2)+2*tan(c+d*x)^1//3)+-91//144*im*3^(1/2)*a^-2*d^-1*log(1+tan(c+d*x)^2//3+3^(1/2)*tan(c+d*x)^1//3)+91//144*im*3^(1/2)*a^-2*d^-1*log(1+tan(c+d*x)^2//3+-1*3^(1/2)*tan(c+d*x)^1//3))
@test integrate((a+im*a*tan(c+d*x))^1//3*tan(c+d*x)^3, x) == :(-18//7*d^-1*(a+im*a*tan(c+d*x))^1//3+-3//28*a^-1*d^-1*(a+im*a*tan(c+d*x))^4//3+3//7*d^-1*(a+im*a*tan(c+d*x))^1//3*tan(c+d*x)^2+-3//4*2^1//3*a^1//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+-1//4*im*x*2^1//3*a^1//3+-1//4*2^1//3*a^1//3*d^-1*log(cos(c+d*x))+(1/2)*2^1//3*3^(1/2)*a^1//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^1//3*tan(c+d*x)^2, x) == :(1//4*x*2^1//3*a^1//3+-3//4*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^4//3+-3//4*im*2^1//3*a^1//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+-1//4*im*2^1//3*a^1//3*d^-1*log(cos(c+d*x))+(1/2)*im*2^1//3*3^(1/2)*a^1//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^1//3*tan(c+d*x), x) == :(3*d^-1*(a+im*a*tan(c+d*x))^1//3+1//4*im*x*2^1//3*a^1//3+1//4*2^1//3*a^1//3*d^-1*log(cos(c+d*x))+3//4*2^1//3*a^1//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+-1//2*2^1//3*3^(1/2)*a^1//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^1//3, x) == :(-1//4*x*2^1//3*a^1//3+1//4*im*2^1//3*a^1//3*d^-1*log(cos(c+d*x))+3//4*im*2^1//3*a^1//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+-1//2*im*2^1//3*3^(1/2)*a^1//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^1//3*cot(c+d*x), x) == :(-1//2*a^1//3*d^-1*log(tan(c+d*x))+3//2*a^1//3*d^-1*log(a^1//3+-1*(a+im*a*tan(c+d*x))^1//3)+-1*3^(1/2)*a^1//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+im*a*tan(c+d*x))^1//3))+-3//4*2^1//3*a^1//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+-1//4*im*x*2^1//3*a^1//3+-1//4*2^1//3*a^1//3*d^-1*log(cos(c+d*x))+(1/2)*2^1//3*3^(1/2)*a^1//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^1//3*cot(c+d*x)^2, x) == :(-1*d^-1*(a+im*a*tan(c+d*x))^1//3*cot(c+d*x)+1//4*x*2^1//3*a^1//3+(1/2)*im*a^1//3*d^-1*log(a^1//3+-1*(a+im*a*tan(c+d*x))^1//3)+-1//6*im*a^1//3*d^-1*log(tan(c+d*x))+-3//4*im*2^1//3*a^1//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+-1//3*im*3^(1/2)*a^1//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+im*a*tan(c+d*x))^1//3))+-1//4*im*2^1//3*a^1//3*d^-1*log(cos(c+d*x))+(1/2)*im*2^1//3*3^(1/2)*a^1//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^1//3*cot(c+d*x)^3, x) == :(-4//3*a^1//3*d^-1*log(a^1//3+-1*(a+im*a*tan(c+d*x))^1//3)+-1//2*d^-1*(a+im*a*tan(c+d*x))^1//3*cot(c+d*x)^2+4//9*a^1//3*d^-1*log(tan(c+d*x))+-1//6*im*d^-1*(a+im*a*tan(c+d*x))^1//3*cot(c+d*x)+1//4*im*x*2^1//3*a^1//3+1//4*2^1//3*a^1//3*d^-1*log(cos(c+d*x))+3//4*2^1//3*a^1//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+8//9*3^(1/2)*a^1//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+im*a*tan(c+d*x))^1//3))+-1//2*2^1//3*3^(1/2)*a^1//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^2//3, x) == :(-1//4*x*2^2//3*a^2//3+1//4*im*2^2//3*a^2//3*d^-1*log(cos(c+d*x))+3//4*im*2^2//3*a^2//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+(1/2)*im*2^2//3*3^(1/2)*a^2//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^4//3*tan(c+d*x)^3, x) == :(-9//20*d^-1*(a+im*a*tan(c+d*x))^4//3+-3*a*d^-1*(a+im*a*tan(c+d*x))^1//3+-6//35*a^-1*d^-1*(a+im*a*tan(c+d*x))^7//3+3//10*d^-1*(a+im*a*tan(c+d*x))^4//3*tan(c+d*x)^2+-3//2*2^1//3*a^4//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+-1//2*im*x*2^1//3*a^4//3+-1//2*2^1//3*a^4//3*d^-1*log(cos(c+d*x))+2^1//3*3^(1/2)*a^4//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^4//3*tan(c+d*x)^2, x) == :((1/2)*x*2^1//3*a^4//3+-3*im*a*d^-1*(a+im*a*tan(c+d*x))^1//3+-3//7*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^7//3+-3//2*im*2^1//3*a^4//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+-1//2*im*2^1//3*a^4//3*d^-1*log(cos(c+d*x))+im*2^1//3*3^(1/2)*a^4//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^4//3*tan(c+d*x), x) == :(3//4*d^-1*(a+im*a*tan(c+d*x))^4//3+3*a*d^-1*(a+im*a*tan(c+d*x))^1//3+(1/2)*im*x*2^1//3*a^4//3+(1/2)*2^1//3*a^4//3*d^-1*log(cos(c+d*x))+3//2*2^1//3*a^4//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+-1*2^1//3*3^(1/2)*a^4//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^4//3, x) == :(-1//2*x*2^1//3*a^4//3+3*im*a*d^-1*(a+im*a*tan(c+d*x))^1//3+(1/2)*im*2^1//3*a^4//3*d^-1*log(cos(c+d*x))+3//2*im*2^1//3*a^4//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+-1*im*2^1//3*3^(1/2)*a^4//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^4//3*cot(c+d*x), x) == :(-1//2*a^4//3*d^-1*log(tan(c+d*x))+3//2*a^4//3*d^-1*log(a^1//3+-1*(a+im*a*tan(c+d*x))^1//3)+-1*3^(1/2)*a^4//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+im*a*tan(c+d*x))^1//3))+-3//2*2^1//3*a^4//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+-1//2*im*x*2^1//3*a^4//3+-1//2*2^1//3*a^4//3*d^-1*log(cos(c+d*x))+2^1//3*3^(1/2)*a^4//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^4//3*cot(c+d*x)^2, x) == :((1/2)*x*2^1//3*a^4//3+-1*d^-1*(a+im*a*tan(c+d*x))^4//3*cot(c+d*x)+im*a*d^-1*(a+im*a*tan(c+d*x))^1//3+2*im*a^4//3*d^-1*log(a^1//3+-1*(a+im*a*tan(c+d*x))^1//3)+-2//3*im*a^4//3*d^-1*log(tan(c+d*x))+-4//3*im*3^(1/2)*a^4//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+im*a*tan(c+d*x))^1//3))+-3//2*im*2^1//3*a^4//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+-1//2*im*2^1//3*a^4//3*d^-1*log(cos(c+d*x))+im*2^1//3*3^(1/2)*a^4//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^4//3*cot(c+d*x)^3, x) == :(-11//6*a^4//3*d^-1*log(a^1//3+-1*(a+im*a*tan(c+d*x))^1//3)+-1//2*d^-1*(a+im*a*tan(c+d*x))^4//3*cot(c+d*x)^2+11//18*a^4//3*d^-1*log(tan(c+d*x))+(1/2)*im*x*2^1//3*a^4//3+(1/2)*2^1//3*a^4//3*d^-1*log(cos(c+d*x))+3//2*2^1//3*a^4//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+11//9*3^(1/2)*a^4//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+im*a*tan(c+d*x))^1//3))+-1*2^1//3*3^(1/2)*a^4//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3))+-2//3*im*a*d^-1*(a+im*a*tan(c+d*x))^1//3*cot(c+d*x))
@test integrate((a+im*a*tan(c+d*x))^5//3, x) == :(-1//2*x*2^2//3*a^5//3+3//2*im*a*d^-1*(a+im*a*tan(c+d*x))^2//3+(1/2)*im*2^2//3*a^5//3*d^-1*log(cos(c+d*x))+3//2*im*2^2//3*a^5//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+im*2^2//3*3^(1/2)*a^5//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^-1//3*tan(c+d*x)^4, x) == :(-1//8*x*2^2//3*a^-1//3+3//8*d^-1*(a+im*a*tan(c+d*x))^-1//3*tan(c+d*x)^3+-39//20*im*a^-2*d^-1*(a+im*a*tan(c+d*x))^5//3+-15//8*im*d^-1*(a+im*a*tan(c+d*x))^-1//3*tan(c+d*x)^2+45//8*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^2//3+1//8*im*2^2//3*a^-1//3*d^-1*log(cos(c+d*x))+3//8*im*2^2//3*a^-1//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+1//4*im*2^2//3*3^(1/2)*a^-1//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^-1//3*tan(c+d*x)^3, x) == :(21//10*d^-1*(a+im*a*tan(c+d*x))^-1//3+3//5*d^-1*(a+im*a*tan(c+d*x))^-1//3*tan(c+d*x)^2+3//10*a^-1*d^-1*(a+im*a*tan(c+d*x))^2//3+-3//8*2^2//3*a^-1//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+-1//8*im*x*2^2//3*a^-1//3+-1//8*2^2//3*a^-1//3*d^-1*log(cos(c+d*x))+-1//4*2^2//3*3^(1/2)*a^-1//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^-1//3*tan(c+d*x)^2, x) == :(-3//2*im*d^-1*(a+im*a*tan(c+d*x))^-1//3+1//8*x*2^2//3*a^-1//3+-3//2*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^2//3+-3//8*im*2^2//3*a^-1//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+-1//8*im*2^2//3*a^-1//3*d^-1*log(cos(c+d*x))+-1//4*im*2^2//3*3^(1/2)*a^-1//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^-1//3*tan(c+d*x), x) == :(-3//2*d^-1*(a+im*a*tan(c+d*x))^-1//3+1//8*im*x*2^2//3*a^-1//3+1//8*2^2//3*a^-1//3*d^-1*log(cos(c+d*x))+3//8*2^2//3*a^-1//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+1//4*2^2//3*3^(1/2)*a^-1//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^-1//3, x) == :(-1//8*x*2^2//3*a^-1//3+3//2*im*d^-1*(a+im*a*tan(c+d*x))^-1//3+1//8*im*2^2//3*a^-1//3*d^-1*log(cos(c+d*x))+3//8*im*2^2//3*a^-1//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+1//4*im*2^2//3*3^(1/2)*a^-1//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^-1//3*cot(c+d*x), x) == :(3//2*d^-1*(a+im*a*tan(c+d*x))^-1//3+-1//2*a^-1//3*d^-1*log(tan(c+d*x))+3//2*a^-1//3*d^-1*log(a^1//3+-1*(a+im*a*tan(c+d*x))^1//3)+3^(1/2)*a^-1//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+im*a*tan(c+d*x))^1//3))+-3//8*2^2//3*a^-1//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+-1//8*im*x*2^2//3*a^-1//3+-1//8*2^2//3*a^-1//3*d^-1*log(cos(c+d*x))+-1//4*2^2//3*3^(1/2)*a^-1//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^-1//3*cot(c+d*x)^2, x) == :(-1*d^-1*(a+im*a*tan(c+d*x))^-1//3*cot(c+d*x)+-5//2*im*d^-1*(a+im*a*tan(c+d*x))^-1//3+1//8*x*2^2//3*a^-1//3+-1//2*im*a^-1//3*d^-1*log(a^1//3+-1*(a+im*a*tan(c+d*x))^1//3)+1//6*im*a^-1//3*d^-1*log(tan(c+d*x))+-3//8*im*2^2//3*a^-1//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+-1//3*im*3^(1/2)*a^-1//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+im*a*tan(c+d*x))^1//3))+-1//8*im*2^2//3*a^-1//3*d^-1*log(cos(c+d*x))+-1//4*im*2^2//3*3^(1/2)*a^-1//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^-2//3, x) == :(-1//8*x*2^1//3*a^-2//3+3//4*im*d^-1*(a+im*a*tan(c+d*x))^-2//3+1//8*im*2^1//3*a^-2//3*d^-1*log(cos(c+d*x))+3//8*im*2^1//3*a^-2//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+-1//4*im*2^1//3*3^(1/2)*a^-2//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^-4//3*tan(c+d*x)^4, x) == :(-1//16*x*2^2//3*a^-4//3+3//5*d^-1*(a+im*a*tan(c+d*x))^-4//3*tan(c+d*x)^3+-87//40*im*a^-2*d^-1*(a+im*a*tan(c+d*x))^2//3+-51//10*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//3+-39//40*im*d^-1*(a+im*a*tan(c+d*x))^-4//3*tan(c+d*x)^2+1//16*im*2^2//3*a^-4//3*d^-1*log(cos(c+d*x))+3//16*im*2^2//3*a^-4//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+1//8*im*2^2//3*3^(1/2)*a^-4//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^-4//3*tan(c+d*x)^3, x) == :(15//8*d^-1*(a+im*a*tan(c+d*x))^-4//3+-27//4*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//3+3//2*d^-1*(a+im*a*tan(c+d*x))^-4//3*tan(c+d*x)^2+-3//16*2^2//3*a^-4//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+-1//16*im*x*2^2//3*a^-4//3+-1//16*2^2//3*a^-4//3*d^-1*log(cos(c+d*x))+-1//8*2^2//3*3^(1/2)*a^-4//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^-4//3*tan(c+d*x)^2, x) == :(-3//8*im*d^-1*(a+im*a*tan(c+d*x))^-4//3+1//16*x*2^2//3*a^-4//3+9//4*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//3+-3//16*im*2^2//3*a^-4//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+-1//16*im*2^2//3*a^-4//3*d^-1*log(cos(c+d*x))+-1//8*im*2^2//3*3^(1/2)*a^-4//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^-4//3*tan(c+d*x), x) == :(-3//8*d^-1*(a+im*a*tan(c+d*x))^-4//3+3//4*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//3+1//16*im*x*2^2//3*a^-4//3+1//16*2^2//3*a^-4//3*d^-1*log(cos(c+d*x))+3//16*2^2//3*a^-4//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+1//8*2^2//3*3^(1/2)*a^-4//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^-4//3, x) == :(-1//16*x*2^2//3*a^-4//3+3//8*im*d^-1*(a+im*a*tan(c+d*x))^-4//3+3//4*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//3+1//16*im*2^2//3*a^-4//3*d^-1*log(cos(c+d*x))+3//16*im*2^2//3*a^-4//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+1//8*im*2^2//3*3^(1/2)*a^-4//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^-4//3*cot(c+d*x), x) == :(3//8*d^-1*(a+im*a*tan(c+d*x))^-4//3+-1//2*a^-4//3*d^-1*log(tan(c+d*x))+3//2*a^-4//3*d^-1*log(a^1//3+-1*(a+im*a*tan(c+d*x))^1//3)+9//4*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//3+3^(1/2)*a^-4//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+im*a*tan(c+d*x))^1//3))+-3//16*2^2//3*a^-4//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+-1//16*im*x*2^2//3*a^-4//3+-1//16*2^2//3*a^-4//3*d^-1*log(cos(c+d*x))+-1//8*2^2//3*3^(1/2)*a^-4//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^-4//3*cot(c+d*x)^2, x) == :(-1*d^-1*(a+im*a*tan(c+d*x))^-4//3*cot(c+d*x)+-11//8*im*d^-1*(a+im*a*tan(c+d*x))^-4//3+1//16*x*2^2//3*a^-4//3+-2*im*a^-4//3*d^-1*log(a^1//3+-1*(a+im*a*tan(c+d*x))^1//3)+-19//4*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//3+2//3*im*a^-4//3*d^-1*log(tan(c+d*x))+-4//3*im*3^(1/2)*a^-4//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2*(a+im*a*tan(c+d*x))^1//3))+-3//16*im*2^2//3*a^-4//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+-1//16*im*2^2//3*a^-4//3*d^-1*log(cos(c+d*x))+-1//8*im*2^2//3*3^(1/2)*a^-4//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((a+im*a*tan(c+d*x))^-5//3, x) == :(-1//16*x*2^1//3*a^-5//3+3//10*im*d^-1*(a+im*a*tan(c+d*x))^-5//3+3//8*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-2//3+1//16*im*2^1//3*a^-5//3*d^-1*log(cos(c+d*x))+3//16*im*2^1//3*a^-5//3*d^-1*log(-1*(a+im*a*tan(c+d*x))^1//3+2^1//3*a^1//3)+-1//8*im*2^1//3*3^(1/2)*a^-5//3*d^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+2^2//3*(a+im*a*tan(c+d*x))^1//3)))
@test integrate((d*tan(e+f*x))^5//2*(a+a*tan(e+f*x)), x) == :(2//5*a*f^-1*(d*tan(e+f*x))^5//2+-2*a*d^2*f^-1*(d*tan(e+f*x))^(1/2)+2//3*a*d*f^-1*(d*tan(e+f*x))^3//2+a*2^(1/2)*d^5//2*f^-1*arctanh((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+d^(1/2)*tan(e+f*x))))
@test integrate((d*tan(e+f*x))^3//2*(a+a*tan(e+f*x)), x) == :(2//3*a*f^-1*(d*tan(e+f*x))^3//2+2*a*d*f^-1*(d*tan(e+f*x))^(1/2)+a*2^(1/2)*d^3//2*f^-1*arctan((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+-1*d^(1/2)*tan(e+f*x))))
@test integrate((d*tan(e+f*x))^(1/2)*(a+a*tan(e+f*x)), x) == :(2*a*f^-1*(d*tan(e+f*x))^(1/2)+-1*a*2^(1/2)*d^(1/2)*f^-1*arctanh((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+d^(1/2)*tan(e+f*x))))
@test integrate((d*tan(e+f*x))^-1//2*(a+a*tan(e+f*x)), x) == :(-1*a*2^(1/2)*d^-1//2*f^-1*arctan((1/2)*2^(1/2)*d^(1/2)*(d*tan(e+f*x))^-1//2*(1+-1*tan(e+f*x))))
@test integrate((d*tan(e+f*x))^-3//2*(a+a*tan(e+f*x)), x) == :(-2*a*d^-1*f^-1*(d*tan(e+f*x))^-1//2+a*2^(1/2)*d^-3//2*f^-1*arctanh((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+d^(1/2)*tan(e+f*x))))
@test integrate((d*tan(e+f*x))^-5//2*(a+a*tan(e+f*x)), x) == :(-2*a*d^-2*f^-1*(d*tan(e+f*x))^-1//2+-2//3*a*d^-1*f^-1*(d*tan(e+f*x))^-3//2+a*2^(1/2)*d^-5//2*f^-1*arctan((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+-1*d^(1/2)*tan(e+f*x))))
@test integrate((d*tan(e+f*x))^-7//2*(a+a*tan(e+f*x)), x) == :(2*a*d^-3*f^-1*(d*tan(e+f*x))^-1//2+-2//3*a*d^-2*f^-1*(d*tan(e+f*x))^-3//2+-2//5*a*d^-1*f^-1*(d*tan(e+f*x))^-5//2+-1*a*2^(1/2)*d^-7//2*f^-1*arctanh((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+d^(1/2)*tan(e+f*x))))
@test integrate((d*tan(e+f*x))^5//2*(a+a*tan(e+f*x))^2, x) == :(4//5*a^2*f^-1*(d*tan(e+f*x))^5//2+-4*a^2*d^2*f^-1*(d*tan(e+f*x))^(1/2)+2//7*a^2*d^-1*f^-1*(d*tan(e+f*x))^7//2+2^(1/2)*a^2*d^5//2*f^-1*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+(1/2)*2^(1/2)*a^2*d^5//2*f^-1*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x))+-1*2^(1/2)*a^2*d^5//2*f^-1*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^2*d^5//2*f^-1*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^3//2*(a+a*tan(e+f*x))^2, x) == :(4//3*a^2*f^-1*(d*tan(e+f*x))^3//2+2//5*a^2*d^-1*f^-1*(d*tan(e+f*x))^5//2+2^(1/2)*a^2*d^3//2*f^-1*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+(1/2)*2^(1/2)*a^2*d^3//2*f^-1*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x))+-1*2^(1/2)*a^2*d^3//2*f^-1*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^2*d^3//2*f^-1*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^(1/2)*(a+a*tan(e+f*x))^2, x) == :(4*a^2*f^-1*(d*tan(e+f*x))^(1/2)+2//3*a^2*d^-1*f^-1*(d*tan(e+f*x))^3//2+2^(1/2)*a^2*d^(1/2)*f^-1*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+(1/2)*2^(1/2)*a^2*d^(1/2)*f^-1*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2))+-1*2^(1/2)*a^2*d^(1/2)*f^-1*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^2*d^(1/2)*f^-1*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x)))
@test integrate((d*tan(e+f*x))^-1//2*(a+a*tan(e+f*x))^2, x) == :(2*a^2*d^-1*f^-1*(d*tan(e+f*x))^(1/2)+2^(1/2)*a^2*d^-1//2*f^-1*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+(1/2)*2^(1/2)*a^2*d^-1//2*f^-1*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2))+-1*2^(1/2)*a^2*d^-1//2*f^-1*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^2*d^-1//2*f^-1*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x)))
@test integrate((d*tan(e+f*x))^-3//2*(a+a*tan(e+f*x))^2, x) == :(-2*a^2*d^-1*f^-1*(d*tan(e+f*x))^-1//2+2^(1/2)*a^2*d^-3//2*f^-1*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+(1/2)*2^(1/2)*a^2*d^-3//2*f^-1*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x))+-1*2^(1/2)*a^2*d^-3//2*f^-1*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^2*d^-3//2*f^-1*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^-5//2*(a+a*tan(e+f*x))^2, x) == :(-4*a^2*d^-2*f^-1*(d*tan(e+f*x))^-1//2+-2//3*a^2*d^-1*f^-1*(d*tan(e+f*x))^-3//2+2^(1/2)*a^2*d^-5//2*f^-1*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+(1/2)*2^(1/2)*a^2*d^-5//2*f^-1*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x))+-1*2^(1/2)*a^2*d^-5//2*f^-1*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^2*d^-5//2*f^-1*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^7//2*(a+a*tan(e+f*x))^3, x) == :(4//7*a^3*f^-1*(d*tan(e+f*x))^7//2+4*a^3*d^3*f^-1*(d*tan(e+f*x))^(1/2)+-4//3*a^3*d^2*f^-1*(d*tan(e+f*x))^3//2+-4//5*d*a^3*f^-1*(d*tan(e+f*x))^5//2+2//11*d^-1*f^-1*(d*tan(e+f*x))^9//2*(a^3+a^3*tan(e+f*x))+16//33*a^3*d^-1*f^-1*(d*tan(e+f*x))^9//2+-2*2^(1/2)*a^3*d^7//2*f^-1*arctanh((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+d^(1/2)*tan(e+f*x))))
@test integrate((d*tan(e+f*x))^5//2*(a+a*tan(e+f*x))^3, x) == :(4//5*a^3*f^-1*(d*tan(e+f*x))^5//2+-4*a^3*d^2*f^-1*(d*tan(e+f*x))^(1/2)+-4//3*d*a^3*f^-1*(d*tan(e+f*x))^3//2+2//9*d^-1*f^-1*(d*tan(e+f*x))^7//2*(a^3+a^3*tan(e+f*x))+40//63*a^3*d^-1*f^-1*(d*tan(e+f*x))^7//2+-2*2^(1/2)*a^3*d^5//2*f^-1*arctan((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+-1*d^(1/2)*tan(e+f*x))))
@test integrate((d*tan(e+f*x))^3//2*(a+a*tan(e+f*x))^3, x) == :(4//3*a^3*f^-1*(d*tan(e+f*x))^3//2+-4*d*a^3*f^-1*(d*tan(e+f*x))^(1/2)+2//7*d^-1*f^-1*(d*tan(e+f*x))^5//2*(a^3+a^3*tan(e+f*x))+32//35*a^3*d^-1*f^-1*(d*tan(e+f*x))^5//2+2*2^(1/2)*a^3*d^3//2*f^-1*arctanh((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+d^(1/2)*tan(e+f*x))))
@test integrate((d*tan(e+f*x))^(1/2)*(a+a*tan(e+f*x))^3, x) == :(4*a^3*f^-1*(d*tan(e+f*x))^(1/2)+2//5*d^-1*f^-1*(d*tan(e+f*x))^3//2*(a^3+a^3*tan(e+f*x))+8//5*a^3*d^-1*f^-1*(d*tan(e+f*x))^3//2+2*2^(1/2)*a^3*d^(1/2)*f^-1*arctan((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+-1*d^(1/2)*tan(e+f*x))))
@test integrate((d*tan(e+f*x))^-1//2*(a+a*tan(e+f*x))^3, x) == :(2//3*d^-1*f^-1*(d*tan(e+f*x))^(1/2)*(a^3+a^3*tan(e+f*x))+16//3*a^3*d^-1*f^-1*(d*tan(e+f*x))^(1/2)+-2*2^(1/2)*a^3*d^-1//2*f^-1*arctanh((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+d^(1/2)*tan(e+f*x))))
@test integrate((d*tan(e+f*x))^-3//2*(a+a*tan(e+f*x))^3, x) == :(-1*d^-1*f^-1*(d*tan(e+f*x))^-1//2*(2*a^3+2*a^3*tan(e+f*x))+4*a^3*d^-2*f^-1*(d*tan(e+f*x))^(1/2)+-2*2^(1/2)*a^3*d^-3//2*f^-1*arctan((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+-1*d^(1/2)*tan(e+f*x))))
@test integrate((d*tan(e+f*x))^-5//2*(a+a*tan(e+f*x))^3, x) == :(-16//3*a^3*d^-2*f^-1*(d*tan(e+f*x))^-1//2+-1//3*d^-1*f^-1*(d*tan(e+f*x))^-3//2*(2*a^3+2*a^3*tan(e+f*x))+2*2^(1/2)*a^3*d^-5//2*f^-1*arctanh((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+d^(1/2)*tan(e+f*x))))
@test integrate((d*tan(e+f*x))^-7//2*(a+a*tan(e+f*x))^3, x) == :(-4*a^3*d^-3*f^-1*(d*tan(e+f*x))^-1//2+-8//5*a^3*d^-2*f^-1*(d*tan(e+f*x))^-3//2+-1//5*d^-1*f^-1*(d*tan(e+f*x))^-5//2*(2*a^3+2*a^3*tan(e+f*x))+2*2^(1/2)*a^3*d^-7//2*f^-1*arctan((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+-1*d^(1/2)*tan(e+f*x))))
@test integrate((d*tan(e+f*x))^-9//2*(a+a*tan(e+f*x))^3, x) == :(4*a^3*d^-4*f^-1*(d*tan(e+f*x))^-1//2+-32//35*a^3*d^-2*f^-1*(d*tan(e+f*x))^-5//2+-4//3*a^3*d^-3*f^-1*(d*tan(e+f*x))^-3//2+-1//7*d^-1*f^-1*(d*tan(e+f*x))^-7//2*(2*a^3+2*a^3*tan(e+f*x))+-2*2^(1/2)*a^3*d^-9//2*f^-1*arctanh((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+d^(1/2)*tan(e+f*x))))
@test integrate((d*tan(e+f*x))^5//2*(a+a*tan(e+f*x))^-1, x) == :(-1*a^-1*d^5//2*f^-1*arctan(d^-1//2*(d*tan(e+f*x))^(1/2))+2*a^-1*d^2*f^-1*(d*tan(e+f*x))^(1/2)+(1/2)*2^(1/2)*a^-1*d^5//2*f^-1*arctan((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+-1*d^(1/2)*tan(e+f*x))))
@test integrate((d*tan(e+f*x))^3//2*(a+a*tan(e+f*x))^-1, x) == :(a^-1*d^3//2*f^-1*arctan(d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-1*d^3//2*f^-1*arctanh((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+d^(1/2)*tan(e+f*x))))
@test integrate((d*tan(e+f*x))^(1/2)*(a+a*tan(e+f*x))^-1, x) == :(-1*a^-1*d^(1/2)*f^-1*arctan(d^-1//2*(d*tan(e+f*x))^(1/2))+-1//2*2^(1/2)*a^-1*d^(1/2)*f^-1*arctan((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+-1*d^(1/2)*tan(e+f*x))))
@test integrate((d*tan(e+f*x))^-1//2*(a+a*tan(e+f*x))^-1, x) == :(a^-1*d^-1//2*f^-1*arctan(d^-1//2*(d*tan(e+f*x))^(1/2))+(1/2)*2^(1/2)*a^-1*d^-1//2*f^-1*arctanh((1/2)*2^(1/2)*d^(1/2)*(d*tan(e+f*x))^-1//2*(1+tan(e+f*x))))
@test integrate((d*tan(e+f*x))^-3//2*(a+a*tan(e+f*x))^-1, x) == :(-1*a^-1*d^-3//2*f^-1*arctan(d^-1//2*(d*tan(e+f*x))^(1/2))+-2*a^-1*d^-1*f^-1*(d*tan(e+f*x))^-1//2+(1/2)*2^(1/2)*a^-1*d^-3//2*f^-1*arctan((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+-1*d^(1/2)*tan(e+f*x))))
@test integrate((d*tan(e+f*x))^-5//2*(a+a*tan(e+f*x))^-1, x) == :(a^-1*d^-5//2*f^-1*arctan(d^-1//2*(d*tan(e+f*x))^(1/2))+2*a^-1*d^-2*f^-1*(d*tan(e+f*x))^-1//2+-2//3*a^-1*d^-1*f^-1*(d*tan(e+f*x))^-3//2+-1//2*2^(1/2)*a^-1*d^-5//2*f^-1*arctanh((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+d^(1/2)*tan(e+f*x))))
@test integrate((d*tan(e+f*x))^5//2*(a+a*tan(e+f*x))^-2, x) == :(-1//2*d^2*f^-1*(d*tan(e+f*x))^(1/2)*(a^2+a^2*tan(e+f*x))^-1+3//2*a^-2*d^5//2*f^-1*arctan(d^-1//2*(d*tan(e+f*x))^(1/2))+-1//4*2^(1/2)*a^-2*d^5//2*f^-1*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//8*2^(1/2)*a^-2*d^5//2*f^-1*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x))+1//4*2^(1/2)*a^-2*d^5//2*f^-1*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+1//8*2^(1/2)*a^-2*d^5//2*f^-1*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^3//2*(a+a*tan(e+f*x))^-2, x) == :((1/2)*d*f^-1*(d*tan(e+f*x))^(1/2)*(a^2+a^2*tan(e+f*x))^-1+-1//2*a^-2*d^3//2*f^-1*arctan(d^-1//2*(d*tan(e+f*x))^(1/2))+-1//4*2^(1/2)*a^-2*d^3//2*f^-1*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//8*2^(1/2)*a^-2*d^3//2*f^-1*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x))+1//4*2^(1/2)*a^-2*d^3//2*f^-1*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+1//8*2^(1/2)*a^-2*d^3//2*f^-1*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^(1/2)*(a+a*tan(e+f*x))^-2, x) == :(-1//2*f^-1*(d*tan(e+f*x))^(1/2)*(a^2+a^2*tan(e+f*x))^-1+-1//2*a^-2*d^(1/2)*f^-1*arctan(d^-1//2*(d*tan(e+f*x))^(1/2))+-1//4*2^(1/2)*a^-2*d^(1/2)*f^-1*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//8*2^(1/2)*a^-2*d^(1/2)*f^-1*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2))+1//4*2^(1/2)*a^-2*d^(1/2)*f^-1*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+1//8*2^(1/2)*a^-2*d^(1/2)*f^-1*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x)))
@test integrate((d*tan(e+f*x))^-1//2*(a+a*tan(e+f*x))^-2, x) == :((1/2)*d^-1*f^-1*(d*tan(e+f*x))^(1/2)*(a^2+a^2*tan(e+f*x))^-1+3//2*a^-2*d^-1//2*f^-1*arctan(d^-1//2*(d*tan(e+f*x))^(1/2))+-1//4*2^(1/2)*a^-2*d^-1//2*f^-1*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//8*2^(1/2)*a^-2*d^-1//2*f^-1*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2))+1//4*2^(1/2)*a^-2*d^-1//2*f^-1*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+1//8*2^(1/2)*a^-2*d^-1//2*f^-1*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x)))
@test integrate((d*tan(e+f*x))^-3//2*(a+a*tan(e+f*x))^-2, x) == :((1/2)*d^-1*f^-1*(d*tan(e+f*x))^-1//2*(a^2+a^2*tan(e+f*x))^-1+-5//2*a^-2*d^-1*f^-1*(d*tan(e+f*x))^-1//2+-5//2*a^-2*d^-3//2*f^-1*arctan(d^-1//2*(d*tan(e+f*x))^(1/2))+-1//4*2^(1/2)*a^-2*d^-3//2*f^-1*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//8*2^(1/2)*a^-2*d^-3//2*f^-1*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x))+1//4*2^(1/2)*a^-2*d^-3//2*f^-1*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+1//8*2^(1/2)*a^-2*d^-3//2*f^-1*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^-5//2*(a+a*tan(e+f*x))^-2, x) == :((1/2)*d^-1*f^-1*(d*tan(e+f*x))^-3//2*(a^2+a^2*tan(e+f*x))^-1+-7//6*a^-2*d^-1*f^-1*(d*tan(e+f*x))^-3//2+7//2*a^-2*d^-5//2*f^-1*arctan(d^-1//2*(d*tan(e+f*x))^(1/2))+9//2*a^-2*d^-2*f^-1*(d*tan(e+f*x))^-1//2+-1//4*2^(1/2)*a^-2*d^-5//2*f^-1*arctan(1+-1*2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+-1//8*2^(1/2)*a^-2*d^-5//2*f^-1*log(d^(1/2)+2^(1/2)*(d*tan(e+f*x))^(1/2)+d^(1/2)*tan(e+f*x))+1//4*2^(1/2)*a^-2*d^-5//2*f^-1*arctan(1+2^(1/2)*d^-1//2*(d*tan(e+f*x))^(1/2))+1//8*2^(1/2)*a^-2*d^-5//2*f^-1*log(d^(1/2)+d^(1/2)*tan(e+f*x)+-1*2^(1/2)*(d*tan(e+f*x))^(1/2)))
@test integrate((d*tan(e+f*x))^9//2*(a+a*tan(e+f*x))^-3, x) == :(-31//8*a^-3*d^9//2*f^-1*arctan(d^-1//2*(d*tan(e+f*x))^(1/2))+27//8*a^-3*d^4*f^-1*(d*tan(e+f*x))^(1/2)+-9//8*a^-3*d^3*f^-1*(d*tan(e+f*x))^3//2*(1+tan(e+f*x))^-1+-1//4*a^-1*d^2*f^-1*(d*tan(e+f*x))^5//2*(a+a*tan(e+f*x))^-2+1//4*2^(1/2)*a^-3*d^9//2*f^-1*arctanh((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+d^(1/2)*tan(e+f*x))))
@test integrate((d*tan(e+f*x))^7//2*(a+a*tan(e+f*x))^-3, x) == :(11//8*a^-3*d^7//2*f^-1*arctan(d^-1//2*(d*tan(e+f*x))^(1/2))+-7//8*a^-3*d^3*f^-1*(d*tan(e+f*x))^(1/2)*(1+tan(e+f*x))^-1+-1//4*a^-1*d^2*f^-1*(d*tan(e+f*x))^3//2*(a+a*tan(e+f*x))^-2+1//4*2^(1/2)*a^-3*d^7//2*f^-1*arctan((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+-1*d^(1/2)*tan(e+f*x))))
@test integrate((d*tan(e+f*x))^5//2*(a+a*tan(e+f*x))^-3, x) == :(1//8*a^-3*d^5//2*f^-1*arctan(d^-1//2*(d*tan(e+f*x))^(1/2))+-1//4*2^(1/2)*a^-3*d^5//2*f^-1*arctanh((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+d^(1/2)*tan(e+f*x)))+-1//4*a^-1*d^2*f^-1*(d*tan(e+f*x))^(1/2)*(a+a*tan(e+f*x))^-2+5//8*a^-3*d^2*f^-1*(d*tan(e+f*x))^(1/2)*(1+tan(e+f*x))^-1)
@test integrate((d*tan(e+f*x))^3//2*(a+a*tan(e+f*x))^-3, x) == :(-5//8*a^-3*d^3//2*f^-1*arctan(d^-1//2*(d*tan(e+f*x))^(1/2))+-1//8*d*f^-1*(d*tan(e+f*x))^(1/2)*(a^3+a^3*tan(e+f*x))^-1+-1//4*2^(1/2)*a^-3*d^3//2*f^-1*arctan((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+-1*d^(1/2)*tan(e+f*x)))+1//4*d*a^-1*f^-1*(d*tan(e+f*x))^(1/2)*(a+a*tan(e+f*x))^-2)
@test integrate((d*tan(e+f*x))^(1/2)*(a+a*tan(e+f*x))^-3, x) == :(-3//8*f^-1*(d*tan(e+f*x))^(1/2)*(a^3+a^3*tan(e+f*x))^-1+-1//4*a^-1*f^-1*(d*tan(e+f*x))^(1/2)*(a+a*tan(e+f*x))^-2+1//8*a^-3*d^(1/2)*f^-1*arctan(d^-1//2*(d*tan(e+f*x))^(1/2))+1//4*2^(1/2)*a^-3*d^(1/2)*f^-1*arctanh((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+d^(1/2)*tan(e+f*x))))
@test integrate((d*tan(e+f*x))^-1//2*(a+a*tan(e+f*x))^-3, x) == :(11//8*a^-3*d^-1//2*f^-1*arctan(d^-1//2*(d*tan(e+f*x))^(1/2))+1//4*2^(1/2)*a^-3*d^-1//2*f^-1*arctan((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+-1*d^(1/2)*tan(e+f*x)))+1//4*a^-1*d^-1*f^-1*(d*tan(e+f*x))^(1/2)*(a+a*tan(e+f*x))^-2+7//8*a^-3*d^-1*f^-1*(d*tan(e+f*x))^(1/2)*(1+tan(e+f*x))^-1)
@test integrate((d*tan(e+f*x))^-3//2*(a+a*tan(e+f*x))^-3, x) == :(-31//8*a^-3*d^-3//2*f^-1*arctan(d^-1//2*(d*tan(e+f*x))^(1/2))+-27//8*a^-3*d^-1*f^-1*(d*tan(e+f*x))^-1//2+-1//4*2^(1/2)*a^-3*d^-3//2*f^-1*arctanh((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+d^(1/2)*tan(e+f*x)))+1//4*a^-1*d^-1*f^-1*(d*tan(e+f*x))^-1//2*(a+a*tan(e+f*x))^-2+9//8*a^-3*d^-1*f^-1*(d*tan(e+f*x))^-1//2*(1+tan(e+f*x))^-1)
@test integrate((d*tan(e+f*x))^-5//2*(a+a*tan(e+f*x))^-3, x) == :(-55//24*a^-3*d^-1*f^-1*(d*tan(e+f*x))^-3//2+59//8*a^-3*d^-5//2*f^-1*arctan(d^-1//2*(d*tan(e+f*x))^(1/2))+63//8*a^-3*d^-2*f^-1*(d*tan(e+f*x))^-1//2+-1//4*2^(1/2)*a^-3*d^-5//2*f^-1*arctan((1/2)*2^(1/2)*(d*tan(e+f*x))^-1//2*(d^(1/2)+-1*d^(1/2)*tan(e+f*x)))+1//4*a^-1*d^-1*f^-1*(d*tan(e+f*x))^-3//2*(a+a*tan(e+f*x))^-2+11//8*a^-3*d^-1*f^-1*(d*tan(e+f*x))^-3//2*(1+tan(e+f*x))^-1)
@test integrate((1+tan(e+f*x))^(1/2)*tan(e+f*x)^5, x) == :(2*f^-1*(1+tan(e+f*x))^(1/2)+52//315*f^-1*(1+tan(e+f*x))^3//2+-1*f^-1*(1/2+(1/2)*2^(1/2))^(1/2)*arctanh((1/2)*(1+tan(e+f*x))^-1//2*(7+5*2^(1/2))^-1//2*(4+3*2^(1/2)+(2+2^(1/2))*tan(e+f*x)))+-1*f^-1*(-1//2+(1/2)*2^(1/2))^(1/2)*arctan((1/2)*(1+tan(e+f*x))^-1//2*(-7+5*2^(1/2))^-1//2*(4+-3*2^(1/2)+(2+-1*2^(1/2))*tan(e+f*x)))+-26//105*f^-1*(1+tan(e+f*x))^3//2*tan(e+f*x)+-4//21*f^-1*(1+tan(e+f*x))^3//2*tan(e+f*x)^2+2//9*f^-1*(1+tan(e+f*x))^3//2*tan(e+f*x)^3)
@test integrate((1+tan(e+f*x))^(1/2)*tan(e+f*x)^3, x) == :(-2*f^-1*(1+tan(e+f*x))^(1/2)+-4//15*f^-1*(1+tan(e+f*x))^3//2+f^-1*(1/2+(1/2)*2^(1/2))^(1/2)*arctanh((1/2)*(1+tan(e+f*x))^-1//2*(7+5*2^(1/2))^-1//2*(4+3*2^(1/2)+(2+2^(1/2))*tan(e+f*x)))+f^-1*(-1//2+(1/2)*2^(1/2))^(1/2)*arctan((1/2)*(1+tan(e+f*x))^-1//2*(-7+5*2^(1/2))^-1//2*(4+-3*2^(1/2)+(2+-1*2^(1/2))*tan(e+f*x)))+2//5*f^-1*(1+tan(e+f*x))^3//2*tan(e+f*x))
@test integrate((1+tan(e+f*x))^(1/2)*tan(e+f*x), x) == :(2*f^-1*(1+tan(e+f*x))^(1/2)+-1*f^-1*(1/2+(1/2)*2^(1/2))^(1/2)*arctanh((1/2)*(1+tan(e+f*x))^-1//2*(7+5*2^(1/2))^-1//2*(4+3*2^(1/2)+(2+2^(1/2))*tan(e+f*x)))+-1*f^-1*(-1//2+(1/2)*2^(1/2))^(1/2)*arctan((1/2)*(1+tan(e+f*x))^-1//2*(-7+5*2^(1/2))^-1//2*(4+-3*2^(1/2)+(2+-1*2^(1/2))*tan(e+f*x))))
@test integrate((1+tan(e+f*x))^(1/2)*cot(e+f*x), x) == :(-2*f^-1*arctanh((1+tan(e+f*x))^(1/2))+f^-1*(1/2+(1/2)*2^(1/2))^(1/2)*arctanh((1/2)*(1+tan(e+f*x))^-1//2*(7+5*2^(1/2))^-1//2*(4+3*2^(1/2)+(2+2^(1/2))*tan(e+f*x)))+f^-1*(-1//2+(1/2)*2^(1/2))^(1/2)*arctan((1/2)*(1+tan(e+f*x))^-1//2*(-7+5*2^(1/2))^-1//2*(4+-3*2^(1/2)+(2+-1*2^(1/2))*tan(e+f*x))))
@test integrate((1+tan(e+f*x))^(1/2)*cot(e+f*x)^3, x) == :(9//4*f^-1*arctanh((1+tan(e+f*x))^(1/2))+-1*f^-1*(1/2+(1/2)*2^(1/2))^(1/2)*arctanh((1/2)*(1+tan(e+f*x))^-1//2*(7+5*2^(1/2))^-1//2*(4+3*2^(1/2)+(2+2^(1/2))*tan(e+f*x)))+-1*f^-1*(-1//2+(1/2)*2^(1/2))^(1/2)*arctan((1/2)*(1+tan(e+f*x))^-1//2*(-7+5*2^(1/2))^-1//2*(4+-3*2^(1/2)+(2+-1*2^(1/2))*tan(e+f*x)))+-1//2*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x)^2+-1//4*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x))
@test integrate((1+tan(e+f*x))^(1/2)*cot(e+f*x)^5, x) == :(-139//64*f^-1*arctanh((1+tan(e+f*x))^(1/2))+f^-1*(1/2+(1/2)*2^(1/2))^(1/2)*arctanh((1/2)*(1+tan(e+f*x))^-1//2*(7+5*2^(1/2))^-1//2*(4+3*2^(1/2)+(2+2^(1/2))*tan(e+f*x)))+f^-1*(-1//2+(1/2)*2^(1/2))^(1/2)*arctan((1/2)*(1+tan(e+f*x))^-1//2*(-7+5*2^(1/2))^-1//2*(4+-3*2^(1/2)+(2+-1*2^(1/2))*tan(e+f*x)))+-1//4*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x)^4+-1//24*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x)^3+11//64*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x)+53//96*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x)^2)
@test integrate((1+tan(e+f*x))^(1/2)*tan(e+f*x)^4, x) == :(-18//35*f^-1*(1+tan(e+f*x))^3//2+f^-1*(1/2+(1/2)*2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+2*(1+tan(e+f*x))^(1/2)))+(1/2)*f^-1*(2+2*2^(1/2))^-1//2*log(1+2^(1/2)+-1*(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x))+-1*f^-1*(1/2+(1/2)*2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+-2*(1+tan(e+f*x))^(1/2)))+-8//35*f^-1*(1+tan(e+f*x))^3//2*tan(e+f*x)+-1//2*f^-1*(2+2*2^(1/2))^-1//2*log(1+2^(1/2)+(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x))+2//7*f^-1*(1+tan(e+f*x))^3//2*tan(e+f*x)^2)
@test integrate((1+tan(e+f*x))^(1/2)*tan(e+f*x)^2, x) == :(2//3*f^-1*(1+tan(e+f*x))^3//2+f^-1*(1/2+(1/2)*2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+-2*(1+tan(e+f*x))^(1/2)))+(1/2)*f^-1*(2+2*2^(1/2))^-1//2*log(1+2^(1/2)+(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x))+-1*f^-1*(1/2+(1/2)*2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+2*(1+tan(e+f*x))^(1/2)))+-1//2*f^-1*(2+2*2^(1/2))^-1//2*log(1+2^(1/2)+-1*(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x)))
@test integrate((1+tan(e+f*x))^(1/2), x) == :(f^-1*(1/2+(1/2)*2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+2*(1+tan(e+f*x))^(1/2)))+(1/2)*f^-1*(2+2*2^(1/2))^-1//2*log(1+2^(1/2)+-1*(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x))+-1*f^-1*(1/2+(1/2)*2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+-2*(1+tan(e+f*x))^(1/2)))+-1//2*f^-1*(2+2*2^(1/2))^-1//2*log(1+2^(1/2)+(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x)))
@test integrate((1+tan(e+f*x))^(1/2)*cot(e+f*x)^2, x) == :(-1*f^-1*arctanh((1+tan(e+f*x))^(1/2))+f^-1*(1/2+(1/2)*2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+-2*(1+tan(e+f*x))^(1/2)))+(1/2)*f^-1*(2+2*2^(1/2))^-1//2*log(1+2^(1/2)+(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x))+-1*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x)+-1*f^-1*(1/2+(1/2)*2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+2*(1+tan(e+f*x))^(1/2)))+-1//2*f^-1*(2+2*2^(1/2))^-1//2*log(1+2^(1/2)+-1*(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x)))
@test integrate((1+tan(e+f*x))^(1/2)*cot(e+f*x)^4, x) == :(7//8*f^-1*arctanh((1+tan(e+f*x))^(1/2))+f^-1*(1/2+(1/2)*2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+2*(1+tan(e+f*x))^(1/2)))+(1/2)*f^-1*(2+2*2^(1/2))^-1//2*log(1+2^(1/2)+-1*(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x))+-1*f^-1*(1/2+(1/2)*2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+-2*(1+tan(e+f*x))^(1/2)))+-1//2*f^-1*(2+2*2^(1/2))^-1//2*log(1+2^(1/2)+(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x))+-1//3*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x)^3+-1//12*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x)^2+9//8*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x))
@test integrate((1+tan(e+f*x))^3//2*tan(e+f*x)^5, x) == :(2*f^-1*(1+tan(e+f*x))^(1/2)+2//3*f^-1*(1+tan(e+f*x))^3//2+20//231*f^-1*(1+tan(e+f*x))^5//2+f^-1*(1+2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+-2*(1+tan(e+f*x))^(1/2)))+(1/2)*f^-1*(1+2^(1/2))^-1//2*log(1+2^(1/2)+-1*(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x))+-1*f^-1*(1+2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+2*(1+tan(e+f*x))^(1/2)))+-50//231*f^-1*(1+tan(e+f*x))^5//2*tan(e+f*x)+-4//33*f^-1*(1+tan(e+f*x))^5//2*tan(e+f*x)^2+-1//2*f^-1*(1+2^(1/2))^-1//2*log(1+2^(1/2)+(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x))+2//11*f^-1*(1+tan(e+f*x))^5//2*tan(e+f*x)^3)
@test integrate((1+tan(e+f*x))^3//2*tan(e+f*x)^3, x) == :(-2*f^-1*(1+tan(e+f*x))^(1/2)+-4//35*f^-1*(1+tan(e+f*x))^5//2+-2//3*f^-1*(1+tan(e+f*x))^3//2+f^-1*(1+2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+2*(1+tan(e+f*x))^(1/2)))+(1/2)*f^-1*(1+2^(1/2))^-1//2*log(1+2^(1/2)+(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x))+-1*f^-1*(1+2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+-2*(1+tan(e+f*x))^(1/2)))+-1//2*f^-1*(1+2^(1/2))^-1//2*log(1+2^(1/2)+-1*(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x))+2//7*f^-1*(1+tan(e+f*x))^5//2*tan(e+f*x))
@test integrate((1+tan(e+f*x))^3//2*tan(e+f*x), x) == :(2*f^-1*(1+tan(e+f*x))^(1/2)+2//3*f^-1*(1+tan(e+f*x))^3//2+f^-1*(1+2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+-2*(1+tan(e+f*x))^(1/2)))+(1/2)*f^-1*(1+2^(1/2))^-1//2*log(1+2^(1/2)+-1*(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x))+-1*f^-1*(1+2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+2*(1+tan(e+f*x))^(1/2)))+-1//2*f^-1*(1+2^(1/2))^-1//2*log(1+2^(1/2)+(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x)))
@test integrate((1+tan(e+f*x))^3//2*cot(e+f*x), x) == :(-2*f^-1*arctanh((1+tan(e+f*x))^(1/2))+f^-1*(1+2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+2*(1+tan(e+f*x))^(1/2)))+(1/2)*f^-1*(1+2^(1/2))^-1//2*log(1+2^(1/2)+(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x))+-1*f^-1*(1+2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+-2*(1+tan(e+f*x))^(1/2)))+-1//2*f^-1*(1+2^(1/2))^-1//2*log(1+2^(1/2)+-1*(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x)))
@test integrate((1+tan(e+f*x))^3//2*cot(e+f*x)^3, x) == :(5//4*f^-1*arctanh((1+tan(e+f*x))^(1/2))+f^-1*(1+2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+-2*(1+tan(e+f*x))^(1/2)))+(1/2)*f^-1*(1+2^(1/2))^-1//2*log(1+2^(1/2)+-1*(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x))+-1*f^-1*(1+2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+2*(1+tan(e+f*x))^(1/2)))+-5//4*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x)+-1//2*f^-1*(1+2^(1/2))^-1//2*log(1+2^(1/2)+(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x))+-1//2*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x)^2)
@test integrate((1+tan(e+f*x))^3//2*cot(e+f*x)^5, x) == :(-83//64*f^-1*arctanh((1+tan(e+f*x))^(1/2))+f^-1*(1+2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+2*(1+tan(e+f*x))^(1/2)))+(1/2)*f^-1*(1+2^(1/2))^-1//2*log(1+2^(1/2)+(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x))+-1*f^-1*(1+2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+-2*(1+tan(e+f*x))^(1/2)))+-3//8*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x)^3+-1//2*f^-1*(1+2^(1/2))^-1//2*log(1+2^(1/2)+-1*(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x))+-1//4*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x)^4+15//32*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x)^2+83//64*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x))
@test integrate((1+tan(e+f*x))^3//2*tan(e+f*x)^4, x) == :(2*f^-1*(1+tan(e+f*x))^(1/2)+-22//63*f^-1*(1+tan(e+f*x))^5//2+-1*f^-1*(1+2^(1/2))^(1/2)*arctanh((1+tan(e+f*x))^-1//2*(14+10*2^(1/2))^-1//2*(3+2*2^(1/2)+(1+2^(1/2))*tan(e+f*x)))+-1*f^-1*(-1+2^(1/2))^(1/2)*arctan((1+tan(e+f*x))^-1//2*(-14+10*2^(1/2))^-1//2*(3+-2*2^(1/2)+(1+-1*2^(1/2))*tan(e+f*x)))+-8//63*f^-1*(1+tan(e+f*x))^5//2*tan(e+f*x)+2//9*f^-1*(1+tan(e+f*x))^5//2*tan(e+f*x)^2)
@test integrate((1+tan(e+f*x))^3//2*tan(e+f*x)^2, x) == :(-2*f^-1*(1+tan(e+f*x))^(1/2)+2//5*f^-1*(1+tan(e+f*x))^5//2+f^-1*(1+2^(1/2))^(1/2)*arctanh((1+tan(e+f*x))^-1//2*(14+10*2^(1/2))^-1//2*(3+2*2^(1/2)+(1+2^(1/2))*tan(e+f*x)))+f^-1*(-1+2^(1/2))^(1/2)*arctan((1+tan(e+f*x))^-1//2*(-14+10*2^(1/2))^-1//2*(3+-2*2^(1/2)+(1+-1*2^(1/2))*tan(e+f*x))))
@test integrate((1+tan(e+f*x))^3//2, x) == :(2*f^-1*(1+tan(e+f*x))^(1/2)+-1*f^-1*(1+2^(1/2))^(1/2)*arctanh((1+tan(e+f*x))^-1//2*(14+10*2^(1/2))^-1//2*(3+2*2^(1/2)+(1+2^(1/2))*tan(e+f*x)))+-1*f^-1*(-1+2^(1/2))^(1/2)*arctan((1+tan(e+f*x))^-1//2*(-14+10*2^(1/2))^-1//2*(3+-2*2^(1/2)+(1+-1*2^(1/2))*tan(e+f*x))))
@test integrate((1+tan(e+f*x))^3//2*cot(e+f*x)^2, x) == :(-3*f^-1*arctanh((1+tan(e+f*x))^(1/2))+f^-1*(1+2^(1/2))^(1/2)*arctanh((1+tan(e+f*x))^-1//2*(14+10*2^(1/2))^-1//2*(3+2*2^(1/2)+(1+2^(1/2))*tan(e+f*x)))+f^-1*(-1+2^(1/2))^(1/2)*arctan((1+tan(e+f*x))^-1//2*(-14+10*2^(1/2))^-1//2*(3+-2*2^(1/2)+(1+-1*2^(1/2))*tan(e+f*x)))+-1*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x))
@test integrate((1+tan(e+f*x))^3//2*cot(e+f*x)^4, x) == :(25//8*f^-1*arctanh((1+tan(e+f*x))^(1/2))+-1*f^-1*(1+2^(1/2))^(1/2)*arctanh((1+tan(e+f*x))^-1//2*(14+10*2^(1/2))^-1//2*(3+2*2^(1/2)+(1+2^(1/2))*tan(e+f*x)))+-1*f^-1*(-1+2^(1/2))^(1/2)*arctan((1+tan(e+f*x))^-1//2*(-14+10*2^(1/2))^-1//2*(3+-2*2^(1/2)+(1+-1*2^(1/2))*tan(e+f*x)))+-7//12*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x)^2+-1//3*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x)^3+7//8*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x))
@test integrate((1+tan(e+f*x))^-1//2*tan(e+f*x)^5, x) == :(44//105*f^-1*(1+tan(e+f*x))^(1/2)+-22//105*f^-1*(1+tan(e+f*x))^(1/2)*tan(e+f*x)+-12//35*f^-1*(1+tan(e+f*x))^(1/2)*tan(e+f*x)^2+-1//2*f^-1*(1+2^(1/2))^(1/2)*arctanh((1+tan(e+f*x))^-1//2*(14+10*2^(1/2))^-1//2*(3+2*2^(1/2)+(1+2^(1/2))*tan(e+f*x)))+-1//2*f^-1*(-1+2^(1/2))^(1/2)*arctan((1+tan(e+f*x))^-1//2*(-14+10*2^(1/2))^-1//2*(3+-2*2^(1/2)+(1+-1*2^(1/2))*tan(e+f*x)))+2//7*f^-1*(1+tan(e+f*x))^(1/2)*tan(e+f*x)^3)
@test integrate((1+tan(e+f*x))^-1//2*tan(e+f*x)^3, x) == :(-4//3*f^-1*(1+tan(e+f*x))^(1/2)+(1/2)*f^-1*(1+2^(1/2))^(1/2)*arctanh((1+tan(e+f*x))^-1//2*(14+10*2^(1/2))^-1//2*(3+2*2^(1/2)+(1+2^(1/2))*tan(e+f*x)))+(1/2)*f^-1*(-1+2^(1/2))^(1/2)*arctan((1+tan(e+f*x))^-1//2*(-14+10*2^(1/2))^-1//2*(3+-2*2^(1/2)+(1+-1*2^(1/2))*tan(e+f*x)))+2//3*f^-1*(1+tan(e+f*x))^(1/2)*tan(e+f*x))
@test integrate((1+tan(e+f*x))^-1//2*tan(e+f*x), x) == :(-1//2*f^-1*(1+2^(1/2))^(1/2)*arctanh((1+tan(e+f*x))^-1//2*(14+10*2^(1/2))^-1//2*(3+2*2^(1/2)+(1+2^(1/2))*tan(e+f*x)))+-1//2*f^-1*(-1+2^(1/2))^(1/2)*arctan((1+tan(e+f*x))^-1//2*(-14+10*2^(1/2))^-1//2*(3+-2*2^(1/2)+(1+-1*2^(1/2))*tan(e+f*x))))
@test integrate((1+tan(e+f*x))^-1//2*cot(e+f*x), x) == :(-2*f^-1*arctanh((1+tan(e+f*x))^(1/2))+(1/2)*f^-1*(1+2^(1/2))^(1/2)*arctanh((1+tan(e+f*x))^-1//2*(14+10*2^(1/2))^-1//2*(3+2*2^(1/2)+(1+2^(1/2))*tan(e+f*x)))+(1/2)*f^-1*(-1+2^(1/2))^(1/2)*arctan((1+tan(e+f*x))^-1//2*(-14+10*2^(1/2))^-1//2*(3+-2*2^(1/2)+(1+-1*2^(1/2))*tan(e+f*x))))
@test integrate((1+tan(e+f*x))^-1//2*cot(e+f*x)^3, x) == :(5//4*f^-1*arctanh((1+tan(e+f*x))^(1/2))+-1//2*f^-1*(1+2^(1/2))^(1/2)*arctanh((1+tan(e+f*x))^-1//2*(14+10*2^(1/2))^-1//2*(3+2*2^(1/2)+(1+2^(1/2))*tan(e+f*x)))+-1//2*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x)^2+-1//2*f^-1*(-1+2^(1/2))^(1/2)*arctan((1+tan(e+f*x))^-1//2*(-14+10*2^(1/2))^-1//2*(3+-2*2^(1/2)+(1+-1*2^(1/2))*tan(e+f*x)))+3//4*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x))
@test integrate((1+tan(e+f*x))^-1//2*cot(e+f*x)^5, x) == :(-115//64*f^-1*arctanh((1+tan(e+f*x))^(1/2))+(1/2)*f^-1*(1+2^(1/2))^(1/2)*arctanh((1+tan(e+f*x))^-1//2*(14+10*2^(1/2))^-1//2*(3+2*2^(1/2)+(1+2^(1/2))*tan(e+f*x)))+(1/2)*f^-1*(-1+2^(1/2))^(1/2)*arctan((1+tan(e+f*x))^-1//2*(-14+10*2^(1/2))^-1//2*(3+-2*2^(1/2)+(1+-1*2^(1/2))*tan(e+f*x)))+-13//64*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x)+-1//4*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x)^4+7//24*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x)^3+13//96*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x)^2)
@test integrate((1+tan(e+f*x))^-1//2*tan(e+f*x)^4, x) == :(-14//15*f^-1*(1+tan(e+f*x))^(1/2)+(1/2)*f^-1*(1+2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+2*(1+tan(e+f*x))^(1/2)))+-8//15*f^-1*(1+tan(e+f*x))^(1/2)*tan(e+f*x)+-1//2*f^-1*(1+2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+-2*(1+tan(e+f*x))^(1/2)))+-1//4*f^-1*(1+2^(1/2))^-1//2*log(1+2^(1/2)+-1*(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x))+1//4*f^-1*(1+2^(1/2))^-1//2*log(1+2^(1/2)+(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x))+2//5*f^-1*(1+tan(e+f*x))^(1/2)*tan(e+f*x)^2)
@test integrate((1+tan(e+f*x))^-1//2*tan(e+f*x)^2, x) == :(2*f^-1*(1+tan(e+f*x))^(1/2)+(1/2)*f^-1*(1+2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+-2*(1+tan(e+f*x))^(1/2)))+-1//2*f^-1*(1+2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+2*(1+tan(e+f*x))^(1/2)))+-1//4*f^-1*(1+2^(1/2))^-1//2*log(1+2^(1/2)+(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x))+1//4*f^-1*(1+2^(1/2))^-1//2*log(1+2^(1/2)+-1*(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x)))
@test integrate((1+tan(e+f*x))^-1//2, x) == :((1/2)*f^-1*(1+2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+2*(1+tan(e+f*x))^(1/2)))+-1//2*f^-1*(1+2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+-2*(1+tan(e+f*x))^(1/2)))+-1//4*f^-1*(1+2^(1/2))^-1//2*log(1+2^(1/2)+-1*(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x))+1//4*f^-1*(1+2^(1/2))^-1//2*log(1+2^(1/2)+(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x)))
@test integrate((1+tan(e+f*x))^-1//2*cot(e+f*x)^2, x) == :(f^-1*arctanh((1+tan(e+f*x))^(1/2))+(1/2)*f^-1*(1+2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+-2*(1+tan(e+f*x))^(1/2)))+-1*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x)+-1//2*f^-1*(1+2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+2*(1+tan(e+f*x))^(1/2)))+-1//4*f^-1*(1+2^(1/2))^-1//2*log(1+2^(1/2)+(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x))+1//4*f^-1*(1+2^(1/2))^-1//2*log(1+2^(1/2)+-1*(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x)))
@test integrate((1+tan(e+f*x))^-1//2*cot(e+f*x)^4, x) == :(-3//8*f^-1*arctanh((1+tan(e+f*x))^(1/2))+(1/2)*f^-1*(1+2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+2*(1+tan(e+f*x))^(1/2)))+-1//2*f^-1*(1+2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+-2*(1+tan(e+f*x))^(1/2)))+-1//3*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x)^3+-1//4*f^-1*(1+2^(1/2))^-1//2*log(1+2^(1/2)+-1*(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x))+1//4*f^-1*(1+2^(1/2))^-1//2*log(1+2^(1/2)+(1+tan(e+f*x))^(1/2)*(2+2*2^(1/2))^(1/2)+tan(e+f*x))+3//8*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x)+5//12*f^-1*(1+tan(e+f*x))^(1/2)*cot(e+f*x)^2)
@test integrate(tan(c+d*x)^5*(a+b*tan(c+d*x)), x) == :(-1*b*x+b*d^-1*tan(c+d*x)+-1*a*d^-1*log(cos(c+d*x))+-1//2*a*d^-1*tan(c+d*x)^2+-1//3*b*d^-1*tan(c+d*x)^3+1//4*a*d^-1*tan(c+d*x)^4+1//5*b*d^-1*tan(c+d*x)^5)
@test integrate(tan(c+d*x)^4*(a+b*tan(c+d*x)), x) == :(a*x+-1*a*d^-1*tan(c+d*x)+-1*b*d^-1*log(cos(c+d*x))+-1//2*b*d^-1*tan(c+d*x)^2+1//3*a*d^-1*tan(c+d*x)^3+1//4*b*d^-1*tan(c+d*x)^4)
@test integrate(tan(c+d*x)^3*(a+b*tan(c+d*x)), x) == :(b*x+a*d^-1*log(cos(c+d*x))+(1/2)*a*d^-1*tan(c+d*x)^2+-1*b*d^-1*tan(c+d*x)+1//3*b*d^-1*tan(c+d*x)^3)
@test integrate(tan(c+d*x)^2*(a+b*tan(c+d*x)), x) == :(-1*a*x+a*d^-1*tan(c+d*x)+b*d^-1*log(cos(c+d*x))+(1/2)*b*d^-1*tan(c+d*x)^2)
@test integrate((a+b*tan(c+d*x))*tan(c+d*x), x) == :(-1*b*x+b*d^-1*tan(c+d*x)+-1*a*d^-1*log(cos(c+d*x)))
@test integrate(a+b*tan(c+d*x), x) == :(a*x+-1*b*d^-1*log(cos(c+d*x)))
@test integrate((a+b*tan(c+d*x))*cot(c+d*x), x) == :(b*x+a*d^-1*log(sin(c+d*x)))
@test integrate(cot(c+d*x)^2*(a+b*tan(c+d*x)), x) == :(-1*a*x+b*d^-1*log(sin(c+d*x))+-1*a*d^-1*cot(c+d*x))
@test integrate(cot(c+d*x)^3*(a+b*tan(c+d*x)), x) == :(-1*b*x+-1*a*d^-1*log(sin(c+d*x))+-1*b*d^-1*cot(c+d*x)+-1//2*a*d^-1*cot(c+d*x)^2)
@test integrate(cot(c+d*x)^4*(a+b*tan(c+d*x)), x) == :(a*x+a*d^-1*cot(c+d*x)+-1*b*d^-1*log(sin(c+d*x))+-1//2*b*d^-1*cot(c+d*x)^2+-1//3*a*d^-1*cot(c+d*x)^3)
@test integrate(cot(c+d*x)^5*(a+b*tan(c+d*x)), x) == :(b*x+a*d^-1*log(sin(c+d*x))+b*d^-1*cot(c+d*x)+(1/2)*a*d^-1*cot(c+d*x)^2+-1//3*b*d^-1*cot(c+d*x)^3+-1//4*a*d^-1*cot(c+d*x)^4)
@test integrate(cot(c+d*x)^6*(a+b*tan(c+d*x)), x) == :(-1*a*x+b*d^-1*log(sin(c+d*x))+(1/2)*b*d^-1*cot(c+d*x)^2+-1*a*d^-1*cot(c+d*x)+-1//4*b*d^-1*cot(c+d*x)^4+-1//5*a*d^-1*cot(c+d*x)^5+1//3*a*d^-1*cot(c+d*x)^3)
@test integrate((a+b*tan(c+d*x))^2*tan(c+d*x)^4, x) == :(x*(a^2+-1*b^2)+-1*d^-1*(a^2+-1*b^2)*tan(c+d*x)+1//3*d^-1*tan(c+d*x)^3*(a^2+-1*b^2)+1//5*b^2*d^-1*tan(c+d*x)^5+(1/2)*a*b*d^-1*tan(c+d*x)^4+-1*a*b*d^-1*tan(c+d*x)^2+-2*a*b*d^-1*log(cos(c+d*x)))
@test integrate((a+b*tan(c+d*x))^2*tan(c+d*x)^3, x) == :(d^-1*(a^2+-1*b^2)*log(cos(c+d*x))+(1/2)*d^-1*tan(c+d*x)^2*(a^2+-1*b^2)+2*a*b*x+1//4*b^2*d^-1*tan(c+d*x)^4+-2*a*b*d^-1*tan(c+d*x)+2//3*a*b*d^-1*tan(c+d*x)^3)
@test integrate((a+b*tan(c+d*x))^2*tan(c+d*x)^2, x) == :(-1*x*(a^2+-1*b^2)+-1*b^2*d^-1*tan(c+d*x)+1//3*b^-1*d^-1*(a+b*tan(c+d*x))^3+2*a*b*d^-1*log(cos(c+d*x)))
@test integrate((a+b*tan(c+d*x))^2*tan(c+d*x), x) == :((1/2)*d^-1*(a+b*tan(c+d*x))^2+-1*d^-1*(a^2+-1*b^2)*log(cos(c+d*x))+-2*a*b*x+a*b*d^-1*tan(c+d*x))
@test integrate((a+b*tan(c+d*x))^2, x) == :(x*(a^2+-1*b^2)+b^2*d^-1*tan(c+d*x)+-2*a*b*d^-1*log(cos(c+d*x)))
@test integrate((a+b*tan(c+d*x))^2*cot(c+d*x), x) == :(a^2*d^-1*log(sin(c+d*x))+-1*b^2*d^-1*log(cos(c+d*x))+2*a*b*x)
@test integrate((a+b*tan(c+d*x))^2*cot(c+d*x)^2, x) == :(-1*x*(a^2+-1*b^2)+-1*a^2*d^-1*cot(c+d*x)+2*a*b*d^-1*log(sin(c+d*x)))
@test integrate((a+b*tan(c+d*x))^2*cot(c+d*x)^3, x) == :(-1*d^-1*(a^2+-1*b^2)*log(sin(c+d*x))+-2*a*b*x+-1//2*a^2*d^-1*cot(c+d*x)^2+-2*a*b*d^-1*cot(c+d*x))
@test integrate((a+b*tan(c+d*x))^2*cot(c+d*x)^4, x) == :(x*(a^2+-1*b^2)+d^-1*(a^2+-1*b^2)*cot(c+d*x)+-1//3*a^2*d^-1*cot(c+d*x)^3+-1*a*b*d^-1*cot(c+d*x)^2+-2*a*b*d^-1*log(sin(c+d*x)))
@test integrate((a+b*tan(c+d*x))^2*cot(c+d*x)^5, x) == :(d^-1*(a^2+-1*b^2)*log(sin(c+d*x))+(1/2)*d^-1*cot(c+d*x)^2*(a^2+-1*b^2)+2*a*b*x+-1//4*a^2*d^-1*cot(c+d*x)^4+2*a*b*d^-1*cot(c+d*x)+-2//3*a*b*d^-1*cot(c+d*x)^3)
@test integrate((a+b*tan(c+d*x))^2*cot(c+d*x)^6, x) == :(-1*x*(a^2+-1*b^2)+-1*d^-1*(a^2+-1*b^2)*cot(c+d*x)+-1//5*a^2*d^-1*cot(c+d*x)^5+1//3*d^-1*cot(c+d*x)^3*(a^2+-1*b^2)+a*b*d^-1*cot(c+d*x)^2+2*a*b*d^-1*log(sin(c+d*x))+-1//2*a*b*d^-1*cot(c+d*x)^4)
@test integrate((a+b*tan(c+d*x))^3*tan(c+d*x)^3, x) == :(-1//3*d^-1*(a+b*tan(c+d*x))^3+b*x*(-1*b^2+3*a^2)+-1//2*a*d^-1*(a+b*tan(c+d*x))^2+a*d^-1*(a^2+-3*b^2)*log(cos(c+d*x))+-1*b*d^-1*(a^2+-1*b^2)*tan(c+d*x)+-1//20*a*b^-2*d^-1*(a+b*tan(c+d*x))^4+1//5*b^-1*d^-1*(a+b*tan(c+d*x))^4*tan(c+d*x))
@test integrate((a+b*tan(c+d*x))^3*tan(c+d*x)^2, x) == :(-1*a*x*(a^2+-3*b^2)+-1//2*b*d^-1*(a+b*tan(c+d*x))^2+1//4*b^-1*d^-1*(a+b*tan(c+d*x))^4+b*d^-1*(-1*b^2+3*a^2)*log(cos(c+d*x))+-2*a*b^2*d^-1*tan(c+d*x))
@test integrate((a+b*tan(c+d*x))^3*tan(c+d*x), x) == :(1//3*d^-1*(a+b*tan(c+d*x))^3+(1/2)*a*d^-1*(a+b*tan(c+d*x))^2+-1*b*x*(-1*b^2+3*a^2)+b*d^-1*(a^2+-1*b^2)*tan(c+d*x)+-1*a*d^-1*(a^2+-3*b^2)*log(cos(c+d*x)))
@test integrate((a+b*tan(c+d*x))^3, x) == :(a*x*(a^2+-3*b^2)+(1/2)*b*d^-1*(a+b*tan(c+d*x))^2+-1*b*d^-1*(-1*b^2+3*a^2)*log(cos(c+d*x))+2*a*b^2*d^-1*tan(c+d*x))
@test integrate((a+b*tan(c+d*x))^3*cot(c+d*x), x) == :(b*x*(-1*b^2+3*a^2)+a^3*d^-1*log(sin(c+d*x))+b^2*d^-1*(a+b*tan(c+d*x))+-3*a*b^2*d^-1*log(cos(c+d*x)))
@test integrate((a+b*tan(c+d*x))^3*cot(c+d*x)^2, x) == :(-1*a*x*(a^2+-3*b^2)+-1*b^3*d^-1*log(cos(c+d*x))+-1*a^2*d^-1*(a+b*tan(c+d*x))*cot(c+d*x)+3*b*a^2*d^-1*log(sin(c+d*x)))
@test integrate((a+b*tan(c+d*x))^3*cot(c+d*x)^3, x) == :(-1*b*x*(-1*b^2+3*a^2)+-1*a*d^-1*(a^2+-3*b^2)*log(sin(c+d*x))+-5//2*b*a^2*d^-1*cot(c+d*x)+-1//2*a^2*d^-1*cot(c+d*x)^2*(a+b*tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^3*cot(c+d*x)^4, x) == :(a*x*(a^2+-3*b^2)+a*d^-1*(a^2+-3*b^2)*cot(c+d*x)+-1*b*d^-1*(-1*b^2+3*a^2)*log(sin(c+d*x))+-7//6*b*a^2*d^-1*cot(c+d*x)^2+-1//3*a^2*d^-1*cot(c+d*x)^3*(a+b*tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^3*cot(c+d*x)^5, x) == :(b*x*(-1*b^2+3*a^2)+a*d^-1*(a^2+-3*b^2)*log(sin(c+d*x))+b*d^-1*(-1*b^2+3*a^2)*cot(c+d*x)+(1/2)*a*d^-1*cot(c+d*x)^2*(a^2+-3*b^2)+-3//4*b*a^2*d^-1*cot(c+d*x)^3+-1//4*a^2*d^-1*cot(c+d*x)^4*(a+b*tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^3*cot(c+d*x)^6, x) == :(-1*a*x*(a^2+-3*b^2)+b*d^-1*(-1*b^2+3*a^2)*log(sin(c+d*x))+(1/2)*b*d^-1*cot(c+d*x)^2*(-1*b^2+3*a^2)+-1*a*d^-1*(a^2+-3*b^2)*cot(c+d*x)+-11//20*b*a^2*d^-1*cot(c+d*x)^4+-1//5*a^2*d^-1*cot(c+d*x)^5*(a+b*tan(c+d*x))+1//3*a*d^-1*cot(c+d*x)^3*(a^2+-3*b^2))
@test integrate((a+b*tan(c+d*x))^4*tan(c+d*x)^3, x) == :(-1//4*d^-1*(a+b*tan(c+d*x))^4+d^-1*(a^4+b^4+-6*a^2*b^2)*log(cos(c+d*x))+-1//2*d^-1*(a+b*tan(c+d*x))^2*(a^2+-1*b^2)+-1//3*a*d^-1*(a+b*tan(c+d*x))^3+4*a*b*x*(a^2+-1*b^2)+-1//30*a*b^-2*d^-1*(a+b*tan(c+d*x))^5+1//6*b^-1*d^-1*(a+b*tan(c+d*x))^5*tan(c+d*x)+-1*a*b*d^-1*(a^2+-3*b^2)*tan(c+d*x))
@test integrate((a+b*tan(c+d*x))^4*tan(c+d*x)^2, x) == :(-1*x*(a^4+b^4+-6*a^2*b^2)+-1//3*b*d^-1*(a+b*tan(c+d*x))^3+1//5*b^-1*d^-1*(a+b*tan(c+d*x))^5+-1*a*b*d^-1*(a+b*tan(c+d*x))^2+-1*b^2*d^-1*(-1*b^2+3*a^2)*tan(c+d*x)+4*a*b*d^-1*(a^2+-1*b^2)*log(cos(c+d*x)))
@test integrate((a+b*tan(c+d*x))^4*tan(c+d*x), x) == :(1//4*d^-1*(a+b*tan(c+d*x))^4+(1/2)*d^-1*(a+b*tan(c+d*x))^2*(a^2+-1*b^2)+-1*d^-1*(a^4+b^4+-6*a^2*b^2)*log(cos(c+d*x))+1//3*a*d^-1*(a+b*tan(c+d*x))^3+-4*a*b*x*(a^2+-1*b^2)+a*b*d^-1*(a^2+-3*b^2)*tan(c+d*x))
@test integrate((a+b*tan(c+d*x))^4, x) == :(x*(a^4+b^4+-6*a^2*b^2)+1//3*b*d^-1*(a+b*tan(c+d*x))^3+a*b*d^-1*(a+b*tan(c+d*x))^2+b^2*d^-1*(-1*b^2+3*a^2)*tan(c+d*x)+-4*a*b*d^-1*(a^2+-1*b^2)*log(cos(c+d*x)))
@test integrate((a+b*tan(c+d*x))^4*cot(c+d*x), x) == :(a^4*d^-1*log(sin(c+d*x))+(1/2)*b^2*d^-1*(a+b*tan(c+d*x))^2+-1*b^2*d^-1*(-1*b^2+6*a^2)*log(cos(c+d*x))+3*a*b^3*d^-1*tan(c+d*x)+4*a*b*x*(a^2+-1*b^2))
@test integrate((a+b*tan(c+d*x))^4*cot(c+d*x)^2, x) == :(-1*x*(a^4+b^4+-6*a^2*b^2)+b^2*d^-1*(a^2+b^2)*tan(c+d*x)+-1*a^2*d^-1*(a+b*tan(c+d*x))^2*cot(c+d*x)+-4*a*b^3*d^-1*log(cos(c+d*x))+4*b*a^3*d^-1*log(sin(c+d*x)))
@test integrate((a+b*tan(c+d*x))^4*cot(c+d*x)^3, x) == :(-1*b^4*d^-1*log(cos(c+d*x))+-1*a^2*d^-1*(a^2+-6*b^2)*log(sin(c+d*x))+-4*a*b*x*(a^2+-1*b^2)+-3*b*a^3*d^-1*cot(c+d*x)+-1//2*a^2*d^-1*(a+b*tan(c+d*x))^2*cot(c+d*x)^2)
@test integrate((a+b*tan(c+d*x))^4*cot(c+d*x)^4, x) == :(x*(a^4+b^4+-6*a^2*b^2)+-4//3*b*a^3*d^-1*cot(c+d*x)^2+-1//3*a^2*d^-1*(a+b*tan(c+d*x))^2*cot(c+d*x)^3+1//3*a^2*d^-1*(-17*b^2+3*a^2)*cot(c+d*x)+-4*a*b*d^-1*(a^2+-1*b^2)*log(sin(c+d*x)))
@test integrate((a+b*tan(c+d*x))^4*cot(c+d*x)^5, x) == :(d^-1*(a^4+b^4+-6*a^2*b^2)*log(sin(c+d*x))+4*a*b*x*(a^2+-1*b^2)+-5//6*b*a^3*d^-1*cot(c+d*x)^3+-1//4*a^2*d^-1*(a+b*tan(c+d*x))^2*cot(c+d*x)^4+1//4*a^2*d^-1*cot(c+d*x)^2*(-11*b^2+2*a^2)+4*a*b*d^-1*(a^2+-1*b^2)*cot(c+d*x))
@test integrate((a+b*tan(c+d*x))^4*cot(c+d*x)^6, x) == :(-1*x*(a^4+b^4+-6*a^2*b^2)+-1*d^-1*(a^4+b^4+-6*a^2*b^2)*cot(c+d*x)+-3//5*b*a^3*d^-1*cot(c+d*x)^4+-1//5*a^2*d^-1*(a+b*tan(c+d*x))^2*cot(c+d*x)^5+1//15*a^2*d^-1*cot(c+d*x)^3*(-27*b^2+5*a^2)+2*a*b*d^-1*cot(c+d*x)^2*(a^2+-1*b^2)+4*a*b*d^-1*(a^2+-1*b^2)*log(sin(c+d*x)))
@test integrate((a+b*tan(c+d*x))^4*cot(c+d*x)^7, x) == :(-1*d^-1*(a^4+b^4+-6*a^2*b^2)*log(sin(c+d*x))+-1//2*d^-1*cot(c+d*x)^2*(a^4+b^4+-6*a^2*b^2)+-4*a*b*x*(a^2+-1*b^2)+-7//15*b*a^3*d^-1*cot(c+d*x)^5+-1//6*a^2*d^-1*(a+b*tan(c+d*x))^2*cot(c+d*x)^6+1//12*a^2*d^-1*cot(c+d*x)^4*(-16*b^2+3*a^2)+-4*a*b*d^-1*(a^2+-1*b^2)*cot(c+d*x)+4//3*a*b*d^-1*cot(c+d*x)^3*(a^2+-1*b^2))
@test integrate((a+b*tan(c+d*x))^-1*tan(c+d*x)^6, x) == :(-1*a*x*(a^2+b^2)^-1+1//4*b^-1*d^-1*tan(c+d*x)^4+(1/2)*b^-3*d^-1*tan(c+d*x)^2*(a^2+-1*b^2)+-1*b*d^-1*(a^2+b^2)^-1*log(cos(c+d*x))+-1//3*a*b^-2*d^-1*tan(c+d*x)^3+a^6*b^-5*d^-1*(a^2+b^2)^-1*log(a+b*tan(c+d*x))+-1*a*b^-4*d^-1*(a^2+-1*b^2)*tan(c+d*x))
@test integrate((a+b*tan(c+d*x))^-1*tan(c+d*x)^5, x) == :(b*x*(a^2+b^2)^-1+1//3*b^-1*d^-1*tan(c+d*x)^3+b^-3*d^-1*(a^2+-1*b^2)*tan(c+d*x)+-1*a*d^-1*(a^2+b^2)^-1*log(cos(c+d*x))+-1//2*a*b^-2*d^-1*tan(c+d*x)^2+-1*a^5*b^-4*d^-1*(a^2+b^2)^-1*log(a+b*tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-1*tan(c+d*x)^4, x) == :(a*x*(a^2+b^2)^-1+(1/2)*b^-1*d^-1*tan(c+d*x)^2+b*d^-1*(a^2+b^2)^-1*log(cos(c+d*x))+-1*a*b^-2*d^-1*tan(c+d*x)+a^4*b^-3*d^-1*(a^2+b^2)^-1*log(a+b*tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-1*tan(c+d*x)^3, x) == :(b^-1*d^-1*tan(c+d*x)+-1*b*x*(a^2+b^2)^-1+a*d^-1*(a^2+b^2)^-1*log(cos(c+d*x))+-1*a^3*b^-2*d^-1*(a^2+b^2)^-1*log(a+b*tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-1*tan(c+d*x), x) == :(b*x*(a^2+b^2)^-1+-1*a*d^-1*(a^2+b^2)^-1*log(a*cos(c+d*x)+b*sin(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-1, x) == :(a*x*(a^2+b^2)^-1+b*d^-1*(a^2+b^2)^-1*log(a*cos(c+d*x)+b*sin(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-1*cot(c+d*x), x) == :(a^-1*d^-1*log(sin(c+d*x))+-1*b*x*(a^2+b^2)^-1+-1*a^-1*b^2*d^-1*(a^2+b^2)^-1*log(a*cos(c+d*x)+b*sin(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-1*cot(c+d*x)^2, x) == :(-1*a*x*(a^2+b^2)^-1+-1*a^-1*d^-1*cot(c+d*x)+-1*b*a^-2*d^-1*log(sin(c+d*x))+a^-2*b^3*d^-1*(a^2+b^2)^-1*log(a*cos(c+d*x)+b*sin(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-1*cot(c+d*x)^3, x) == :(b*x*(a^2+b^2)^-1+-1//2*a^-1*d^-1*cot(c+d*x)^2+b*a^-2*d^-1*cot(c+d*x)+-1*a^-3*d^-1*(a^2+-1*b^2)*log(sin(c+d*x))+-1*a^-3*b^4*d^-1*(a^2+b^2)^-1*log(a*cos(c+d*x)+b*sin(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-1*cot(c+d*x)^4, x) == :(a*x*(a^2+b^2)^-1+-1//3*a^-1*d^-1*cot(c+d*x)^3+a^-3*d^-1*(a^2+-1*b^2)*cot(c+d*x)+(1/2)*b*a^-2*d^-1*cot(c+d*x)^2+b*a^-4*d^-1*(a^2+-1*b^2)*log(sin(c+d*x))+a^-4*b^5*d^-1*(a^2+b^2)^-1*log(a*cos(c+d*x)+b*sin(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-2*tan(c+d*x)^6, x) == :(-1*x*(a^2+b^2)^-2*(a^2+-1*b^2)+b^-4*d^-1*(a^2+b^2)^-1*(-1*b^4+4*a^4+2*a^2*b^2)*tan(c+d*x)+-2*a*b*d^-1*(a^2+b^2)^-2*log(cos(c+d*x))+1//3*b^-2*d^-1*(a^2+b^2)^-1*tan(c+d*x)^3*(b^2+4*a^2)+-1*a*b^-3*d^-1*(a^2+b^2)^-1*tan(c+d*x)^2*(b^2+2*a^2)+-1*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-1*tan(c+d*x)^4+-2*a^5*b^-5*d^-1*(a^2+b^2)^-2*(2*a^2+3*b^2)*log(a+b*tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-2*tan(c+d*x)^5, x) == :(-1*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2)*log(cos(c+d*x))+2*a*b*x*(a^2+b^2)^-2+(1/2)*b^-2*d^-1*(a^2+b^2)^-1*tan(c+d*x)^2*(b^2+3*a^2)+a^4*b^-4*d^-1*(a^2+b^2)^-2*(3*a^2+5*b^2)*log(a+b*tan(c+d*x))+-1*a*b^-3*d^-1*(a^2+b^2)^-1*(2*b^2+3*a^2)*tan(c+d*x)+-1*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-1*tan(c+d*x)^3)
@test integrate((a+b*tan(c+d*x))^-2*tan(c+d*x)^4, x) == :(x*(a^2+b^2)^-2*(a^2+-1*b^2)+b^-2*d^-1*(a^2+b^2)^-1*(b^2+2*a^2)*tan(c+d*x)+2*a*b*d^-1*(a^2+b^2)^-2*log(cos(c+d*x))+-1*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-1*tan(c+d*x)^2+-2*a^3*b^-3*d^-1*(a^2+b^2)^-2*(a^2+2*b^2)*log(a+b*tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-2*tan(c+d*x)^2, x) == :(-1*x*(a^2+b^2)^-2*(a^2+-1*b^2)+-1*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-1+-2*a*b*d^-1*(a^2+b^2)^-2*log(a*cos(c+d*x)+b*sin(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-2*tan(c+d*x), x) == :(a*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-1+-1*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2)*log(a*cos(c+d*x)+b*sin(c+d*x))+2*a*b*x*(a^2+b^2)^-2)
@test integrate((a+b*tan(c+d*x))^-2, x) == :(x*(a^2+b^2)^-2*(a^2+-1*b^2)+-1*b*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-1+2*a*b*d^-1*(a^2+b^2)^-2*log(a*cos(c+d*x)+b*sin(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-2*cot(c+d*x), x) == :(a^-2*d^-1*log(sin(c+d*x))+-2*a*b*x*(a^2+b^2)^-2+a^-1*b^2*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-1+-1*a^-2*b^2*d^-1*(a^2+b^2)^-2*(b^2+3*a^2)*log(a*cos(c+d*x)+b*sin(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-2*cot(c+d*x)^2, x) == :(-1*x*(a^2+b^2)^-2*(a^2+-1*b^2)+-1*a^-1*d^-1*(a+b*tan(c+d*x))^-1*cot(c+d*x)+-2*b*a^-3*d^-1*log(sin(c+d*x))+-1*b*a^-2*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-1*(a^2+2*b^2)+2*a^-3*b^3*d^-1*(a^2+b^2)^-2*(b^2+2*a^2)*log(a*cos(c+d*x)+b*sin(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-2*cot(c+d*x)^3, x) == :(-1*a^-4*d^-1*(a^2+-3*b^2)*log(sin(c+d*x))+2*a*b*x*(a^2+b^2)^-2+-1//2*a^-1*d^-1*(a+b*tan(c+d*x))^-1*cot(c+d*x)^2+3//2*b*a^-2*d^-1*(a+b*tan(c+d*x))^-1*cot(c+d*x)+a^-3*b^2*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-1*(2*a^2+3*b^2)+-1*a^-4*b^4*d^-1*(a^2+b^2)^-2*(3*b^2+5*a^2)*log(a*cos(c+d*x)+b*sin(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-3*tan(c+d*x)^6, x) == :(-1*a*x*(a^2+b^2)^-3*(a^2+-3*b^2)+(1/2)*b^-3*d^-1*(a^2+b^2)^-2*tan(c+d*x)^2*(b^4+6*a^4+11*a^2*b^2)+-1*b*d^-1*(a^2+b^2)^-3*(-1*b^2+3*a^2)*log(cos(c+d*x))+a^4*b^-5*d^-1*(a^2+b^2)^-3*(6*a^4+15*b^4+17*a^2*b^2)*log(a+b*tan(c+d*x))+-1*a*b^-4*d^-1*(a^2+b^2)^-2*(3*b^4+6*a^4+11*a^2*b^2)*tan(c+d*x)+-1//2*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-2*(a^2+b^2)^-1*tan(c+d*x)^4+-2*a^2*b^-2*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-2*tan(c+d*x)^3*(a^2+2*b^2))
@test integrate((a+b*tan(c+d*x))^-3*tan(c+d*x)^5, x) == :(b*x*(a^2+b^2)^-3*(-1*b^2+3*a^2)+b^-3*d^-1*(a^2+b^2)^-2*(b^4+3*a^4+6*a^2*b^2)*tan(c+d*x)+-1*a*d^-1*(a^2+b^2)^-3*(a^2+-3*b^2)*log(cos(c+d*x))+-1*a^3*b^-4*d^-1*(a^2+b^2)^-3*(3*a^4+10*b^4+9*a^2*b^2)*log(a+b*tan(c+d*x))+-1//2*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-2*(a^2+b^2)^-1*tan(c+d*x)^3+-1//2*a^2*b^-2*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-2*tan(c+d*x)^2*(3*a^2+7*b^2))
@test integrate((a+b*tan(c+d*x))^-3*tan(c+d*x)^4, x) == :(a*x*(a^2+b^2)^-3*(a^2+-3*b^2)+b*d^-1*(a^2+b^2)^-3*(-1*b^2+3*a^2)*log(cos(c+d*x))+a^2*b^-3*d^-1*(a^2+b^2)^-3*(a^4+6*b^4+3*a^2*b^2)*log(a+b*tan(c+d*x))+a^3*b^-3*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-2*(a^2+3*b^2)+-1//2*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-2*(a^2+b^2)^-1*tan(c+d*x)^2)
@test integrate((a+b*tan(c+d*x))^-3*tan(c+d*x)^3, x) == :(-1*b*x*(a^2+b^2)^-3*(-1*b^2+3*a^2)+a*d^-1*(a^2+b^2)^-3*(a^2+-3*b^2)*log(a*cos(c+d*x)+b*sin(c+d*x))+-1//2*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-2*(a^2+b^2)^-1*tan(c+d*x)+-1//2*a^2*b^-2*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-2*(a^2+5*b^2))
@test integrate((a+b*tan(c+d*x))^-3*tan(c+d*x)^2, x) == :(-1*a*x*(a^2+b^2)^-3*(a^2+-3*b^2)+-1*b*d^-1*(a^2+b^2)^-3*(-1*b^2+3*a^2)*log(a*cos(c+d*x)+b*sin(c+d*x))+2*a*b*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-2+-1//2*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-2*(a^2+b^2)^-1)
@test integrate((a+b*tan(c+d*x))^-3*tan(c+d*x), x) == :(a*d^-1*(a+b*tan(c+d*x))^-2*(2*a^2+2*b^2)^-1+b*x*(a^2+b^2)^-3*(-1*b^2+3*a^2)+d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-2*(a^2+-1*b^2)+-1*a*d^-1*(a^2+b^2)^-3*(a^2+-3*b^2)*log(a*cos(c+d*x)+b*sin(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-3, x) == :(a*x*(a^2+b^2)^-3*(a^2+-3*b^2)+-1*b*d^-1*(a+b*tan(c+d*x))^-2*(2*a^2+2*b^2)^-1+b*d^-1*(a^2+b^2)^-3*(-1*b^2+3*a^2)*log(a*cos(c+d*x)+b*sin(c+d*x))+-2*a*b*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-2)
@test integrate((a+b*tan(c+d*x))^-3*cot(c+d*x), x) == :(a^-3*d^-1*log(sin(c+d*x))+-1*b*x*(a^2+b^2)^-3*(-1*b^2+3*a^2)+(1/2)*a^-1*b^2*d^-1*(a+b*tan(c+d*x))^-2*(a^2+b^2)^-1+a^-2*b^2*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-2*(b^2+3*a^2)+-1*a^-3*b^2*d^-1*(a^2+b^2)^-3*(b^4+6*a^4+3*a^2*b^2)*log(a*cos(c+d*x)+b*sin(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-3*cot(c+d*x)^2, x) == :(-1*a*x*(a^2+b^2)^-3*(a^2+-3*b^2)+-1*a^-1*d^-1*(a+b*tan(c+d*x))^-2*cot(c+d*x)+-3*b*a^-4*d^-1*log(sin(c+d*x))+a^-4*b^3*d^-1*(a^2+b^2)^-3*(3*b^4+10*a^4+9*a^2*b^2)*log(a*cos(c+d*x)+b*sin(c+d*x))+-1*b*a^-3*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-2*(a^4+3*b^4+6*a^2*b^2)+-1//2*b*a^-2*d^-1*(a+b*tan(c+d*x))^-2*(a^2+b^2)^-1*(2*a^2+3*b^2))
@test integrate((a+b*tan(c+d*x))^-4*tan(c+d*x)^6, x) == :(-1*x*(a^2+b^2)^-4*(a^4+b^4+-6*a^2*b^2)+b^-4*d^-1*(a^2+b^2)^-3*(b^6+4*a^6+12*a^4*b^2+13*a^2*b^4)*tan(c+d*x)+-4*a*b*d^-1*(a^2+b^2)^-4*(a^2+-1*b^2)*log(cos(c+d*x))+-4*a^3*b^-5*d^-1*(a^2+b^2)^-4*(a^6+5*b^6+4*a^4*b^2+6*a^2*b^4)*log(a+b*tan(c+d*x))+-1//3*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-3*(a^2+b^2)^-1*tan(c+d*x)^4+-2*a^2*b^-3*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-3*tan(c+d*x)^2*(a^4+4*b^4+3*a^2*b^2)+-1//3*a^2*b^-2*d^-1*(a+b*tan(c+d*x))^-2*(a^2+b^2)^-2*tan(c+d*x)^3*(2*a^2+5*b^2))
@test integrate((a+b*tan(c+d*x))^-4*tan(c+d*x)^5, x) == :(-1*d^-1*(a^2+b^2)^-4*(a^4+b^4+-6*a^2*b^2)*log(cos(c+d*x))+4*a*b*x*(a^2+b^2)^-4*(a^2+-1*b^2)+a^2*b^-4*d^-1*(a^2+b^2)^-4*(a^6+10*b^6+4*a^4*b^2+5*a^2*b^4)*log(a+b*tan(c+d*x))+a^3*b^-4*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-3*(a^4+6*b^4+3*a^2*b^2)+-1//3*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-3*(a^2+b^2)^-1*tan(c+d*x)^3+-1//2*a^2*b^-2*d^-1*(a+b*tan(c+d*x))^-2*(a^2+b^2)^-2*tan(c+d*x)^2*(a^2+3*b^2))
@test integrate((a+b*tan(c+d*x))^-4*tan(c+d*x)^4, x) == :(x*(a^2+b^2)^-4*(a^4+b^4+-6*a^2*b^2)+4*a*b*d^-1*(a^2+b^2)^-4*(a^2+-1*b^2)*log(a*cos(c+d*x)+b*sin(c+d*x))+-1//3*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-3*(a^2+b^2)^-1*tan(c+d*x)^2+-1//3*a^2*b^-3*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-3*(2*a^4+17*b^4+7*a^2*b^2)+1//3*a^3*b^-3*d^-1*(a+b*tan(c+d*x))^-2*(a^2+b^2)^-2*(a^2+4*b^2))
@test integrate((a+b*tan(c+d*x))^-4*tan(c+d*x)^3, x) == :(d^-1*(a^2+b^2)^-4*(a^4+b^4+-6*a^2*b^2)*log(a*cos(c+d*x)+b*sin(c+d*x))+-1*a*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-3*(a^2+-3*b^2)+-4*a*b*x*(a^2+b^2)^-4*(a^2+-1*b^2)+-1//3*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-3*(a^2+b^2)^-1*tan(c+d*x)+-1//6*a^2*b^-2*d^-1*(a+b*tan(c+d*x))^-2*(a^2+b^2)^-2*(a^2+7*b^2))
@test integrate((a+b*tan(c+d*x))^-4*tan(c+d*x)^2, x) == :(-1*x*(a^2+b^2)^-4*(a^4+b^4+-6*a^2*b^2)+a*b*d^-1*(a+b*tan(c+d*x))^-2*(a^2+b^2)^-2+b*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-3*(-1*b^2+3*a^2)+-1//3*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-3*(a^2+b^2)^-1+-4*a*b*d^-1*(a^2+b^2)^-4*(a^2+-1*b^2)*log(a*cos(c+d*x)+b*sin(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-4*tan(c+d*x), x) == :(a*d^-1*(a+b*tan(c+d*x))^-3*(3*a^2+3*b^2)^-1+(1/2)*d^-1*(a+b*tan(c+d*x))^-2*(a^2+b^2)^-2*(a^2+-1*b^2)+-1*d^-1*(a^2+b^2)^-4*(a^4+b^4+-6*a^2*b^2)*log(a*cos(c+d*x)+b*sin(c+d*x))+a*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-3*(a^2+-3*b^2)+4*a*b*x*(a^2+b^2)^-4*(a^2+-1*b^2))
@test integrate((a+b*tan(c+d*x))^-4, x) == :(x*(a^2+b^2)^-4*(a^4+b^4+-6*a^2*b^2)+-1*b*d^-1*(a+b*tan(c+d*x))^-3*(3*a^2+3*b^2)^-1+-1*a*b*d^-1*(a+b*tan(c+d*x))^-2*(a^2+b^2)^-2+-1*b*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-3*(-1*b^2+3*a^2)+4*a*b*d^-1*(a^2+b^2)^-4*(a^2+-1*b^2)*log(a*cos(c+d*x)+b*sin(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-4*cot(c+d*x), x) == :(a^-4*d^-1*log(sin(c+d*x))+-4*a*b*x*(a^2+b^2)^-4*(a^2+-1*b^2)+1//3*a^-1*b^2*d^-1*(a+b*tan(c+d*x))^-3*(a^2+b^2)^-1+a^-3*b^2*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-3*(b^4+6*a^4+3*a^2*b^2)+(1/2)*a^-2*b^2*d^-1*(a+b*tan(c+d*x))^-2*(a^2+b^2)^-2*(b^2+3*a^2)+-1*a^-4*b^2*d^-1*(a^2+b^2)^-4*(b^6+10*a^6+4*a^2*b^4+5*a^4*b^2)*log(a*cos(c+d*x)+b*sin(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-4*cot(c+d*x)^2, x) == :(-1*x*(a^2+b^2)^-4*(a^4+b^4+-6*a^2*b^2)+-1*a^-1*d^-1*(a+b*tan(c+d*x))^-3*cot(c+d*x)+-4*b*a^-5*d^-1*log(sin(c+d*x))+-1*b*a^-4*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-3*(a^6+4*b^6+12*a^2*b^4+13*a^4*b^2)+-1*b*a^-3*d^-1*(a+b*tan(c+d*x))^-2*(a^2+b^2)^-2*(a^4+2*b^4+4*a^2*b^2)+4*a^-5*b^3*d^-1*(a^2+b^2)^-4*(b^6+5*a^6+4*a^2*b^4+6*a^4*b^2)*log(a*cos(c+d*x)+b*sin(c+d*x))+-1//3*b*a^-2*d^-1*(a+b*tan(c+d*x))^-3*(a^2+b^2)^-1*(3*a^2+4*b^2))
@test integrate((3+5*tan(c+d*x))^-1, x) == :(3//34*x+5//34*d^-1*log(3*cos(c+d*x)+5*sin(c+d*x)))
@test integrate((3+5*tan(c+d*x))^-2, x) == :(-4//289*x+-5//34*d^-1*(3+5*tan(c+d*x))^-1+15//578*d^-1*log(3*cos(c+d*x)+5*sin(c+d*x)))
@test integrate((3+5*tan(c+d*x))^-3, x) == :(-99//19652*x+-15//578*d^-1*(3+5*tan(c+d*x))^-1+-5//68*d^-1*(3+5*tan(c+d*x))^-2+5//19652*d^-1*log(3*cos(c+d*x)+5*sin(c+d*x)))
@test integrate((3+5*tan(c+d*x))^-4, x) == :(-161//334084*x+-60//83521*d^-1*log(3*cos(c+d*x)+5*sin(c+d*x))+-15//1156*d^-1*(3+5*tan(c+d*x))^-2+-5//102*d^-1*(3+5*tan(c+d*x))^-3+-5//19652*d^-1*(3+5*tan(c+d*x))^-1)
@test integrate((5+3*tan(c+d*x))^-1, x) == :(5//34*x+3//34*d^-1*log(3*sin(c+d*x)+5*cos(c+d*x)))
@test integrate((5+3*tan(c+d*x))^-2, x) == :(4//289*x+-3//34*d^-1*(5+3*tan(c+d*x))^-1+15//578*d^-1*log(3*sin(c+d*x)+5*cos(c+d*x)))
@test integrate((5+3*tan(c+d*x))^-3, x) == :(-5//19652*x+-15//578*d^-1*(5+3*tan(c+d*x))^-1+-3//68*d^-1*(5+3*tan(c+d*x))^-2+99//19652*d^-1*log(3*sin(c+d*x)+5*cos(c+d*x)))
@test integrate((5+3*tan(c+d*x))^-4, x) == :(-161//334084*x+-99//19652*d^-1*(5+3*tan(c+d*x))^-1+-15//1156*d^-1*(5+3*tan(c+d*x))^-2+-1//34*d^-1*(5+3*tan(c+d*x))^-3+60//83521*d^-1*log(3*sin(c+d*x)+5*cos(c+d*x)))
@test integrate((a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^4, x) == :(1//105*b^-3*d^-1*(a+b*tan(c+d*x))^3//2*(-70*b^2+16*a^2)+2//7*b^-1*d^-1*(a+b*tan(c+d*x))^3//2*tan(c+d*x)^2+(1/2)*b*2^(1/2)*d^-1*(a+-1*(a^2+b^2)^(1/2))^-1//2*arctanh((a+-1*(a^2+b^2)^(1/2))^-1//2*((a+(a^2+b^2)^(1/2))^(1/2)+-1*2^(1/2)*(a+b*tan(c+d*x))^(1/2)))+-8//35*a*b^-2*d^-1*(a+b*tan(c+d*x))^3//2*tan(c+d*x)+-1//2*b*2^(1/2)*d^-1*(a+-1*(a^2+b^2)^(1/2))^-1//2*arctanh((a+-1*(a^2+b^2)^(1/2))^-1//2*((a+(a^2+b^2)^(1/2))^(1/2)+2^(1/2)*(a+b*tan(c+d*x))^(1/2)))+-1//4*b*2^(1/2)*d^-1*(a+(a^2+b^2)^(1/2))^-1//2*log(a+(a^2+b^2)^(1/2)+b*tan(c+d*x)+2^(1/2)*(a+(a^2+b^2)^(1/2))^(1/2)*(a+b*tan(c+d*x))^(1/2))+1//4*b*2^(1/2)*d^-1*(a+(a^2+b^2)^(1/2))^-1//2*log(a+(a^2+b^2)^(1/2)+b*tan(c+d*x)+-1*2^(1/2)*(a+(a^2+b^2)^(1/2))^(1/2)*(a+b*tan(c+d*x))^(1/2)))
@test integrate((a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^3, x) == :(-2*d^-1*(a+b*tan(c+d*x))^(1/2)+d^-1*(a+im*b)^(1/2)*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+d^-1*(a+-1*im*b)^(1/2)*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-4//15*a*b^-2*d^-1*(a+b*tan(c+d*x))^3//2+2//5*b^-1*d^-1*(a+b*tan(c+d*x))^3//2*tan(c+d*x))
@test integrate((a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^2, x) == :(2//3*b^-1*d^-1*(a+b*tan(c+d*x))^3//2+(1/2)*b*2^(1/2)*d^-1*(a+-1*(a^2+b^2)^(1/2))^-1//2*arctanh((a+-1*(a^2+b^2)^(1/2))^-1//2*((a+(a^2+b^2)^(1/2))^(1/2)+2^(1/2)*(a+b*tan(c+d*x))^(1/2)))+-1//2*b*2^(1/2)*d^-1*(a+-1*(a^2+b^2)^(1/2))^-1//2*arctanh((a+-1*(a^2+b^2)^(1/2))^-1//2*((a+(a^2+b^2)^(1/2))^(1/2)+-1*2^(1/2)*(a+b*tan(c+d*x))^(1/2)))+-1//4*b*2^(1/2)*d^-1*(a+(a^2+b^2)^(1/2))^-1//2*log(a+(a^2+b^2)^(1/2)+b*tan(c+d*x)+-1*2^(1/2)*(a+(a^2+b^2)^(1/2))^(1/2)*(a+b*tan(c+d*x))^(1/2))+1//4*b*2^(1/2)*d^-1*(a+(a^2+b^2)^(1/2))^-1//2*log(a+(a^2+b^2)^(1/2)+b*tan(c+d*x)+2^(1/2)*(a+(a^2+b^2)^(1/2))^(1/2)*(a+b*tan(c+d*x))^(1/2)))
@test integrate((a+b*tan(c+d*x))^(1/2)*tan(c+d*x), x) == :(2*d^-1*(a+b*tan(c+d*x))^(1/2)+-1*d^-1*(a+im*b)^(1/2)*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*d^-1*(a+-1*im*b)^(1/2)*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2))
@test integrate((a+b*tan(c+d*x))^(1/2), x) == :((1/2)*b*2^(1/2)*d^-1*(a+-1*(a^2+b^2)^(1/2))^-1//2*arctanh((a+-1*(a^2+b^2)^(1/2))^-1//2*((a+(a^2+b^2)^(1/2))^(1/2)+-1*2^(1/2)*(a+b*tan(c+d*x))^(1/2)))+-1//2*b*2^(1/2)*d^-1*(a+-1*(a^2+b^2)^(1/2))^-1//2*arctanh((a+-1*(a^2+b^2)^(1/2))^-1//2*((a+(a^2+b^2)^(1/2))^(1/2)+2^(1/2)*(a+b*tan(c+d*x))^(1/2)))+-1//4*b*2^(1/2)*d^-1*(a+(a^2+b^2)^(1/2))^-1//2*log(a+(a^2+b^2)^(1/2)+b*tan(c+d*x)+2^(1/2)*(a+(a^2+b^2)^(1/2))^(1/2)*(a+b*tan(c+d*x))^(1/2))+1//4*b*2^(1/2)*d^-1*(a+(a^2+b^2)^(1/2))^-1//2*log(a+(a^2+b^2)^(1/2)+b*tan(c+d*x)+-1*2^(1/2)*(a+(a^2+b^2)^(1/2))^(1/2)*(a+b*tan(c+d*x))^(1/2)))
@test integrate((a+b*tan(c+d*x))^(1/2)*cot(c+d*x), x) == :(d^-1*(a+im*b)^(1/2)*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+d^-1*(a+-1*im*b)^(1/2)*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-2*a^(1/2)*d^-1*arctanh(a^-1//2*(a+b*tan(c+d*x))^(1/2)))
@test integrate((a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^2, x) == :(-1*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)+-1*b*a^-1//2*d^-1*arctanh(a^-1//2*(a+b*tan(c+d*x))^(1/2))+(1/2)*b*2^(1/2)*d^-1*(a+-1*(a^2+b^2)^(1/2))^-1//2*arctanh((a+-1*(a^2+b^2)^(1/2))^-1//2*((a+(a^2+b^2)^(1/2))^(1/2)+2^(1/2)*(a+b*tan(c+d*x))^(1/2)))+-1//2*b*2^(1/2)*d^-1*(a+-1*(a^2+b^2)^(1/2))^-1//2*arctanh((a+-1*(a^2+b^2)^(1/2))^-1//2*((a+(a^2+b^2)^(1/2))^(1/2)+-1*2^(1/2)*(a+b*tan(c+d*x))^(1/2)))+-1//4*b*2^(1/2)*d^-1*(a+(a^2+b^2)^(1/2))^-1//2*log(a+(a^2+b^2)^(1/2)+b*tan(c+d*x)+-1*2^(1/2)*(a+(a^2+b^2)^(1/2))^(1/2)*(a+b*tan(c+d*x))^(1/2))+1//4*b*2^(1/2)*d^-1*(a+(a^2+b^2)^(1/2))^-1//2*log(a+(a^2+b^2)^(1/2)+b*tan(c+d*x)+2^(1/2)*(a+(a^2+b^2)^(1/2))^(1/2)*(a+b*tan(c+d*x))^(1/2)))
@test integrate((a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^3, x) == :(-1*d^-1*(a+im*b)^(1/2)*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*d^-1*(a+-1*im*b)^(1/2)*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-1//2*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^2+1//4*a^-3//2*d^-1*(b^2+8*a^2)*arctanh(a^-1//2*(a+b*tan(c+d*x))^(1/2))+-1//4*b*a^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x))
@test integrate((a+b*tan(c+d*x))^3//2*tan(c+d*x)^4, x) == :(2*b*d^-1*(a+b*tan(c+d*x))^(1/2)+im*d^-1*(a+im*b)^3//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*im*d^-1*(a+-1*im*b)^3//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+1//315*b^-3*d^-1*(a+b*tan(c+d*x))^5//2*(-126*b^2+16*a^2)+2//9*b^-1*d^-1*(a+b*tan(c+d*x))^5//2*tan(c+d*x)^2+-8//63*a*b^-2*d^-1*(a+b*tan(c+d*x))^5//2*tan(c+d*x))
@test integrate((a+b*tan(c+d*x))^3//2*tan(c+d*x)^3, x) == :(-2//3*d^-1*(a+b*tan(c+d*x))^3//2+d^-1*(a+im*b)^3//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+d^-1*(a+-1*im*b)^3//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-2*a*d^-1*(a+b*tan(c+d*x))^(1/2)+-4//35*a*b^-2*d^-1*(a+b*tan(c+d*x))^5//2+2//7*b^-1*d^-1*(a+b*tan(c+d*x))^5//2*tan(c+d*x))
@test integrate((a+b*tan(c+d*x))^3//2*tan(c+d*x)^2, x) == :(-2*b*d^-1*(a+b*tan(c+d*x))^(1/2)+2//5*b^-1*d^-1*(a+b*tan(c+d*x))^5//2+im*d^-1*(a+-1*im*b)^3//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-1*im*d^-1*(a+im*b)^3//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2)))
@test integrate((a+b*tan(c+d*x))^3//2*tan(c+d*x), x) == :(2//3*d^-1*(a+b*tan(c+d*x))^3//2+-1*d^-1*(a+im*b)^3//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*d^-1*(a+-1*im*b)^3//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+2*a*d^-1*(a+b*tan(c+d*x))^(1/2))
@test integrate((a+b*tan(c+d*x))^3//2, x) == :(2*b*d^-1*(a+b*tan(c+d*x))^(1/2)+im*d^-1*(a+im*b)^3//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*im*d^-1*(a+-1*im*b)^3//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2))
@test integrate((a+b*tan(c+d*x))^3//2*cot(c+d*x), x) == :(d^-1*(a+im*b)^3//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+d^-1*(a+-1*im*b)^3//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-2*a^3//2*d^-1*arctanh(a^-1//2*(a+b*tan(c+d*x))^(1/2)))
@test integrate((a+b*tan(c+d*x))^3//2*cot(c+d*x)^2, x) == :(im*d^-1*(a+-1*im*b)^3//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-1*im*d^-1*(a+im*b)^3//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*a*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)+-3*b*a^(1/2)*d^-1*arctanh(a^-1//2*(a+b*tan(c+d*x))^(1/2)))
@test integrate((a+b*tan(c+d*x))^3//2*cot(c+d*x)^3, x) == :(-1*d^-1*(a+im*b)^3//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*d^-1*(a+-1*im*b)^3//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-5//4*b*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)+-1//2*a*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^2+1//4*a^-1//2*d^-1*(-3*b^2+8*a^2)*arctanh(a^-1//2*(a+b*tan(c+d*x))^(1/2)))
@test integrate((a+b*tan(c+d*x))^5//2*tan(c+d*x)^3, x) == :(-2//5*d^-1*(a+b*tan(c+d*x))^5//2+d^-1*(a+im*b)^5//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+d^-1*(a+-1*im*b)^5//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-1*d^-1*(a+b*tan(c+d*x))^(1/2)*(-2*b^2+2*a^2)+-2//3*a*d^-1*(a+b*tan(c+d*x))^3//2+-4//63*a*b^-2*d^-1*(a+b*tan(c+d*x))^7//2+2//9*b^-1*d^-1*(a+b*tan(c+d*x))^7//2*tan(c+d*x))
@test integrate((a+b*tan(c+d*x))^5//2*tan(c+d*x)^2, x) == :(-2//3*b*d^-1*(a+b*tan(c+d*x))^3//2+2//7*b^-1*d^-1*(a+b*tan(c+d*x))^7//2+im*d^-1*(a+-1*im*b)^5//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-1*im*d^-1*(a+im*b)^5//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-4*a*b*d^-1*(a+b*tan(c+d*x))^(1/2))
@test integrate((a+b*tan(c+d*x))^5//2*tan(c+d*x), x) == :(2//5*d^-1*(a+b*tan(c+d*x))^5//2+d^-1*(a+b*tan(c+d*x))^(1/2)*(-2*b^2+2*a^2)+-1*d^-1*(a+im*b)^5//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*d^-1*(a+-1*im*b)^5//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+2//3*a*d^-1*(a+b*tan(c+d*x))^3//2)
@test integrate((a+b*tan(c+d*x))^5//2, x) == :(2//3*b*d^-1*(a+b*tan(c+d*x))^3//2+im*d^-1*(a+im*b)^5//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*im*d^-1*(a+-1*im*b)^5//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+4*a*b*d^-1*(a+b*tan(c+d*x))^(1/2))
@test integrate((a+b*tan(c+d*x))^5//2*cot(c+d*x), x) == :(d^-1*(a+im*b)^5//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+d^-1*(a+-1*im*b)^5//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-2*a^5//2*d^-1*arctanh(a^-1//2*(a+b*tan(c+d*x))^(1/2))+2*b^2*d^-1*(a+b*tan(c+d*x))^(1/2))
@test integrate((a+b*tan(c+d*x))^5//2*cot(c+d*x)^2, x) == :(im*d^-1*(a+-1*im*b)^5//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-1*im*d^-1*(a+im*b)^5//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*a^2*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)+-5*b*a^3//2*d^-1*arctanh(a^-1//2*(a+b*tan(c+d*x))^(1/2)))
@test integrate((a+b*tan(c+d*x))^5//2*cot(c+d*x)^3, x) == :(-1*d^-1*(a+im*b)^5//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*d^-1*(a+-1*im*b)^5//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-1//2*a^2*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^2+1//4*a^(1/2)*d^-1*(-15*b^2+8*a^2)*arctanh(a^-1//2*(a+b*tan(c+d*x))^(1/2))+-9//4*a*b*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x))
@test integrate((a+b*tan(c+d*x))^5//2*cot(c+d*x)^4, x) == :(im*d^-1*(a+im*b)^5//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*im*d^-1*(a+-1*im*b)^5//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-1//3*a^2*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^3+1//8*d^-1*(a+b*tan(c+d*x))^(1/2)*(-11*b^2+8*a^2)*cot(c+d*x)+-13//12*a*b*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^2+5//8*b*a^-1//2*d^-1*(-1*b^2+8*a^2)*arctanh(a^-1//2*(a+b*tan(c+d*x))^(1/2)))
@test integrate((a+b*tan(c+d*x))^7//2, x) == :(2//5*b*d^-1*(a+b*tan(c+d*x))^5//2+im*d^-1*(a+im*b)^7//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*im*d^-1*(a+-1*im*b)^7//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+2*b*d^-1*(a+b*tan(c+d*x))^(1/2)*(-1*b^2+3*a^2)+4//3*a*b*d^-1*(a+b*tan(c+d*x))^3//2)
@test integrate((a+b*tan(c+d*x))^-1//2*tan(c+d*x)^5, x) == :(-1*d^-1*(a+im*b)^-1//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*d^-1*(a+-1*im*b)^-1//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+2//7*b^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^3+-12//35*a*b^-2*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^2+-4//105*a*b^-4*d^-1*(a+b*tan(c+d*x))^(1/2)*(-35*b^2+24*a^2)+1//105*b^-3*d^-1*(a+b*tan(c+d*x))^(1/2)*(-70*b^2+48*a^2)*tan(c+d*x))
@test integrate((a+b*tan(c+d*x))^-1//2*tan(c+d*x)^4, x) == :(1//15*b^-3*d^-1*(a+b*tan(c+d*x))^(1/2)*(-30*b^2+16*a^2)+2//5*b^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^2+-8//15*a*b^-2*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)+(1/2)*b*2^(1/2)*d^-1*(a+-1*(a^2+b^2)^(1/2))^-1//2*(a^2+b^2)^-1//2*arctanh((a+-1*(a^2+b^2)^(1/2))^-1//2*((a+(a^2+b^2)^(1/2))^(1/2)+-1*2^(1/2)*(a+b*tan(c+d*x))^(1/2)))+-1//2*b*2^(1/2)*d^-1*(a+-1*(a^2+b^2)^(1/2))^-1//2*(a^2+b^2)^-1//2*arctanh((a+-1*(a^2+b^2)^(1/2))^-1//2*((a+(a^2+b^2)^(1/2))^(1/2)+2^(1/2)*(a+b*tan(c+d*x))^(1/2)))+-1//4*b*2^(1/2)*d^-1*(a+(a^2+b^2)^(1/2))^-1//2*(a^2+b^2)^-1//2*log(a+(a^2+b^2)^(1/2)+b*tan(c+d*x)+-1*2^(1/2)*(a+(a^2+b^2)^(1/2))^(1/2)*(a+b*tan(c+d*x))^(1/2))+1//4*b*2^(1/2)*d^-1*(a+(a^2+b^2)^(1/2))^-1//2*(a^2+b^2)^-1//2*log(a+(a^2+b^2)^(1/2)+b*tan(c+d*x)+2^(1/2)*(a+(a^2+b^2)^(1/2))^(1/2)*(a+b*tan(c+d*x))^(1/2)))
@test integrate((a+b*tan(c+d*x))^-1//2*tan(c+d*x)^3, x) == :(d^-1*(a+im*b)^-1//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+d^-1*(a+-1*im*b)^-1//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-4//3*a*b^-2*d^-1*(a+b*tan(c+d*x))^(1/2)+2//3*b^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x))
@test integrate((a+b*tan(c+d*x))^-1//2*tan(c+d*x)^2, x) == :(2*b^-1*d^-1*(a+b*tan(c+d*x))^(1/2)+(1/2)*b*2^(1/2)*d^-1*(a+-1*(a^2+b^2)^(1/2))^-1//2*(a^2+b^2)^-1//2*arctanh((a+-1*(a^2+b^2)^(1/2))^-1//2*((a+(a^2+b^2)^(1/2))^(1/2)+2^(1/2)*(a+b*tan(c+d*x))^(1/2)))+-1//2*b*2^(1/2)*d^-1*(a+-1*(a^2+b^2)^(1/2))^-1//2*(a^2+b^2)^-1//2*arctanh((a+-1*(a^2+b^2)^(1/2))^-1//2*((a+(a^2+b^2)^(1/2))^(1/2)+-1*2^(1/2)*(a+b*tan(c+d*x))^(1/2)))+-1//4*b*2^(1/2)*d^-1*(a+(a^2+b^2)^(1/2))^-1//2*(a^2+b^2)^-1//2*log(a+(a^2+b^2)^(1/2)+b*tan(c+d*x)+2^(1/2)*(a+(a^2+b^2)^(1/2))^(1/2)*(a+b*tan(c+d*x))^(1/2))+1//4*b*2^(1/2)*d^-1*(a+(a^2+b^2)^(1/2))^-1//2*(a^2+b^2)^-1//2*log(a+(a^2+b^2)^(1/2)+b*tan(c+d*x)+-1*2^(1/2)*(a+(a^2+b^2)^(1/2))^(1/2)*(a+b*tan(c+d*x))^(1/2)))
@test integrate((a+b*tan(c+d*x))^-1//2*tan(c+d*x), x) == :(-1*d^-1*(a+im*b)^-1//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*d^-1*(a+-1*im*b)^-1//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2))
@test integrate((a+b*tan(c+d*x))^-1//2, x) == :((1/2)*b*2^(1/2)*d^-1*(a+-1*(a^2+b^2)^(1/2))^-1//2*(a^2+b^2)^-1//2*arctanh((a+-1*(a^2+b^2)^(1/2))^-1//2*((a+(a^2+b^2)^(1/2))^(1/2)+-1*2^(1/2)*(a+b*tan(c+d*x))^(1/2)))+-1//2*b*2^(1/2)*d^-1*(a+-1*(a^2+b^2)^(1/2))^-1//2*(a^2+b^2)^-1//2*arctanh((a+-1*(a^2+b^2)^(1/2))^-1//2*((a+(a^2+b^2)^(1/2))^(1/2)+2^(1/2)*(a+b*tan(c+d*x))^(1/2)))+-1//4*b*2^(1/2)*d^-1*(a+(a^2+b^2)^(1/2))^-1//2*(a^2+b^2)^-1//2*log(a+(a^2+b^2)^(1/2)+b*tan(c+d*x)+-1*2^(1/2)*(a+(a^2+b^2)^(1/2))^(1/2)*(a+b*tan(c+d*x))^(1/2))+1//4*b*2^(1/2)*d^-1*(a+(a^2+b^2)^(1/2))^-1//2*(a^2+b^2)^-1//2*log(a+(a^2+b^2)^(1/2)+b*tan(c+d*x)+2^(1/2)*(a+(a^2+b^2)^(1/2))^(1/2)*(a+b*tan(c+d*x))^(1/2)))
@test integrate((a+b*tan(c+d*x))^-1//2*cot(c+d*x), x) == :(d^-1*(a+im*b)^-1//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+d^-1*(a+-1*im*b)^-1//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-2*a^-1//2*d^-1*arctanh(a^-1//2*(a+b*tan(c+d*x))^(1/2)))
@test integrate((a+b*tan(c+d*x))^-1//2*cot(c+d*x)^2, x) == :(b*a^-3//2*d^-1*arctanh(a^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*a^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)+(1/2)*b*2^(1/2)*d^-1*(a+-1*(a^2+b^2)^(1/2))^-1//2*(a^2+b^2)^-1//2*arctanh((a+-1*(a^2+b^2)^(1/2))^-1//2*((a+(a^2+b^2)^(1/2))^(1/2)+2^(1/2)*(a+b*tan(c+d*x))^(1/2)))+-1//2*b*2^(1/2)*d^-1*(a+-1*(a^2+b^2)^(1/2))^-1//2*(a^2+b^2)^-1//2*arctanh((a+-1*(a^2+b^2)^(1/2))^-1//2*((a+(a^2+b^2)^(1/2))^(1/2)+-1*2^(1/2)*(a+b*tan(c+d*x))^(1/2)))+-1//4*b*2^(1/2)*d^-1*(a+(a^2+b^2)^(1/2))^-1//2*(a^2+b^2)^-1//2*log(a+(a^2+b^2)^(1/2)+b*tan(c+d*x)+2^(1/2)*(a+(a^2+b^2)^(1/2))^(1/2)*(a+b*tan(c+d*x))^(1/2))+1//4*b*2^(1/2)*d^-1*(a+(a^2+b^2)^(1/2))^-1//2*(a^2+b^2)^-1//2*log(a+(a^2+b^2)^(1/2)+b*tan(c+d*x)+-1*2^(1/2)*(a+(a^2+b^2)^(1/2))^(1/2)*(a+b*tan(c+d*x))^(1/2)))
@test integrate((a+b*tan(c+d*x))^-1//2*cot(c+d*x)^3, x) == :(-1*d^-1*(a+im*b)^-1//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*d^-1*(a+-1*im*b)^-1//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-1//2*a^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^2+1//4*a^-5//2*d^-1*(-3*b^2+8*a^2)*arctanh(a^-1//2*(a+b*tan(c+d*x))^(1/2))+3//4*b*a^-2*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x))
@test integrate((a+b*tan(c+d*x))^-3//2*tan(c+d*x)^5, x) == :(-1*d^-1*(a+im*b)^-3//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*d^-1*(a+-1*im*b)^-3//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+1//5*b^-4*d^-1*(a+b*tan(c+d*x))^(1/2)*(a^2+b^2)^-1*(-10*b^4+32*a^4+12*a^2*b^2)+-2*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-1*tan(c+d*x)^3+1//5*b^-2*d^-1*(a+b*tan(c+d*x))^(1/2)*(a^2+b^2)^-1*tan(c+d*x)^2*(2*b^2+12*a^2)+-2//5*a*b^-3*d^-1*(a+b*tan(c+d*x))^(1/2)*(a^2+b^2)^-1*(3*b^2+8*a^2)*tan(c+d*x))
@test integrate((a+b*tan(c+d*x))^-3//2*tan(c+d*x)^4, x) == :(im*d^-1*(a+im*b)^-3//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*im*d^-1*(a+-1*im*b)^-3//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-2*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-1*tan(c+d*x)^2+-2//3*a*b^-3*d^-1*(a+b*tan(c+d*x))^(1/2)*(a^2+b^2)^-1*(5*b^2+8*a^2)+1//3*b^-2*d^-1*(a+b*tan(c+d*x))^(1/2)*(a^2+b^2)^-1*(2*b^2+8*a^2)*tan(c+d*x))
@test integrate((a+b*tan(c+d*x))^-3//2*tan(c+d*x)^3, x) == :(d^-1*(a+im*b)^-3//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+d^-1*(a+-1*im*b)^-3//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+b^-2*d^-1*(a+b*tan(c+d*x))^(1/2)*(a^2+b^2)^-1*(2*b^2+4*a^2)+-2*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-1*tan(c+d*x))
@test integrate((a+b*tan(c+d*x))^-3//2*tan(c+d*x)^2, x) == :(im*d^-1*(a+-1*im*b)^-3//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-1*im*d^-1*(a+im*b)^-3//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-2*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-1)
@test integrate((a+b*tan(c+d*x))^-3//2*tan(c+d*x), x) == :(-1*d^-1*(a+im*b)^-3//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*d^-1*(a+-1*im*b)^-3//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+2*a*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-1)
@test integrate((a+b*tan(c+d*x))^-3//2, x) == :(im*d^-1*(a+im*b)^-3//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*im*d^-1*(a+-1*im*b)^-3//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-2*b*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-1)
@test integrate((a+b*tan(c+d*x))^-3//2*cot(c+d*x), x) == :(d^-1*(a+im*b)^-3//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+d^-1*(a+-1*im*b)^-3//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-2*a^-3//2*d^-1*arctanh(a^-1//2*(a+b*tan(c+d*x))^(1/2))+2*a^-1*b^2*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-1)
@test integrate((a+b*tan(c+d*x))^-3//2*cot(c+d*x)^2, x) == :(im*d^-1*(a+-1*im*b)^-3//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-1*im*d^-1*(a+im*b)^-3//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*a^-1*d^-1*(a+b*tan(c+d*x))^-1//2*cot(c+d*x)+3*b*a^-5//2*d^-1*arctanh(a^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*b*a^-2*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-1*(a^2+3*b^2))
@test integrate((a+b*tan(c+d*x))^-3//2*cot(c+d*x)^3, x) == :(-1*d^-1*(a+im*b)^-3//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*d^-1*(a+-1*im*b)^-3//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-1//2*a^-1*d^-1*(a+b*tan(c+d*x))^-1//2*cot(c+d*x)^2+1//4*a^-7//2*d^-1*(-15*b^2+8*a^2)*arctanh(a^-1//2*(a+b*tan(c+d*x))^(1/2))+5//4*b*a^-2*d^-1*(a+b*tan(c+d*x))^-1//2*cot(c+d*x)+1//4*a^-3*b^2*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-1*(7*a^2+15*b^2))
@test integrate((a+b*tan(c+d*x))^-5//2*tan(c+d*x)^5, x) == :(-1*d^-1*(a+im*b)^-5//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*d^-1*(a+-1*im*b)^-5//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-4//3*a*b^-4*d^-1*(a+b*tan(c+d*x))^(1/2)*(a^2+b^2)^-2*(4*b^4+8*a^4+15*a^2*b^2)+-2//3*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-3//2*(a^2+b^2)^-1*tan(c+d*x)^3+1//3*b^-3*d^-1*(a+b*tan(c+d*x))^(1/2)*(a^2+b^2)^-2*(2*b^4+16*a^4+30*a^2*b^2)*tan(c+d*x)+-4*a^2*b^-2*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-2*tan(c+d*x)^2*(a^2+2*b^2))
@test integrate((a+b*tan(c+d*x))^-5//2*tan(c+d*x)^4, x) == :(im*d^-1*(a+im*b)^-5//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*im*d^-1*(a+-1*im*b)^-5//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+1//3*b^-3*d^-1*(a+b*tan(c+d*x))^(1/2)*(a^2+b^2)^-1*(6*b^2+8*a^2)+-2//3*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-3//2*(a^2+b^2)^-1*tan(c+d*x)^2+4//3*a^3*b^-3*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-2*(2*a^2+5*b^2))
@test integrate((a+b*tan(c+d*x))^-5//2*tan(c+d*x)^3, x) == :(d^-1*(a+im*b)^-5//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+d^-1*(a+-1*im*b)^-5//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-4//3*a^2*b^-2*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-2*(a^2+4*b^2)+-2//3*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-3//2*(a^2+b^2)^-1*tan(c+d*x))
@test integrate((a+b*tan(c+d*x))^-5//2*tan(c+d*x)^2, x) == :(im*d^-1*(a+-1*im*b)^-5//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-1*im*d^-1*(a+im*b)^-5//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+4*a*b*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-2+-2//3*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-3//2*(a^2+b^2)^-1)
@test integrate((a+b*tan(c+d*x))^-5//2*tan(c+d*x), x) == :(-1*d^-1*(a+im*b)^-5//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*d^-1*(a+-1*im*b)^-5//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-2*(-2*b^2+2*a^2)+2*a*d^-1*(a+b*tan(c+d*x))^-3//2*(3*a^2+3*b^2)^-1)
@test integrate((a+b*tan(c+d*x))^-5//2, x) == :(im*d^-1*(a+im*b)^-5//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*im*d^-1*(a+-1*im*b)^-5//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-2*b*d^-1*(a+b*tan(c+d*x))^-3//2*(3*a^2+3*b^2)^-1+-4*a*b*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-2)
@test integrate((a+b*tan(c+d*x))^-5//2*cot(c+d*x), x) == :(d^-1*(a+im*b)^-5//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+d^-1*(a+-1*im*b)^-5//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-2*a^-5//2*d^-1*arctanh(a^-1//2*(a+b*tan(c+d*x))^(1/2))+2//3*a^-1*b^2*d^-1*(a+b*tan(c+d*x))^-3//2*(a^2+b^2)^-1+2*a^-2*b^2*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-2*(b^2+3*a^2))
@test integrate((a+b*tan(c+d*x))^-5//2*cot(c+d*x)^2, x) == :(im*d^-1*(a+-1*im*b)^-5//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-1*im*d^-1*(a+im*b)^-5//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*a^-1*d^-1*(a+b*tan(c+d*x))^-3//2*cot(c+d*x)+5*b*a^-7//2*d^-1*arctanh(a^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*b*a^-3*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-2*(a^4+5*b^4+10*a^2*b^2)+-1//3*b*a^-2*d^-1*(a+b*tan(c+d*x))^-3//2*(a^2+b^2)^-1*(3*a^2+5*b^2))
@test integrate((a+b*tan(c+d*x))^-7//2, x) == :(im*d^-1*(a+im*b)^-7//2*arctanh((a+im*b)^-1//2*(a+b*tan(c+d*x))^(1/2))+-1*im*d^-1*(a+-1*im*b)^-7//2*arctanh((a+b*tan(c+d*x))^(1/2)*(a+-1*im*b)^-1//2)+-2*b*d^-1*(a+b*tan(c+d*x))^-5//2*(5*a^2+5*b^2)^-1+-2*b*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-3*(-1*b^2+3*a^2)+-4//3*a*b*d^-1*(a+b*tan(c+d*x))^-3//2*(a^2+b^2)^-2)
@test integrate(tan(c+d*x)^5//2*(a+b*tan(c+d*x)), x) == :(-2*b*d^-1*tan(c+d*x)^(1/2)+2//3*a*d^-1*tan(c+d*x)^3//2+2//5*b*d^-1*tan(c+d*x)^5//2+(1/2)*2^(1/2)*d^-1*(a+-1b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+-1b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a+b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate(tan(c+d*x)^3//2*(a+b*tan(c+d*x)), x) == :(2*a*d^-1*tan(c+d*x)^(1/2)+2//3*b*d^-1*tan(c+d*x)^3//2+(1/2)*2^(1/2)*d^-1*(a+b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+-1b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a+-1b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate(tan(c+d*x)^(1/2)*(a+b*tan(c+d*x)), x) == :(2*b*d^-1*tan(c+d*x)^(1/2)+(1/2)*2^(1/2)*d^-1*(a+-1b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+-1b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a+b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate(tan(c+d*x)^-1//2*(a+b*tan(c+d*x)), x) == :((1/2)*2^(1/2)*d^-1*(a+b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+-1b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a+-1b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate(tan(c+d*x)^-3//2*(a+b*tan(c+d*x)), x) == :(-2*a*d^-1*tan(c+d*x)^-1//2+(1/2)*2^(1/2)*d^-1*(a+-1b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+-1b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a+b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate(tan(c+d*x)^-5//2*(a+b*tan(c+d*x)), x) == :(-2*b*d^-1*tan(c+d*x)^-1//2+-2//3*a*d^-1*tan(c+d*x)^-3//2+(1/2)*2^(1/2)*d^-1*(a+b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+-1b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a+-1b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate(tan(c+d*x)^-7//2*(a+b*tan(c+d*x)), x) == :(2*a*d^-1*tan(c+d*x)^-1//2+-2//3*b*d^-1*tan(c+d*x)^-3//2+-2//5*a*d^-1*tan(c+d*x)^-5//2+(1/2)*2^(1/2)*d^-1*(a+-1b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+-1b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a+b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^2*tan(c+d*x)^5//2, x) == :(1//3*d^-1*tan(c+d*x)^3//2*(-2*b^2+2*a^2)+2//7*b^2*d^-1*tan(c+d*x)^7//2+(1/2)*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-4*a*b*d^-1*tan(c+d*x)^(1/2)+-1//2*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+4//5*a*b*d^-1*tan(c+d*x)^5//2)
@test integrate((a+b*tan(c+d*x))^2*tan(c+d*x)^3//2, x) == :(d^-1*tan(c+d*x)^(1/2)*(-2*b^2+2*a^2)+2//5*b^2*d^-1*tan(c+d*x)^5//2+(1/2)*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+4//3*a*b*d^-1*tan(c+d*x)^3//2)
@test integrate((a+b*tan(c+d*x))^2*tan(c+d*x)^(1/2), x) == :(2//3*b^2*d^-1*tan(c+d*x)^3//2+(1/2)*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+4*a*b*d^-1*tan(c+d*x)^(1/2)+-1//2*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^2*tan(c+d*x)^-1//2, x) == :(2*b^2*d^-1*tan(c+d*x)^(1/2)+(1/2)*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^2*tan(c+d*x)^-3//2, x) == :(-2*a^2*d^-1*tan(c+d*x)^-1//2+(1/2)*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^2*tan(c+d*x)^-5//2, x) == :(-2//3*a^2*d^-1*tan(c+d*x)^-3//2+(1/2)*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-4*a*b*d^-1*tan(c+d*x)^-1//2+-1//2*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^2*tan(c+d*x)^-7//2, x) == :(d^-1*tan(c+d*x)^-1//2*(-2*b^2+2*a^2)+-2//5*a^2*d^-1*tan(c+d*x)^-5//2+(1/2)*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-4//3*a*b*d^-1*tan(c+d*x)^-3//2+-1//2*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^3*tan(c+d*x)^5//2, x) == :(-2*b*d^-1*tan(c+d*x)^(1/2)*(-1*b^2+3*a^2)+2//3*a*d^-1*tan(c+d*x)^3//2*(a^2+-3*b^2)+2//5*b*d^-1*tan(c+d*x)^5//2*(-1*b^2+3*a^2)+2//9*b^2*d^-1*tan(c+d*x)^7//2*(a+b*tan(c+d*x))+40//63*a*b^2*d^-1*tan(c+d*x)^7//2+(1/2)*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^3*tan(c+d*x)^3//2, x) == :(2*a*d^-1*tan(c+d*x)^(1/2)*(a^2+-3*b^2)+2//3*b*d^-1*tan(c+d*x)^3//2*(-1*b^2+3*a^2)+2//7*b^2*d^-1*tan(c+d*x)^5//2*(a+b*tan(c+d*x))+32//35*a*b^2*d^-1*tan(c+d*x)^5//2+(1/2)*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^3*tan(c+d*x)^(1/2), x) == :(2*b*d^-1*tan(c+d*x)^(1/2)*(-1*b^2+3*a^2)+2//5*b^2*d^-1*tan(c+d*x)^3//2*(a+b*tan(c+d*x))+8//5*a*b^2*d^-1*tan(c+d*x)^3//2+(1/2)*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^3*tan(c+d*x)^-1//2, x) == :(2//3*b^2*d^-1*tan(c+d*x)^(1/2)*(a+b*tan(c+d*x))+16//3*a*b^2*d^-1*tan(c+d*x)^(1/2)+(1/2)*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^3*tan(c+d*x)^-3//2, x) == :(-2*a^2*d^-1*tan(c+d*x)^-1//2*(a+b*tan(c+d*x))+2*b*d^-1*tan(c+d*x)^(1/2)*(a^2+b^2)+(1/2)*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^3*tan(c+d*x)^-5//2, x) == :(-16//3*b*a^2*d^-1*tan(c+d*x)^-1//2+-2//3*a^2*d^-1*tan(c+d*x)^-3//2*(a+b*tan(c+d*x))+(1/2)*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^3*tan(c+d*x)^-7//2, x) == :(2*a*d^-1*tan(c+d*x)^-1//2*(a^2+-3*b^2)+-8//5*b*a^2*d^-1*tan(c+d*x)^-3//2+-2//5*a^2*d^-1*tan(c+d*x)^-5//2*(a+b*tan(c+d*x))+(1/2)*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^3*tan(c+d*x)^-9//2, x) == :(2*b*d^-1*tan(c+d*x)^-1//2*(-1*b^2+3*a^2)+-32//35*b*a^2*d^-1*tan(c+d*x)^-5//2+-2//7*a^2*d^-1*tan(c+d*x)^-7//2*(a+b*tan(c+d*x))+2//3*a*d^-1*tan(c+d*x)^-3//2*(a^2+-3*b^2)+(1/2)*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^3*tan(c+d*x)^-11//2, x) == :(-2*a*d^-1*tan(c+d*x)^-1//2*(a^2+-3*b^2)+-40//63*b*a^2*d^-1*tan(c+d*x)^-7//2+-2//9*a^2*d^-1*tan(c+d*x)^-9//2*(a+b*tan(c+d*x))+2//3*b*d^-1*tan(c+d*x)^-3//2*(-1*b^2+3*a^2)+2//5*a*d^-1*tan(c+d*x)^-5//2*(a^2+-3*b^2)+(1/2)*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate(tan(c+d*x)^-1//2*(a+b*tan(c+d*x)), x) == :((1/2)*2^(1/2)*d^-1*(a+b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+-1b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a+-1b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((-1*tan(c+d*x))^-1//2*(a+b*tan(c+d*x)), x) == :((1/2)*2^(1/2)*d^-1*(a+-1b)*arctan(1+-1*2^(1/2)*(-1*tan(c+d*x))^(1/2))+-1//2*2^(1/2)*d^-1*(a+-1b)*arctan(1+2^(1/2)*(-1*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*d^-1*(a+b)*log(1+-1*tan(c+d*x)+2^(1/2)*(-1*tan(c+d*x))^(1/2))+1//4*2^(1/2)*d^-1*(a+b)*log(1+-1*tan(c+d*x)+-1*2^(1/2)*(-1*tan(c+d*x))^(1/2)))
@test integrate((e*tan(c+d*x))^-1//2*(a+b*tan(c+d*x)), x) == :((1/2)*2^(1/2)*d^-1*e^-1//2*(a+b)*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//2*2^(1/2)*d^-1*e^-1//2*(a+b)*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*d^-1*e^-1//2*(a+-1b)*log(e^(1/2)+e^(1/2)*tan(c+d*x)+-1*2^(1/2)*(e*tan(c+d*x))^(1/2))+1//4*2^(1/2)*d^-1*e^-1//2*(a+-1b)*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x)))
@test integrate((-1*e*tan(c+d*x))^-1//2*(a+b*tan(c+d*x)), x) == :((1/2)*2^(1/2)*d^-1*e^-1//2*(a+-1b)*arctan(1+-1*2^(1/2)*e^-1//2*(-1*e*tan(c+d*x))^(1/2))+-1//2*2^(1/2)*d^-1*e^-1//2*(a+-1b)*arctan(1+2^(1/2)*e^-1//2*(-1*e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*d^-1*e^-1//2*(a+b)*log(e^(1/2)+2^(1/2)*(-1*e*tan(c+d*x))^(1/2)+-1*e^(1/2)*tan(c+d*x))+1//4*2^(1/2)*d^-1*e^-1//2*(a+b)*log(e^(1/2)+-1*2^(1/2)*(-1*e*tan(c+d*x))^(1/2)+-1*e^(1/2)*tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-1*tan(c+d*x)^9//2, x) == :(2//5*b^-1*d^-1*tan(c+d*x)^5//2+b^-3*d^-1*tan(c+d*x)^(1/2)*(-2*b^2+2*a^2)+-2//3*a*b^-2*d^-1*tan(c+d*x)^3//2+(1/2)*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-2*a^9//2*b^-7//2*d^-1*(a^2+b^2)^-1*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-1*tan(c+d*x)^7//2, x) == :(2//3*b^-1*d^-1*tan(c+d*x)^3//2+-2*a*b^-2*d^-1*tan(c+d*x)^(1/2)+(1/2)*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+2*a^7//2*b^-5//2*d^-1*(a^2+b^2)^-1*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-1*tan(c+d*x)^5//2, x) == :(2*b^-1*d^-1*tan(c+d*x)^(1/2)+(1/2)*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-2*a^5//2*b^-3//2*d^-1*(a^2+b^2)^-1*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-1*tan(c+d*x)^3//2, x) == :((1/2)*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+2*a^3//2*b^-1//2*d^-1*(a^2+b^2)^-1*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-1*tan(c+d*x)^(1/2), x) == :((1/2)*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-2*a^(1/2)*b^(1/2)*d^-1*(a^2+b^2)^-1*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-1*tan(c+d*x)^-1//2, x) == :((1/2)*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+2*a^-1//2*b^3//2*d^-1*(a^2+b^2)^-1*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-1*tan(c+d*x)^-3//2, x) == :(-2*a^-1*d^-1*tan(c+d*x)^-1//2+(1/2)*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-2*a^-3//2*b^5//2*d^-1*(a^2+b^2)^-1*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-1*tan(c+d*x)^-5//2, x) == :(-2//3*a^-1*d^-1*tan(c+d*x)^-3//2+2*b*a^-2*d^-1*tan(c+d*x)^-1//2+(1/2)*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+2*a^-5//2*b^7//2*d^-1*(a^2+b^2)^-1*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-1*tan(c+d*x)^-7//2, x) == :(-2//5*a^-1*d^-1*tan(c+d*x)^-5//2+a^-3*d^-1*tan(c+d*x)^-1//2*(-2*b^2+2*a^2)+2//3*b*a^-2*d^-1*tan(c+d*x)^-3//2+(1/2)*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-2*a^-7//2*b^9//2*d^-1*(a^2+b^2)^-1*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-2*tan(c+d*x)^9//2, x) == :((1/2)*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//3*b^-2*d^-1*(a^2+b^2)^-1*tan(c+d*x)^3//2*(2*b^2+5*a^2)+1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+a^7//2*b^-7//2*d^-1*(a^2+b^2)^-2*(5*a^2+9*b^2)*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2))+-1*a*b^-3*d^-1*(a^2+b^2)^-1*tan(c+d*x)^(1/2)*(4*b^2+5*a^2)+-1*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-1*tan(c+d*x)^5//2)
@test integrate((a+b*tan(c+d*x))^-2*tan(c+d*x)^7//2, x) == :(b^-2*d^-1*(a^2+b^2)^-1*tan(c+d*x)^(1/2)*(2*b^2+3*a^2)+(1/2)*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+-1*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-1*tan(c+d*x)^3//2+-1*a^5//2*b^-5//2*d^-1*(a^2+b^2)^-2*(3*a^2+7*b^2)*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^-2*tan(c+d*x)^5//2, x) == :((1/2)*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+a^3//2*b^-3//2*d^-1*(a^2+b^2)^-2*(a^2+5*b^2)*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2))+-1*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-1*tan(c+d*x)^(1/2))
@test integrate((a+b*tan(c+d*x))^-2*tan(c+d*x)^3//2, x) == :(a*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-1*tan(c+d*x)^(1/2)+(1/2)*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+a^(1/2)*b^-1//2*d^-1*(a^2+b^2)^-2*(a^2+-3*b^2)*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^-2*tan(c+d*x)^(1/2), x) == :((1/2)*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1*b*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-1*tan(c+d*x)^(1/2)+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+-1*a^-1//2*b^(1/2)*d^-1*(a^2+b^2)^-2*(-1*b^2+3*a^2)*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^-2*tan(c+d*x)^-1//2, x) == :((1/2)*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+a^-1*b^2*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-1*tan(c+d*x)^(1/2)+a^-3//2*b^3//2*d^-1*(a^2+b^2)^-2*(b^2+5*a^2)*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^-2*tan(c+d*x)^-3//2, x) == :((1/2)*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1*a^-2*d^-1*(a^2+b^2)^-1*tan(c+d*x)^-1//2*(2*a^2+3*b^2)+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+a^-1*b^2*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-1*tan(c+d*x)^-1//2+-1*a^-5//2*b^5//2*d^-1*(a^2+b^2)^-2*(3*b^2+7*a^2)*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^-2*tan(c+d*x)^-5//2, x) == :((1/2)*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//3*a^-2*d^-1*(a^2+b^2)^-1*tan(c+d*x)^-3//2*(2*a^2+5*b^2)+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+b*a^-3*d^-1*(a^2+b^2)^-1*tan(c+d*x)^-1//2*(4*a^2+5*b^2)+a^-1*b^2*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-1*tan(c+d*x)^-3//2+a^-7//2*b^7//2*d^-1*(a^2+b^2)^-2*(5*b^2+9*a^2)*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^-3*tan(c+d*x)^11//2, x) == :(1//12*b^-3*d^-1*(a^2+b^2)^-2*tan(c+d*x)^3//2*(8*b^4+35*a^4+67*a^2*b^2)+(1/2)*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//2*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-2*(a^2+b^2)^-1*tan(c+d*x)^7//2+-1//4*a*b^-4*d^-1*(a^2+b^2)^-2*tan(c+d*x)^(1/2)*(24*b^4+35*a^4+67*a^2*b^2)+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*a^7//2*b^-9//2*d^-1*(a^2+b^2)^-3*(35*a^4+99*b^4+102*a^2*b^2)*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2))+-1//4*a^2*b^-2*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-2*tan(c+d*x)^5//2*(7*a^2+15*b^2))
@test integrate((a+b*tan(c+d*x))^-3*tan(c+d*x)^9//2, x) == :(1//4*b^-3*d^-1*(a^2+b^2)^-2*tan(c+d*x)^(1/2)*(8*b^4+15*a^4+31*a^2*b^2)+(1/2)*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-2*(a^2+b^2)^-1*tan(c+d*x)^5//2+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+-1//4*a^5//2*b^-7//2*d^-1*(a^2+b^2)^-3*(15*a^4+63*b^4+46*a^2*b^2)*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+-1//4*a^2*b^-2*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-2*tan(c+d*x)^3//2*(5*a^2+13*b^2))
@test integrate((a+b*tan(c+d*x))^-3*tan(c+d*x)^7//2, x) == :((1/2)*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-2*(a^2+b^2)^-1*tan(c+d*x)^3//2+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*a^3//2*b^-5//2*d^-1*(a^2+b^2)^-3*(3*a^4+35*b^4+6*a^2*b^2)*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2))+-1//4*a^2*b^-2*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-2*tan(c+d*x)^(1/2)*(3*a^2+11*b^2))
@test integrate((a+b*tan(c+d*x))^-3*tan(c+d*x)^5//2, x) == :((1/2)*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//2*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-2*(a^2+b^2)^-1*tan(c+d*x)^(1/2)+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*a^(1/2)*b^-3//2*d^-1*(a^2+b^2)^-3*(a^4+-15*b^4+18*a^2*b^2)*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2))+1//4*a*b^-1*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-2*tan(c+d*x)^(1/2)*(a^2+9*b^2))
@test integrate((a+b*tan(c+d*x))^-3*tan(c+d*x)^3//2, x) == :(a*d^-1*(a+b*tan(c+d*x))^-2*(2*a^2+2*b^2)^-1*tan(c+d*x)^(1/2)+1//4*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-2*tan(c+d*x)^(1/2)*(-5*b^2+3*a^2)+(1/2)*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*a^-1//2*b^-1//2*d^-1*(a^2+b^2)^-3*(3*a^4+3*b^4+-26*a^2*b^2)*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^-3*tan(c+d*x)^(1/2), x) == :(-1*b*d^-1*(a+b*tan(c+d*x))^-2*(2*a^2+2*b^2)^-1*tan(c+d*x)^(1/2)+(1/2)*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+-1//4*a^-3//2*b^(1/2)*d^-1*(a^2+b^2)^-3*(-1*b^4+15*a^4+-18*a^2*b^2)*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+-1//4*b*a^-1*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-2*tan(c+d*x)^(1/2)*(-1*b^2+7*a^2))
@test integrate((a+b*tan(c+d*x))^-3*tan(c+d*x)^-1//2, x) == :((1/2)*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+(1/2)*a^-1*b^2*d^-1*(a+b*tan(c+d*x))^-2*(a^2+b^2)^-1*tan(c+d*x)^(1/2)+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*a^-5//2*b^3//2*d^-1*(a^2+b^2)^-3*(3*b^4+35*a^4+6*a^2*b^2)*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2))+1//4*a^-2*b^2*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-2*tan(c+d*x)^(1/2)*(3*b^2+11*a^2))
@test integrate((a+b*tan(c+d*x))^-3*tan(c+d*x)^-3//2, x) == :(-1//4*a^-3*d^-1*(a^2+b^2)^-2*tan(c+d*x)^-1//2*(8*a^4+15*b^4+31*a^2*b^2)+(1/2)*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+(1/2)*a^-1*b^2*d^-1*(a+b*tan(c+d*x))^-2*(a^2+b^2)^-1*tan(c+d*x)^-1//2+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+-1//4*a^-7//2*b^5//2*d^-1*(a^2+b^2)^-3*(15*b^4+63*a^4+46*a^2*b^2)*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*a^-2*b^2*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-2*tan(c+d*x)^-1//2*(5*b^2+13*a^2))
@test integrate((a+b*tan(c+d*x))^-3*tan(c+d*x)^-5//2, x) == :(-1//12*a^-3*d^-1*(a^2+b^2)^-2*tan(c+d*x)^-3//2*(8*a^4+35*b^4+67*a^2*b^2)+(1/2)*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+(1/2)*a^-1*b^2*d^-1*(a+b*tan(c+d*x))^-2*(a^2+b^2)^-1*tan(c+d*x)^-3//2+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*b*a^-4*d^-1*(a^2+b^2)^-2*tan(c+d*x)^-1//2*(24*a^4+35*b^4+67*a^2*b^2)+1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*a^-9//2*b^7//2*d^-1*(a^2+b^2)^-3*(35*b^4+99*a^4+102*a^2*b^2)*arctan(a^-1//2*b^(1/2)*tan(c+d*x)^(1/2))+1//4*a^-2*b^2*d^-1*(a+b*tan(c+d*x))^-1*(a^2+b^2)^-2*tan(c+d*x)^-3//2*(7*b^2+15*a^2))
@test integrate((a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^5//2, x) == :(d^-1*(b+im*a)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(-1b+im*a)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+(1/2)*b^-1*d^-1*(a+b*tan(c+d*x))^3//2*tan(c+d*x)^(1/2)+-1//4*b^-3//2*d^-1*(a^2+8*b^2)*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+-1//4*a*b^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^(1/2))
@test integrate((a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^3//2, x) == :(d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^(1/2)+im*d^-1*(b+im*a)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+im*d^-1*(-1b+im*a)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+a*b^-1//2*d^-1*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^(1/2), x) == :(d^-1*(-1b+im*a)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(b+im*a)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+2*b^(1/2)*d^-1*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2, x) == :(-1*im*d^-1*(b+im*a)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(-1b+im*a)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-3//2, x) == :(d^-1*(b+im*a)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(-1b+im*a)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-2*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2)
@test integrate((a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-5//2, x) == :(-2//3*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-3//2+im*d^-1*(b+im*a)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+im*d^-1*(-1b+im*a)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-2//3*b*a^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2)
@test integrate((a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-7//2, x) == :(d^-1*(-1b+im*a)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(b+im*a)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-2//5*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-5//2+-2//15*b*a^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-3//2+1//15*a^-2*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2*(4*b^2+30*a^2))
@test integrate((a+b*tan(c+d*x))^3//2*tan(c+d*x)^5//2, x) == :(im*d^-1*(-1b+im*a)^3//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(b+im*a)^3//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+1//3*b^-1*d^-1*(a+b*tan(c+d*x))^5//2*tan(c+d*x)^(1/2)+-1//8*a*b^-3//2*d^-1*(a^2+24*b^2)*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+-1//8*b^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^(1/2)*(a^2+8*b^2)+-1//12*a*b^-1*d^-1*(a+b*tan(c+d*x))^3//2*tan(c+d*x)^(1/2))
@test integrate((a+b*tan(c+d*x))^3//2*tan(c+d*x)^3//2, x) == :(d^-1*(b+im*a)^3//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+d^-1*(-1b+im*a)^3//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+(1/2)*d^-1*(a+b*tan(c+d*x))^3//2*tan(c+d*x)^(1/2)+1//4*b^-1//2*d^-1*(-8*b^2+3*a^2)*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+3//4*a*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^(1/2))
@test integrate((a+b*tan(c+d*x))^3//2*tan(c+d*x)^(1/2), x) == :(im*d^-1*(b+im*a)^3//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+b*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^(1/2)+-1*im*d^-1*(-1b+im*a)^3//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+3*a*b^(1/2)*d^-1*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^3//2*tan(c+d*x)^-1//2, x) == :(-1*d^-1*(b+im*a)^3//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(-1b+im*a)^3//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+2*b^3//2*d^-1*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^3//2*tan(c+d*x)^-3//2, x) == :(im*d^-1*(-1b+im*a)^3//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(b+im*a)^3//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-2*a*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2)
@test integrate((a+b*tan(c+d*x))^3//2*tan(c+d*x)^-5//2, x) == :(d^-1*(b+im*a)^3//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+d^-1*(-1b+im*a)^3//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-8//3*b*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2+-2//3*a*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-3//2)
@test integrate((a+b*tan(c+d*x))^3//2*tan(c+d*x)^-7//2, x) == :(im*d^-1*(b+im*a)^3//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(-1b+im*a)^3//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-4//5*b*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-3//2+-2//5*a*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-5//2+1//5*a^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2*(-2*b^2+10*a^2))
@test integrate((a+b*tan(c+d*x))^3//2*tan(c+d*x)^-9//2, x) == :(-1*d^-1*(b+im*a)^3//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(-1b+im*a)^3//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-16//35*b*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-5//2+-2//7*a*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-7//2+1//105*a^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-3//2*(-6*b^2+70*a^2)+4//105*b*a^-2*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2*(3*b^2+70*a^2))
@test integrate((a+b*tan(c+d*x))^5//2*tan(c+d*x)^5//2, x) == :(d^-1*(-1b+im*a)^5//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(b+im*a)^5//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1//64*b^-3//2*d^-1*(-128*b^4+5*a^4+240*a^2*b^2)*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+1//4*b^-1*d^-1*(a+b*tan(c+d*x))^7//2*tan(c+d*x)^(1/2)+-1//24*a*b^-1*d^-1*(a+b*tan(c+d*x))^5//2*tan(c+d*x)^(1/2)+-1//96*b^-1*d^-1*(a+b*tan(c+d*x))^3//2*tan(c+d*x)^(1/2)*(5*a^2+48*b^2)+-1//64*a*b^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^(1/2)*(5*a^2+112*b^2))
@test integrate((a+b*tan(c+d*x))^5//2*tan(c+d*x)^3//2, x) == :(-1*im*d^-1*(b+im*a)^5//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(-1b+im*a)^5//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+1//3*b^2*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^5//2+1//8*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^(1/2)*(-8*b^2+11*a^2)+5//8*a*b^-1//2*d^-1*(a^2+-8*b^2)*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+13//12*a*b*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^3//2)
@test integrate((a+b*tan(c+d*x))^5//2*tan(c+d*x)^(1/2), x) == :(d^-1*(b+im*a)^5//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(-1b+im*a)^5//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+(1/2)*b^2*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^3//2+1//4*b^(1/2)*d^-1*(-8*b^2+15*a^2)*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+9//4*a*b*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^(1/2))
@test integrate((a+b*tan(c+d*x))^5//2*tan(c+d*x)^-1//2, x) == :(im*d^-1*(b+im*a)^5//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+im*d^-1*(-1b+im*a)^5//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+b^2*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^(1/2)+5*a*b^3//2*d^-1*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^5//2*tan(c+d*x)^-3//2, x) == :(d^-1*(-1b+im*a)^5//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(b+im*a)^5//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+2*b^5//2*d^-1*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+-2*a^2*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2)
@test integrate((a+b*tan(c+d*x))^5//2*tan(c+d*x)^-5//2, x) == :(-1*im*d^-1*(b+im*a)^5//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(-1b+im*a)^5//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-2//3*a^2*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-3//2+-14//3*a*b*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2)
@test integrate((a+b*tan(c+d*x))^5//2*tan(c+d*x)^-7//2, x) == :(d^-1*(b+im*a)^5//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(-1b+im*a)^5//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-2//5*a^2*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-5//2+1//15*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2*(-46*b^2+30*a^2)+-22//15*a*b*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-3//2)
@test integrate((a+b*tan(c+d*x))^5//2*tan(c+d*x)^-9//2, x) == :(im*d^-1*(b+im*a)^5//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+im*d^-1*(-1b+im*a)^5//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-2//7*a^2*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-7//2+1//21*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-3//2*(-18*b^2+14*a^2)+-6//7*a*b*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-5//2+2//21*b*a^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2*(-3*b^2+49*a^2))
@test integrate((a+b*tan(c+d*x))^5//2*tan(c+d*x)^-11//2, x) == :(d^-1*(-1b+im*a)^5//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(b+im*a)^5//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-2//9*a^2*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-9//2+1//105*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-5//2*(-50*b^2+42*a^2)+-38//63*a*b*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-7//2+-1//315*a^-2*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2*(-20*b^4+630*a^4+-966*a^2*b^2)+2//315*b*a^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-3//2*(-5*b^2+231*a^2))
@test integrate((a+b*tan(c+d*x))^-1//2*tan(c+d*x)^7//2, x) == :(d^-1*(b+im*a)^-1//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+d^-1*(-1b+im*a)^-1//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+(1/2)*b^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^3//2+1//4*b^-5//2*d^-1*(-8*b^2+3*a^2)*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+-3//4*a*b^-2*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^(1/2))
@test integrate((a+b*tan(c+d*x))^-1//2*tan(c+d*x)^5//2, x) == :(im*d^-1*(b+im*a)^-1//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+b^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^(1/2)+-1*im*d^-1*(-1b+im*a)^-1//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*a*b^-3//2*d^-1*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^-1//2*tan(c+d*x)^3//2, x) == :(-1*d^-1*(b+im*a)^-1//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(-1b+im*a)^-1//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+2*b^-1//2*d^-1*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2), x) == :(im*d^-1*(-1b+im*a)^-1//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(b+im*a)^-1//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^-1//2*tan(c+d*x)^-1//2, x) == :(d^-1*(b+im*a)^-1//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+d^-1*(-1b+im*a)^-1//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^-1//2*tan(c+d*x)^-3//2, x) == :(im*d^-1*(b+im*a)^-1//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(-1b+im*a)^-1//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-2*a^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2)
@test integrate((a+b*tan(c+d*x))^-1//2*tan(c+d*x)^-5//2, x) == :(-1*d^-1*(b+im*a)^-1//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(-1b+im*a)^-1//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-2//3*a^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-3//2+4//3*b*a^-2*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2)
@test integrate((a+b*tan(c+d*x))^-1//2*tan(c+d*x)^-7//2, x) == :(im*d^-1*(-1b+im*a)^-1//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(b+im*a)^-1//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-2//5*a^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-5//2+1//15*a^-3*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-1//2*(-16*b^2+30*a^2)+8//15*b*a^-2*d^-1*(a+b*tan(c+d*x))^(1/2)*tan(c+d*x)^-3//2)
@test integrate((a+b*tan(c+d*x))^-3//2*tan(c+d*x)^7//2, x) == :(im*d^-1*(b+im*a)^-3//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+im*d^-1*(-1b+im*a)^-3//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-3*a*b^-5//2*d^-1*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+b^-2*d^-1*(a+b*tan(c+d*x))^(1/2)*(a^2+b^2)^-1*tan(c+d*x)^(1/2)*(b^2+3*a^2)+-2*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-1*tan(c+d*x)^3//2)
@test integrate((a+b*tan(c+d*x))^-3//2*tan(c+d*x)^5//2, x) == :(d^-1*(-1b+im*a)^-3//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(b+im*a)^-3//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+2*b^-3//2*d^-1*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+-2*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-1*tan(c+d*x)^(1/2))
@test integrate((a+b*tan(c+d*x))^-3//2*tan(c+d*x)^3//2, x) == :(-1*im*d^-1*(b+im*a)^-3//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(-1b+im*a)^-3//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+2*a*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-1*tan(c+d*x)^(1/2))
@test integrate((a+b*tan(c+d*x))^-3//2*tan(c+d*x)^(1/2), x) == :(d^-1*(b+im*a)^-3//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(-1b+im*a)^-3//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-2*b*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-1*tan(c+d*x)^(1/2))
@test integrate((a+b*tan(c+d*x))^-3//2*tan(c+d*x)^-1//2, x) == :(im*d^-1*(b+im*a)^-3//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+im*d^-1*(-1b+im*a)^-3//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+2*a^-1*b^2*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-1*tan(c+d*x)^(1/2))
@test integrate((a+b*tan(c+d*x))^-3//2*tan(c+d*x)^-3//2, x) == :(d^-1*(-1b+im*a)^-3//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(b+im*a)^-3//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-2*a^-1*d^-1*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^-1//2+-2*b*a^-2*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-1*tan(c+d*x)^(1/2)*(a^2+2*b^2))
@test integrate((a+b*tan(c+d*x))^-3//2*tan(c+d*x)^-5//2, x) == :(-1*im*d^-1*(b+im*a)^-3//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(-1b+im*a)^-3//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-2//3*a^-1*d^-1*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^-3//2+8//3*b*a^-2*d^-1*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^-1//2+2//3*a^-3*b^2*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-1*tan(c+d*x)^(1/2)*(5*a^2+8*b^2))
@test integrate((a+b*tan(c+d*x))^-5//2*tan(c+d*x)^9//2, x) == :(im*d^-1*(b+im*a)^-5//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(-1b+im*a)^-5//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-5*a*b^-7//2*d^-1*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+b^-3*d^-1*(a+b*tan(c+d*x))^(1/2)*(a^2+b^2)^-2*tan(c+d*x)^(1/2)*(b^4+5*a^4+10*a^2*b^2)+-2//3*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-3//2*(a^2+b^2)^-1*tan(c+d*x)^5//2+-2//3*a^2*b^-2*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-2*tan(c+d*x)^3//2*(5*a^2+11*b^2))
@test integrate((a+b*tan(c+d*x))^-5//2*tan(c+d*x)^7//2, x) == :(-1*d^-1*(b+im*a)^-5//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(-1b+im*a)^-5//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+2*b^-5//2*d^-1*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+-2//3*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-3//2*(a^2+b^2)^-1*tan(c+d*x)^3//2+-2*a^2*b^-2*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-2*tan(c+d*x)^(1/2)*(a^2+3*b^2))
@test integrate((a+b*tan(c+d*x))^-5//2*tan(c+d*x)^5//2, x) == :(im*d^-1*(-1b+im*a)^-5//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(b+im*a)^-5//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-2//3*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-3//2*(a^2+b^2)^-1*tan(c+d*x)^(1/2)+2//3*a*b^-1*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-2*tan(c+d*x)^(1/2)*(a^2+7*b^2))
@test integrate((a+b*tan(c+d*x))^-5//2*tan(c+d*x)^3//2, x) == :(d^-1*(b+im*a)^-5//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+d^-1*(-1b+im*a)^-5//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+2*a*d^-1*(a+b*tan(c+d*x))^-3//2*(3*a^2+3*b^2)^-1*tan(c+d*x)^(1/2)+1//3*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-2*tan(c+d*x)^(1/2)*(-8*b^2+4*a^2))
@test integrate((a+b*tan(c+d*x))^-5//2*tan(c+d*x)^(1/2), x) == :(im*d^-1*(b+im*a)^-5//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(-1b+im*a)^-5//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-2*b*d^-1*(a+b*tan(c+d*x))^-3//2*(3*a^2+3*b^2)^-1*tan(c+d*x)^(1/2)+-2//3*b*a^-1*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-2*tan(c+d*x)^(1/2)*(-1*b^2+5*a^2))
@test integrate((a+b*tan(c+d*x))^-5//2*tan(c+d*x)^-1//2, x) == :(-1*d^-1*(b+im*a)^-5//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(-1b+im*a)^-5//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+2//3*a^-1*b^2*d^-1*(a+b*tan(c+d*x))^-3//2*(a^2+b^2)^-1*tan(c+d*x)^(1/2)+4//3*a^-2*b^2*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-2*tan(c+d*x)^(1/2)*(b^2+4*a^2))
@test integrate((a+b*tan(c+d*x))^-5//2*tan(c+d*x)^-3//2, x) == :(im*d^-1*(-1b+im*a)^-5//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(b+im*a)^-5//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-2*a^-1*d^-1*(a+b*tan(c+d*x))^-3//2*tan(c+d*x)^-1//2+-2//3*b*a^-3*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-2*tan(c+d*x)^(1/2)*(3*a^4+8*b^4+17*a^2*b^2)+-2//3*b*a^-2*d^-1*(a+b*tan(c+d*x))^-3//2*(a^2+b^2)^-1*tan(c+d*x)^(1/2)*(3*a^2+4*b^2))
@test integrate((a+b*tan(c+d*x))^-5//2*tan(c+d*x)^-5//2, x) == :(d^-1*(b+im*a)^-5//2*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+d^-1*(-1b+im*a)^-5//2*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-2//3*a^-1*d^-1*(a+b*tan(c+d*x))^-3//2*tan(c+d*x)^-3//2+4*b*a^-2*d^-1*(a+b*tan(c+d*x))^-3//2*tan(c+d*x)^-1//2+2//3*a^-3*b^2*d^-1*(a+b*tan(c+d*x))^-3//2*(a^2+b^2)^-1*tan(c+d*x)^(1/2)*(7*a^2+8*b^2)+4//3*a^-4*b^2*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-2*tan(c+d*x)^(1/2)*(4*a^4+8*b^4+15*a^2*b^2))
@test integrate((2+3*tan(c+d*x))^-1//2*tan(c+d*x)^-1//2, x) == :(d^-1*(3+-2im)^-1//2*arctanh((2+3*tan(c+d*x))^-1//2*(3+-2im)^(1/2)*tan(c+d*x)^(1/2))+d^-1*(3+2im)^-1//2*arctanh((2+3*tan(c+d*x))^-1//2*(3+2im)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((-2+3*tan(c+d*x))^-1//2*tan(c+d*x)^-1//2, x) == :(d^-1*(3+-2im)^-1//2*arctanh((-2+3*tan(c+d*x))^-1//2*(3+-2im)^(1/2)*tan(c+d*x)^(1/2))+d^-1*(3+2im)^-1//2*arctanh((-2+3*tan(c+d*x))^-1//2*(3+2im)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((2+-3*tan(c+d*x))^-1//2*tan(c+d*x)^-1//2, x) == :(d^-1*(3+-2im)^-1//2*arctan((2+-3*tan(c+d*x))^-1//2*(3+-2im)^(1/2)*tan(c+d*x)^(1/2))+d^-1*(3+2im)^-1//2*arctan((2+-3*tan(c+d*x))^-1//2*(3+2im)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((-2+-3*tan(c+d*x))^-1//2*tan(c+d*x)^-1//2, x) == :(d^-1*(3+-2im)^-1//2*arctan((-2+-3*tan(c+d*x))^-1//2*(3+-2im)^(1/2)*tan(c+d*x)^(1/2))+d^-1*(3+2im)^-1//2*arctan((-2+-3*tan(c+d*x))^-1//2*(3+2im)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((3+2*tan(c+d*x))^-1//2*tan(c+d*x)^-1//2, x) == :(d^-1*(2+-3im)^-1//2*arctanh((2+-3im)^(1/2)*(3+2*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+d^-1*(2+3im)^-1//2*arctanh((2+3im)^(1/2)*(3+2*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((3+-2*tan(c+d*x))^-1//2*tan(c+d*x)^-1//2, x) == :(d^-1*(2+-3im)^-1//2*arctan((2+-3im)^(1/2)*(3+-2*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+d^-1*(2+3im)^-1//2*arctan((2+3im)^(1/2)*(3+-2*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((-3+2*tan(c+d*x))^-1//2*tan(c+d*x)^-1//2, x) == :(d^-1*(2+-3im)^-1//2*arctanh((-3+2*tan(c+d*x))^-1//2*(2+-3im)^(1/2)*tan(c+d*x)^(1/2))+d^-1*(2+3im)^-1//2*arctanh((-3+2*tan(c+d*x))^-1//2*(2+3im)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((-3+-2*tan(c+d*x))^-1//2*tan(c+d*x)^-1//2, x) == :(d^-1*(2+-3im)^-1//2*arctan((-3+-2*tan(c+d*x))^-1//2*(2+-3im)^(1/2)*tan(c+d*x)^(1/2))+d^-1*(2+3im)^-1//2*arctan((-3+-2*tan(c+d*x))^-1//2*(2+3im)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((2+3*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2), x) == :(im*d^-1*(3+-2im)^-1//2*arctanh((2+3*tan(c+d*x))^-1//2*(3+-2im)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(3+2im)^-1//2*arctanh((2+3*tan(c+d*x))^-1//2*(3+2im)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((-2+3*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2), x) == :(im*d^-1*(3+2im)^-1//2*arctanh((-2+3*tan(c+d*x))^-1//2*(3+2im)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(3+-2im)^-1//2*arctanh((-2+3*tan(c+d*x))^-1//2*(3+-2im)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((2+-3*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2), x) == :(im*d^-1*(3+2im)^-1//2*arctan((2+-3*tan(c+d*x))^-1//2*(3+2im)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(3+-2im)^-1//2*arctan((2+-3*tan(c+d*x))^-1//2*(3+-2im)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((-2+-3*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2), x) == :(im*d^-1*(3+-2im)^-1//2*arctan((-2+-3*tan(c+d*x))^-1//2*(3+-2im)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(3+2im)^-1//2*arctan((-2+-3*tan(c+d*x))^-1//2*(3+2im)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((3+2*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2), x) == :(im*d^-1*(2+-3im)^-1//2*arctanh((2+-3im)^(1/2)*(3+2*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+-1*im*d^-1*(2+3im)^-1//2*arctanh((2+3im)^(1/2)*(3+2*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((3+-2*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2), x) == :(im*d^-1*(2+3im)^-1//2*arctan((2+3im)^(1/2)*(3+-2*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+-1*im*d^-1*(2+-3im)^-1//2*arctan((2+-3im)^(1/2)*(3+-2*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((-3+2*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2), x) == :(im*d^-1*(2+3im)^-1//2*arctanh((-3+2*tan(c+d*x))^-1//2*(2+3im)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(2+-3im)^-1//2*arctanh((-3+2*tan(c+d*x))^-1//2*(2+-3im)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((-3+-2*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2), x) == :(im*d^-1*(2+-3im)^-1//2*arctan((-3+-2*tan(c+d*x))^-1//2*(2+-3im)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(2+3im)^-1//2*arctan((-3+-2*tan(c+d*x))^-1//2*(2+3im)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^-1*tan(c+d*x)^5//3, x) == :(a*d^-1*(4*a^2+4*b^2)^-1*log(1+tan(c+d*x)^4//3+-1*tan(c+d*x)^2//3)+b*d^-1*(a^2+b^2)^-1*arctan(tan(c+d*x)^1//3)+b*d^-1*(2*a^2+2*b^2)^-1*arctan(3^(1/2)+2*tan(c+d*x)^1//3)+-1*a*d^-1*(2*a^2+2*b^2)^-1*log(1+tan(c+d*x)^2//3)+-1*b*d^-1*(2*a^2+2*b^2)^-1*arctan(3^(1/2)+-2*tan(c+d*x)^1//3)+a*3^(1/2)*d^-1*(2*a^2+2*b^2)^-1*arctan(1//3*3^(1/2)*(1+-2*tan(c+d*x)^2//3))+b*3^(1/2)*d^-1*(4*a^2+4*b^2)^-1*log(1+tan(c+d*x)^2//3+-1*3^(1/2)*tan(c+d*x)^1//3)+(1/2)*a^5//3*b^-2//3*d^-1*(a^2+b^2)^-1*log(a+b*tan(c+d*x))+-1*b*3^(1/2)*d^-1*(4*a^2+4*b^2)^-1*log(1+tan(c+d*x)^2//3+3^(1/2)*tan(c+d*x)^1//3)+-3//2*a^5//3*b^-2//3*d^-1*(a^2+b^2)^-1*log(a^1//3+b^1//3*tan(c+d*x)^1//3)+-1*3^(1/2)*a^5//3*b^-2//3*d^-1*(a^2+b^2)^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*tan(c+d*x)^1//3)))
@test integrate((a+b*tan(c+d*x))^-1*tan(c+d*x)^1//3, x) == :(a*d^-1*(4*a^2+4*b^2)^-1*log(1+tan(c+d*x)^4//3+-1*tan(c+d*x)^2//3)+b*d^-1*(a^2+b^2)^-1*arctan(tan(c+d*x)^1//3)+b*d^-1*(2*a^2+2*b^2)^-1*arctan(3^(1/2)+2*tan(c+d*x)^1//3)+-1*a*d^-1*(2*a^2+2*b^2)^-1*log(1+tan(c+d*x)^2//3)+-1*b*d^-1*(2*a^2+2*b^2)^-1*arctan(3^(1/2)+-2*tan(c+d*x)^1//3)+b*3^(1/2)*d^-1*(4*a^2+4*b^2)^-1*log(1+tan(c+d*x)^2//3+3^(1/2)*tan(c+d*x)^1//3)+a^1//3*b^2//3*d^-1*(2*a^2+2*b^2)^-1*log(a+b*tan(c+d*x))+-1*a*3^(1/2)*d^-1*(2*a^2+2*b^2)^-1*arctan(1//3*3^(1/2)*(1+-2*tan(c+d*x)^2//3))+-1*b*3^(1/2)*d^-1*(4*a^2+4*b^2)^-1*log(1+tan(c+d*x)^2//3+-1*3^(1/2)*tan(c+d*x)^1//3)+-3*a^1//3*b^2//3*d^-1*(2*a^2+2*b^2)^-1*log(a^1//3+b^1//3*tan(c+d*x)^1//3)+3^(1/2)*a^1//3*b^2//3*d^-1*(a^2+b^2)^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*tan(c+d*x)^1//3)))
@test integrate((a+b*tan(c+d*x))^-1*tan(c+d*x)^-1//3, x) == :(a*d^-1*(2*a^2+2*b^2)^-1*log(1+tan(c+d*x)^2//3)+b*d^-1*(2*a^2+2*b^2)^-1*arctan(3^(1/2)+-2*tan(c+d*x)^1//3)+-1*a*d^-1*(4*a^2+4*b^2)^-1*log(1+tan(c+d*x)^4//3+-1*tan(c+d*x)^2//3)+-1*b*d^-1*(a^2+b^2)^-1*arctan(tan(c+d*x)^1//3)+-1*b*d^-1*(2*a^2+2*b^2)^-1*arctan(3^(1/2)+2*tan(c+d*x)^1//3)+b*3^(1/2)*d^-1*(4*a^2+4*b^2)^-1*log(1+tan(c+d*x)^2//3+3^(1/2)*tan(c+d*x)^1//3)+(1/2)*a^-1//3*b^4//3*d^-1*(a^2+b^2)^-1*log(a+b*tan(c+d*x))+-1*a*3^(1/2)*d^-1*(2*a^2+2*b^2)^-1*arctan(1//3*3^(1/2)*(1+-2*tan(c+d*x)^2//3))+-1*b*3^(1/2)*d^-1*(4*a^2+4*b^2)^-1*log(1+tan(c+d*x)^2//3+-1*3^(1/2)*tan(c+d*x)^1//3)+-3//2*a^-1//3*b^4//3*d^-1*(a^2+b^2)^-1*log(a^1//3+b^1//3*tan(c+d*x)^1//3)+-1*3^(1/2)*a^-1//3*b^4//3*d^-1*(a^2+b^2)^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*tan(c+d*x)^1//3)))
@test integrate((a+b*tan(c+d*x))^-1*tan(c+d*x)^-5//3, x) == :(a*d^-1*(2*a^2+2*b^2)^-1*log(1+tan(c+d*x)^2//3)+b*d^-1*(2*a^2+2*b^2)^-1*arctan(3^(1/2)+-2*tan(c+d*x)^1//3)+-1*a*d^-1*(4*a^2+4*b^2)^-1*log(1+tan(c+d*x)^4//3+-1*tan(c+d*x)^2//3)+-1*b*d^-1*(a^2+b^2)^-1*arctan(tan(c+d*x)^1//3)+-1*b*d^-1*(2*a^2+2*b^2)^-1*arctan(3^(1/2)+2*tan(c+d*x)^1//3)+-3*a*d^-1*(2*a^2+2*b^2)^-1*tan(c+d*x)^-2//3+a*3^(1/2)*d^-1*(2*a^2+2*b^2)^-1*arctan(1//3*3^(1/2)*(1+-2*tan(c+d*x)^2//3))+b*3^(1/2)*d^-1*(4*a^2+4*b^2)^-1*log(1+tan(c+d*x)^2//3+-1*3^(1/2)*tan(c+d*x)^1//3)+(1/2)*a^-5//3*b^8//3*d^-1*(a^2+b^2)^-1*log(a+b*tan(c+d*x))+-1*b*3^(1/2)*d^-1*(4*a^2+4*b^2)^-1*log(1+tan(c+d*x)^2//3+3^(1/2)*tan(c+d*x)^1//3)+-3//2*a^-1*b^2*d^-1*(a^2+b^2)^-1*tan(c+d*x)^-2//3+-3//2*a^-5//3*b^8//3*d^-1*(a^2+b^2)^-1*log(a^1//3+b^1//3*tan(c+d*x)^1//3)+3^(1/2)*a^-5//3*b^8//3*d^-1*(a^2+b^2)^-1*arctan(1//3*3^(1/2)*a^-1//3*(a^1//3+-2*b^1//3*tan(c+d*x)^1//3)))
@test integrate((c+d*tan(e+f*x))^1//3*tan(e+f*x)^4, x) == :(-1//4*x*(c+(-1*d^2)^(1/2))^1//3+-1//4*x*(c+-1*(-1*d^2)^(1/2))^1//3+1//140*d^-3*f^-1*(c+d*tan(e+f*x))^4//3*(-105*d^2+27*c^2)+3//10*d^-1*f^-1*(c+d*tan(e+f*x))^4//3*tan(e+f*x)^2+-9//35*c*d^-2*f^-1*(c+d*tan(e+f*x))^4//3*tan(e+f*x)+-3//4*d^-1*f^-1*(-1*d^2)^(1/2)*(c+(-1*d^2)^(1/2))^1//3*log((c+(-1*d^2)^(1/2))^1//3+-1*(c+d*tan(e+f*x))^1//3)+-1//4*d^-1*f^-1*(-1*d^2)^(1/2)*(c+(-1*d^2)^(1/2))^1//3*log(cos(e+f*x))+1//4*d^-1*f^-1*(-1*d^2)^(1/2)*(c+-1*(-1*d^2)^(1/2))^1//3*log(cos(e+f*x))+3//4*d^-1*f^-1*(-1*d^2)^(1/2)*(c+-1*(-1*d^2)^(1/2))^1//3*log((c+-1*(-1*d^2)^(1/2))^1//3+-1*(c+d*tan(e+f*x))^1//3)+(1/2)*3^(1/2)*d^-1*f^-1*(-1*d^2)^(1/2)*(c+(-1*d^2)^(1/2))^1//3*arctan(1//3*3^(1/2)*(1+2*(c+(-1*d^2)^(1/2))^-1//3*(c+d*tan(e+f*x))^1//3))+-1//2*3^(1/2)*d^-1*f^-1*(-1*d^2)^(1/2)*(c+-1*(-1*d^2)^(1/2))^1//3*arctan(1//3*3^(1/2)*(1+2*(c+-1*(-1*d^2)^(1/2))^-1//3*(c+d*tan(e+f*x))^1//3)))
@test integrate((c+d*tan(e+f*x))^1//3*tan(e+f*x)^3, x) == :(-3*f^-1*(c+d*tan(e+f*x))^1//3+-3//4*f^-1*(c+im*d)^1//3*log((c+im*d)^1//3+-1*(c+d*tan(e+f*x))^1//3)+-3//4*f^-1*(c+-1*im*d)^1//3*log((c+-1*im*d)^1//3+-1*(c+d*tan(e+f*x))^1//3)+-1//4*im*x*(c+-1*im*d)^1//3+-1//4*f^-1*(c+im*d)^1//3*log(cos(e+f*x))+-1//4*f^-1*(c+-1*im*d)^1//3*log(cos(e+f*x))+1//4*im*x*(c+im*d)^1//3+(1/2)*3^(1/2)*f^-1*(c+im*d)^1//3*arctan(1//3*3^(1/2)*(1+2*(c+im*d)^-1//3*(c+d*tan(e+f*x))^1//3))+(1/2)*3^(1/2)*f^-1*(c+-1*im*d)^1//3*arctan(1//3*3^(1/2)*(1+2*(c+d*tan(e+f*x))^1//3*(c+-1*im*d)^-1//3))+-9//28*c*d^-2*f^-1*(c+d*tan(e+f*x))^4//3+3//7*d^-1*f^-1*(c+d*tan(e+f*x))^4//3*tan(e+f*x))
@test integrate((c+d*tan(e+f*x))^1//3*tan(e+f*x)^2, x) == :(1//4*x*(c+(-1*d^2)^(1/2))^1//3+1//4*x*(c+-1*(-1*d^2)^(1/2))^1//3+3//4*d^-1*f^-1*(c+d*tan(e+f*x))^4//3+-3//4*d*f^-1*(-1*d^2)^-1//2*(c+(-1*d^2)^(1/2))^1//3*log((c+(-1*d^2)^(1/2))^1//3+-1*(c+d*tan(e+f*x))^1//3)+-1//4*d*f^-1*(-1*d^2)^-1//2*(c+(-1*d^2)^(1/2))^1//3*log(cos(e+f*x))+1//4*d*f^-1*(-1*d^2)^-1//2*(c+-1*(-1*d^2)^(1/2))^1//3*log(cos(e+f*x))+3//4*d*f^-1*(-1*d^2)^-1//2*(c+-1*(-1*d^2)^(1/2))^1//3*log((c+-1*(-1*d^2)^(1/2))^1//3+-1*(c+d*tan(e+f*x))^1//3)+(1/2)*d*3^(1/2)*f^-1*(-1*d^2)^-1//2*(c+(-1*d^2)^(1/2))^1//3*arctan(1//3*3^(1/2)*(1+2*(c+(-1*d^2)^(1/2))^-1//3*(c+d*tan(e+f*x))^1//3))+-1//2*d*3^(1/2)*f^-1*(-1*d^2)^-1//2*(c+-1*(-1*d^2)^(1/2))^1//3*arctan(1//3*3^(1/2)*(1+2*(c+-1*(-1*d^2)^(1/2))^-1//3*(c+d*tan(e+f*x))^1//3)))
@test integrate((c+d*tan(e+f*x))^1//3*tan(e+f*x), x) == :(3*f^-1*(c+d*tan(e+f*x))^1//3+-1//4*im*x*(c+im*d)^1//3+1//4*im*x*(c+-1*im*d)^1//3+1//4*f^-1*(c+im*d)^1//3*log(cos(e+f*x))+1//4*f^-1*(c+-1*im*d)^1//3*log(cos(e+f*x))+3//4*f^-1*(c+im*d)^1//3*log((c+im*d)^1//3+-1*(c+d*tan(e+f*x))^1//3)+3//4*f^-1*(c+-1*im*d)^1//3*log((c+-1*im*d)^1//3+-1*(c+d*tan(e+f*x))^1//3)+-1//2*3^(1/2)*f^-1*(c+im*d)^1//3*arctan(1//3*3^(1/2)*(1+2*(c+im*d)^-1//3*(c+d*tan(e+f*x))^1//3))+-1//2*3^(1/2)*f^-1*(c+-1*im*d)^1//3*arctan(1//3*3^(1/2)*(1+2*(c+d*tan(e+f*x))^1//3*(c+-1*im*d)^-1//3)))
@test integrate((c+d*tan(e+f*x))^1//3, x) == :(-1//4*x*(c+(-1*d^2)^(1/2))^1//3+-1//4*x*(c+-1*(-1*d^2)^(1/2))^1//3+-3//4*d*f^-1*(-1*d^2)^-1//2*(c+-1*(-1*d^2)^(1/2))^1//3*log((c+-1*(-1*d^2)^(1/2))^1//3+-1*(c+d*tan(e+f*x))^1//3)+-1//4*d*f^-1*(-1*d^2)^-1//2*(c+-1*(-1*d^2)^(1/2))^1//3*log(cos(e+f*x))+1//4*d*f^-1*(-1*d^2)^-1//2*(c+(-1*d^2)^(1/2))^1//3*log(cos(e+f*x))+3//4*d*f^-1*(-1*d^2)^-1//2*(c+(-1*d^2)^(1/2))^1//3*log((c+(-1*d^2)^(1/2))^1//3+-1*(c+d*tan(e+f*x))^1//3)+(1/2)*d*3^(1/2)*f^-1*(-1*d^2)^-1//2*(c+-1*(-1*d^2)^(1/2))^1//3*arctan(1//3*3^(1/2)*(1+2*(c+-1*(-1*d^2)^(1/2))^-1//3*(c+d*tan(e+f*x))^1//3))+-1//2*d*3^(1/2)*f^-1*(-1*d^2)^-1//2*(c+(-1*d^2)^(1/2))^1//3*arctan(1//3*3^(1/2)*(1+2*(c+(-1*d^2)^(1/2))^-1//3*(c+d*tan(e+f*x))^1//3)))
@test integrate((c+d*tan(e+f*x))^1//3*cot(e+f*x), x) == :(-3//4*f^-1*(c+im*d)^1//3*log((c+im*d)^1//3+-1*(c+d*tan(e+f*x))^1//3)+-3//4*f^-1*(c+-1*im*d)^1//3*log((c+-1*im*d)^1//3+-1*(c+d*tan(e+f*x))^1//3)+-1//2*c^1//3*f^-1*log(tan(e+f*x))+-1//4*im*x*(c+-1*im*d)^1//3+-1//4*f^-1*(c+im*d)^1//3*log(cos(e+f*x))+-1//4*f^-1*(c+-1*im*d)^1//3*log(cos(e+f*x))+1//4*im*x*(c+im*d)^1//3+3//2*c^1//3*f^-1*log(c^1//3+-1*(c+d*tan(e+f*x))^1//3)+(1/2)*3^(1/2)*f^-1*(c+im*d)^1//3*arctan(1//3*3^(1/2)*(1+2*(c+im*d)^-1//3*(c+d*tan(e+f*x))^1//3))+(1/2)*3^(1/2)*f^-1*(c+-1*im*d)^1//3*arctan(1//3*3^(1/2)*(1+2*(c+d*tan(e+f*x))^1//3*(c+-1*im*d)^-1//3))+-1*3^(1/2)*c^1//3*f^-1*arctan(1//3*3^(1/2)*c^-1//3*(c^1//3+2*(c+d*tan(e+f*x))^1//3)))
@test integrate((c+d*tan(e+f*x))^1//3*cot(e+f*x)^2, x) == :(1//4*x*(c+(-1*d^2)^(1/2))^1//3+1//4*x*(c+-1*(-1*d^2)^(1/2))^1//3+-1*f^-1*(c+d*tan(e+f*x))^1//3*cot(e+f*x)+(1/2)*d*c^-2//3*f^-1*log(c^1//3+-1*(c+d*tan(e+f*x))^1//3)+-1//6*d*c^-2//3*f^-1*log(tan(e+f*x))+-3//4*d*f^-1*(-1*d^2)^-1//2*(c+(-1*d^2)^(1/2))^1//3*log((c+(-1*d^2)^(1/2))^1//3+-1*(c+d*tan(e+f*x))^1//3)+-1//3*d*3^(1/2)*c^-2//3*f^-1*arctan(1//3*3^(1/2)*c^-1//3*(c^1//3+2*(c+d*tan(e+f*x))^1//3))+-1//4*d*f^-1*(-1*d^2)^-1//2*(c+(-1*d^2)^(1/2))^1//3*log(cos(e+f*x))+1//4*d*f^-1*(-1*d^2)^-1//2*(c+-1*(-1*d^2)^(1/2))^1//3*log(cos(e+f*x))+3//4*d*f^-1*(-1*d^2)^-1//2*(c+-1*(-1*d^2)^(1/2))^1//3*log((c+-1*(-1*d^2)^(1/2))^1//3+-1*(c+d*tan(e+f*x))^1//3)+(1/2)*d*3^(1/2)*f^-1*(-1*d^2)^-1//2*(c+(-1*d^2)^(1/2))^1//3*arctan(1//3*3^(1/2)*(1+2*(c+(-1*d^2)^(1/2))^-1//3*(c+d*tan(e+f*x))^1//3))+-1//2*d*3^(1/2)*f^-1*(-1*d^2)^-1//2*(c+-1*(-1*d^2)^(1/2))^1//3*arctan(1//3*3^(1/2)*(1+2*(c+-1*(-1*d^2)^(1/2))^-1//3*(c+d*tan(e+f*x))^1//3)))
@test integrate((a+b*tan(c+d*x))^5//3, x) == :(-1//4*x*(a+im*b)^5//3+-1//4*x*(a+-1*im*b)^5//3+3//2*b*d^-1*(a+b*tan(c+d*x))^2//3+-3//4*im*d^-1*(a+im*b)^5//3*log((a+im*b)^1//3+-1*(a+b*tan(c+d*x))^1//3)+-1//4*im*d^-1*(a+im*b)^5//3*log(cos(c+d*x))+1//4*im*d^-1*(a+-1*im*b)^5//3*log(cos(c+d*x))+3//4*im*d^-1*(a+-1*im*b)^5//3*log((a+-1*im*b)^1//3+-1*(a+b*tan(c+d*x))^1//3)+(1/2)*im*3^(1/2)*d^-1*(a+-1*im*b)^5//3*arctan(1//3*3^(1/2)*(1+2*(a+b*tan(c+d*x))^1//3*(a+-1*im*b)^-1//3))+-1//2*im*3^(1/2)*d^-1*(a+im*b)^5//3*arctan(1//3*3^(1/2)*(1+2*(a+im*b)^-1//3*(a+b*tan(c+d*x))^1//3)))
@test integrate((a+b*tan(c+d*x))^4//3, x) == :(-1//4*x*(a+im*b)^4//3+-1//4*x*(a+-1*im*b)^4//3+3*b*d^-1*(a+b*tan(c+d*x))^1//3+-3//4*im*d^-1*(a+im*b)^4//3*log((a+im*b)^1//3+-1*(a+b*tan(c+d*x))^1//3)+-1//4*im*d^-1*(a+im*b)^4//3*log(cos(c+d*x))+1//4*im*d^-1*(a+-1*im*b)^4//3*log(cos(c+d*x))+3//4*im*d^-1*(a+-1*im*b)^4//3*log((a+-1*im*b)^1//3+-1*(a+b*tan(c+d*x))^1//3)+(1/2)*im*3^(1/2)*d^-1*(a+im*b)^4//3*arctan(1//3*3^(1/2)*(1+2*(a+im*b)^-1//3*(a+b*tan(c+d*x))^1//3))+-1//2*im*3^(1/2)*d^-1*(a+-1*im*b)^4//3*arctan(1//3*3^(1/2)*(1+2*(a+b*tan(c+d*x))^1//3*(a+-1*im*b)^-1//3)))
@test integrate((a+b*tan(c+d*x))^2//3, x) == :(-1//4*x*(a+(-1*b^2)^(1/2))^2//3+-1//4*x*(a+-1*(-1*b^2)^(1/2))^2//3+-3//4*b*d^-1*(-1*b^2)^-1//2*(a+-1*(-1*b^2)^(1/2))^2//3*log((a+-1*(-1*b^2)^(1/2))^1//3+-1*(a+b*tan(c+d*x))^1//3)+-1//4*b*d^-1*(-1*b^2)^-1//2*(a+-1*(-1*b^2)^(1/2))^2//3*log(cos(c+d*x))+1//4*b*d^-1*(-1*b^2)^-1//2*(a+(-1*b^2)^(1/2))^2//3*log(cos(c+d*x))+3//4*b*d^-1*(-1*b^2)^-1//2*(a+(-1*b^2)^(1/2))^2//3*log((a+(-1*b^2)^(1/2))^1//3+-1*(a+b*tan(c+d*x))^1//3)+(1/2)*b*3^(1/2)*d^-1*(-1*b^2)^-1//2*(a+(-1*b^2)^(1/2))^2//3*arctan(1//3*3^(1/2)*(1+2*(a+(-1*b^2)^(1/2))^-1//3*(a+b*tan(c+d*x))^1//3))+-1//2*b*3^(1/2)*d^-1*(-1*b^2)^-1//2*(a+-1*(-1*b^2)^(1/2))^2//3*arctan(1//3*3^(1/2)*(1+2*(a+-1*(-1*b^2)^(1/2))^-1//3*(a+b*tan(c+d*x))^1//3)))
@test integrate((a+b*tan(c+d*x))^1//3, x) == :(-1//4*x*(a+(-1*b^2)^(1/2))^1//3+-1//4*x*(a+-1*(-1*b^2)^(1/2))^1//3+-3//4*b*d^-1*(-1*b^2)^-1//2*(a+-1*(-1*b^2)^(1/2))^1//3*log((a+-1*(-1*b^2)^(1/2))^1//3+-1*(a+b*tan(c+d*x))^1//3)+-1//4*b*d^-1*(-1*b^2)^-1//2*(a+-1*(-1*b^2)^(1/2))^1//3*log(cos(c+d*x))+1//4*b*d^-1*(-1*b^2)^-1//2*(a+(-1*b^2)^(1/2))^1//3*log(cos(c+d*x))+3//4*b*d^-1*(-1*b^2)^-1//2*(a+(-1*b^2)^(1/2))^1//3*log((a+(-1*b^2)^(1/2))^1//3+-1*(a+b*tan(c+d*x))^1//3)+(1/2)*b*3^(1/2)*d^-1*(-1*b^2)^-1//2*(a+-1*(-1*b^2)^(1/2))^1//3*arctan(1//3*3^(1/2)*(1+2*(a+-1*(-1*b^2)^(1/2))^-1//3*(a+b*tan(c+d*x))^1//3))+-1//2*b*3^(1/2)*d^-1*(-1*b^2)^-1//2*(a+(-1*b^2)^(1/2))^1//3*arctan(1//3*3^(1/2)*(1+2*(a+(-1*b^2)^(1/2))^-1//3*(a+b*tan(c+d*x))^1//3)))
@test integrate((a+b*tan(c+d*x))^-1//3, x) == :(-1//4*x*(a+(-1*b^2)^(1/2))^-1//3+-1//4*x*(a+-1*(-1*b^2)^(1/2))^-1//3+-3//4*b*d^-1*(-1*b^2)^-1//2*(a+-1*(-1*b^2)^(1/2))^-1//3*log((a+-1*(-1*b^2)^(1/2))^1//3+-1*(a+b*tan(c+d*x))^1//3)+-1//4*b*d^-1*(-1*b^2)^-1//2*(a+-1*(-1*b^2)^(1/2))^-1//3*log(cos(c+d*x))+1//4*b*d^-1*(-1*b^2)^-1//2*(a+(-1*b^2)^(1/2))^-1//3*log(cos(c+d*x))+3//4*b*d^-1*(-1*b^2)^-1//2*(a+(-1*b^2)^(1/2))^-1//3*log((a+(-1*b^2)^(1/2))^1//3+-1*(a+b*tan(c+d*x))^1//3)+(1/2)*b*3^(1/2)*d^-1*(-1*b^2)^-1//2*(a+(-1*b^2)^(1/2))^-1//3*arctan(1//3*3^(1/2)*(1+2*(a+(-1*b^2)^(1/2))^-1//3*(a+b*tan(c+d*x))^1//3))+-1//2*b*3^(1/2)*d^-1*(-1*b^2)^-1//2*(a+-1*(-1*b^2)^(1/2))^-1//3*arctan(1//3*3^(1/2)*(1+2*(a+-1*(-1*b^2)^(1/2))^-1//3*(a+b*tan(c+d*x))^1//3)))
@test integrate((a+b*tan(c+d*x))^-2//3, x) == :(-1//4*x*(a+(-1*b^2)^(1/2))^-2//3+-1//4*x*(a+-1*(-1*b^2)^(1/2))^-2//3+-3//4*b*d^-1*(-1*b^2)^-1//2*(a+-1*(-1*b^2)^(1/2))^-2//3*log((a+-1*(-1*b^2)^(1/2))^1//3+-1*(a+b*tan(c+d*x))^1//3)+-1//4*b*d^-1*(-1*b^2)^-1//2*(a+-1*(-1*b^2)^(1/2))^-2//3*log(cos(c+d*x))+1//4*b*d^-1*(-1*b^2)^-1//2*(a+(-1*b^2)^(1/2))^-2//3*log(cos(c+d*x))+3//4*b*d^-1*(-1*b^2)^-1//2*(a+(-1*b^2)^(1/2))^-2//3*log((a+(-1*b^2)^(1/2))^1//3+-1*(a+b*tan(c+d*x))^1//3)+(1/2)*b*3^(1/2)*d^-1*(-1*b^2)^-1//2*(a+-1*(-1*b^2)^(1/2))^-2//3*arctan(1//3*3^(1/2)*(1+2*(a+-1*(-1*b^2)^(1/2))^-1//3*(a+b*tan(c+d*x))^1//3))+-1//2*b*3^(1/2)*d^-1*(-1*b^2)^-1//2*(a+(-1*b^2)^(1/2))^-2//3*arctan(1//3*3^(1/2)*(1+2*(a+(-1*b^2)^(1/2))^-1//3*(a+b*tan(c+d*x))^1//3)))
@test integrate((a+b*tan(c+d*x))^-4//3, x) == :(-1//4*x*(a+im*b)^-4//3+-1//4*x*(a+-1*im*b)^-4//3+-3*b*d^-1*(a+b*tan(c+d*x))^-1//3*(a^2+b^2)^-1+-3//4*im*d^-1*(a+im*b)^-4//3*log((a+im*b)^1//3+-1*(a+b*tan(c+d*x))^1//3)+-1//4*im*d^-1*(a+im*b)^-4//3*log(cos(c+d*x))+1//4*im*d^-1*(a+-1*im*b)^-4//3*log(cos(c+d*x))+3//4*im*d^-1*(a+-1*im*b)^-4//3*log((a+-1*im*b)^1//3+-1*(a+b*tan(c+d*x))^1//3)+(1/2)*im*3^(1/2)*d^-1*(a+-1*im*b)^-4//3*arctan(1//3*3^(1/2)*(1+2*(a+b*tan(c+d*x))^1//3*(a+-1*im*b)^-1//3))+-1//2*im*3^(1/2)*d^-1*(a+im*b)^-4//3*arctan(1//3*3^(1/2)*(1+2*(a+im*b)^-1//3*(a+b*tan(c+d*x))^1//3)))
@test integrate((a+b*tan(c+d*x))^-5//3, x) == :(-1//4*x*(a+im*b)^-5//3+-1//4*x*(a+-1*im*b)^-5//3+-3*b*d^-1*(a+b*tan(c+d*x))^-2//3*(2*a^2+2*b^2)^-1+-3//4*im*d^-1*(a+im*b)^-5//3*log((a+im*b)^1//3+-1*(a+b*tan(c+d*x))^1//3)+-1//4*im*d^-1*(a+im*b)^-5//3*log(cos(c+d*x))+1//4*im*d^-1*(a+-1*im*b)^-5//3*log(cos(c+d*x))+3//4*im*d^-1*(a+-1*im*b)^-5//3*log((a+-1*im*b)^1//3+-1*(a+b*tan(c+d*x))^1//3)+(1/2)*im*3^(1/2)*d^-1*(a+im*b)^-5//3*arctan(1//3*3^(1/2)*(1+2*(a+im*b)^-1//3*(a+b*tan(c+d*x))^1//3))+-1//2*im*3^(1/2)*d^-1*(a+-1*im*b)^-5//3*arctan(1//3*3^(1/2)*(1+2*(a+b*tan(c+d*x))^1//3*(a+-1*im*b)^-1//3)))
@test integrate(cot(c+d*x)^5//2*(a+im*a*tan(c+d*x)), x) == :(-2//3*a*d^-1*cot(c+d*x)^3//2+-2*im*a*d^-1*cot(c+d*x)^(1/2)+-2*a*(-1)^3//4*d^-1*arctanh((-1)^3//4*cot(c+d*x)^(1/2)))
@test integrate(cot(c+d*x)^3//2*(a+im*a*tan(c+d*x)), x) == :(-2*a*d^-1*cot(c+d*x)^(1/2)+-2*a*(-1)^1//4*d^-1*arctanh((-1)^3//4*cot(c+d*x)^(1/2)))
@test integrate(cot(c+d*x)^(1/2)*(a+im*a*tan(c+d*x)), x) == :(2*a*(-1)^3//4*d^-1*arctanh((-1)^3//4*cot(c+d*x)^(1/2)))
@test integrate(cot(c+d*x)^-1//2*(a+im*a*tan(c+d*x)), x) == :(2*im*a*d^-1*cot(c+d*x)^-1//2+2*a*(-1)^1//4*d^-1*arctanh((-1)^3//4*cot(c+d*x)^(1/2)))
@test integrate(cot(c+d*x)^-3//2*(a+im*a*tan(c+d*x)), x) == :(2*a*d^-1*cot(c+d*x)^-1//2+-2*a*(-1)^3//4*d^-1*arctanh((-1)^3//4*cot(c+d*x)^(1/2))+2//3*im*a*d^-1*cot(c+d*x)^-3//2)
@test integrate((a+im*a*tan(c+d*x))^2*cot(c+d*x)^7//2, x) == :(4*a^2*d^-1*cot(c+d*x)^(1/2)+-2//5*a^2*d^-1*cot(c+d*x)^5//2+4*(-1)^1//4*a^2*d^-1*arctanh((-1)^3//4*cot(c+d*x)^(1/2))+-4//3*im*a^2*d^-1*cot(c+d*x)^3//2)
@test integrate((a+im*a*tan(c+d*x))^2*cot(c+d*x)^5//2, x) == :(-2//3*a^2*d^-1*cot(c+d*x)^3//2+-4*im*a^2*d^-1*cot(c+d*x)^(1/2)+-4*(-1)^3//4*a^2*d^-1*arctanh((-1)^3//4*cot(c+d*x)^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^2*cot(c+d*x)^3//2, x) == :(-2*a^2*d^-1*cot(c+d*x)^(1/2)+-4*(-1)^1//4*a^2*d^-1*arctanh((-1)^3//4*cot(c+d*x)^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^2*cot(c+d*x)^(1/2), x) == :(-2*a^2*d^-1*cot(c+d*x)^-1//2+4*(-1)^3//4*a^2*d^-1*arctanh((-1)^3//4*cot(c+d*x)^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^2*cot(c+d*x)^-1//2, x) == :(-2//3*a^2*d^-1*cot(c+d*x)^-3//2+4*im*a^2*d^-1*cot(c+d*x)^-1//2+4*(-1)^1//4*a^2*d^-1*arctanh((-1)^3//4*cot(c+d*x)^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^2*cot(c+d*x)^-3//2, x) == :(4*a^2*d^-1*cot(c+d*x)^-1//2+-2//5*a^2*d^-1*cot(c+d*x)^-5//2+-4*(-1)^3//4*a^2*d^-1*arctanh((-1)^3//4*cot(c+d*x)^(1/2))+4//3*im*a^2*d^-1*cot(c+d*x)^-3//2)
@test integrate((a+im*a*tan(c+d*x))^3*cot(c+d*x)^7//2, x) == :(8*a^3*d^-1*cot(c+d*x)^(1/2)+-2//5*d^-1*cot(c+d*x)^3//2*(im*a^3+a^3*cot(c+d*x))+8*(-1)^1//4*a^3*d^-1*arctanh((-1)^3//4*cot(c+d*x)^(1/2))+-8//5*im*a^3*d^-1*cot(c+d*x)^3//2)
@test integrate((a+im*a*tan(c+d*x))^3*cot(c+d*x)^5//2, x) == :(-2//3*d^-1*cot(c+d*x)^(1/2)*(im*a^3+a^3*cot(c+d*x))+-8*(-1)^3//4*a^3*d^-1*arctanh((-1)^3//4*cot(c+d*x)^(1/2))+-16//3*im*a^3*d^-1*cot(c+d*x)^(1/2))
@test integrate((a+im*a*tan(c+d*x))^3*cot(c+d*x)^3//2, x) == :(-1*d^-1*cot(c+d*x)^-1//2*(2*im*a^3+2*a^3*cot(c+d*x))+-8*(-1)^1//4*a^3*d^-1*arctanh((-1)^3//4*cot(c+d*x)^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^3*cot(c+d*x)^(1/2), x) == :(-16//3*a^3*d^-1*cot(c+d*x)^-1//2+-1//3*d^-1*cot(c+d*x)^-3//2*(2*im*a^3+2*a^3*cot(c+d*x))+8*(-1)^3//4*a^3*d^-1*arctanh((-1)^3//4*cot(c+d*x)^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^3*cot(c+d*x)^-1//2, x) == :(-8//5*a^3*d^-1*cot(c+d*x)^-3//2+-1//5*d^-1*cot(c+d*x)^-5//2*(2*im*a^3+2*a^3*cot(c+d*x))+8*im*a^3*d^-1*cot(c+d*x)^-1//2+8*(-1)^1//4*a^3*d^-1*arctanh((-1)^3//4*cot(c+d*x)^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-1*cot(c+d*x)^3//2, x) == :((1/2)*d^-1*(im*a+a*cot(c+d*x))^-1*cot(c+d*x)^3//2+-5//2*a^-1*d^-1*cot(c+d*x)^(1/2)+(1/2)*2^(1/2)*a^-1*d^-1*(5//4+3//4*im)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+(1/2)*2^(1/2)*a^-1*d^-1*(5//8+-3//8*im)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+-1//2*2^(1/2)*a^-1*d^-1*(5//4+3//4*im)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*a^-1*d^-1*(5//8+-3//8*im)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+im*a*tan(c+d*x))^-1*cot(c+d*x)^(1/2), x) == :((1/2)*d^-1*(im*a+a*cot(c+d*x))^-1*cot(c+d*x)^(1/2)+(1/2)*2^(1/2)*a^-1*d^-1*(3//4+-1//4*im)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+(1/2)*2^(1/2)*a^-1*d^-1*(3//8+1//8*im)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+-1//2*2^(1/2)*a^-1*d^-1*(3//4+-1//4*im)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*a^-1*d^-1*(3//8+1//8*im)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+im*a*tan(c+d*x))^-1*cot(c+d*x)^-1//2, x) == :((1/2)*im*d^-1*(im*a+a*cot(c+d*x))^-1*cot(c+d*x)^(1/2)+(1/2)*(-1)^1//4*a^-1*d^-1*arctanh((-1)^3//4*cot(c+d*x)^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-1*cot(c+d*x)^-3//2, x) == :(-1//2*d^-1*(im*a+a*cot(c+d*x))^-1*cot(c+d*x)^(1/2)+(1/2)*2^(1/2)*a^-1*d^-1*(1//4+-3//4*im)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+(1/2)*2^(1/2)*a^-1*d^-1*(1//8+3//8*im)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+-1//2*2^(1/2)*a^-1*d^-1*(1//4+-3//4*im)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*a^-1*d^-1*(1//8+3//8*im)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+im*a*tan(c+d*x))^-1*cot(c+d*x)^-5//2, x) == :(-1//2*d^-1*(im*a+a*cot(c+d*x))^-1*cot(c+d*x)^-1//2+-5//2*im*a^-1*d^-1*cot(c+d*x)^-1//2+(1/2)*2^(1/2)*a^-1*d^-1*(3//4+5//4*im)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+(1/2)*2^(1/2)*a^-1*d^-1*(3//8+-5//8*im)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+-1//2*2^(1/2)*a^-1*d^-1*(3//4+5//4*im)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*a^-1*d^-1*(3//8+-5//8*im)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+im*a*tan(c+d*x))^-2*cot(c+d*x)^3//2, x) == :(-25//8*a^-2*d^-1*cot(c+d*x)^(1/2)+1//4*d^-1*(im*a+a*cot(c+d*x))^-2*cot(c+d*x)^5//2+7//8*a^-2*d^-1*(im+cot(c+d*x))^-1*cot(c+d*x)^3//2+(1/2)*2^(1/2)*a^-2*d^-1*(25//16+21//16*im)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+(1/2)*2^(1/2)*a^-2*d^-1*(25//32+-21//32*im)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+-1//2*2^(1/2)*a^-2*d^-1*(25//16+21//16*im)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*a^-2*d^-1*(25//32+-21//32*im)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+im*a*tan(c+d*x))^-2*cot(c+d*x)^(1/2), x) == :(1//4*d^-1*(im*a+a*cot(c+d*x))^-2*cot(c+d*x)^3//2+5//8*a^-2*d^-1*(im+cot(c+d*x))^-1*cot(c+d*x)^(1/2)+(1/2)*2^(1/2)*a^-2*d^-1*(9//16+-5//16*im)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+(1/2)*2^(1/2)*a^-2*d^-1*(9//32+5//32*im)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+-1//2*2^(1/2)*a^-2*d^-1*(9//16+-5//16*im)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*a^-2*d^-1*(9//32+5//32*im)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+im*a*tan(c+d*x))^-2*cot(c+d*x)^-1//2, x) == :(1//4*d^-1*(im*a+a*cot(c+d*x))^-2*cot(c+d*x)^(1/2)+(1/2)*2^(1/2)*a^-2*d^-1*(1//16+-3//16*im)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+(1/2)*2^(1/2)*a^-2*d^-1*(1//32+3//32*im)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+-1//2*2^(1/2)*a^-2*d^-1*(1//16+-3//16*im)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*a^-2*d^-1*(1//32+3//32*im)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+3//8*im*a^-2*d^-1*(im+cot(c+d*x))^-1*cot(c+d*x)^(1/2))
@test integrate((a+im*a*tan(c+d*x))^-2*cot(c+d*x)^-3//2, x) == :(1//4*im*d^-1*(im*a+a*cot(c+d*x))^-2*cot(c+d*x)^(1/2)+1//8*a^-2*d^-1*(im+cot(c+d*x))^-1*cot(c+d*x)^(1/2)+(1/2)*2^(1/2)*a^-2*d^-1*(1//16+3//16*im)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+(1/2)*2^(1/2)*a^-2*d^-1*(1//32+-3//32*im)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+-1//2*2^(1/2)*a^-2*d^-1*(1//16+3//16*im)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*a^-2*d^-1*(1//32+-3//32*im)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+im*a*tan(c+d*x))^-2*cot(c+d*x)^-5//2, x) == :(-1//4*d^-1*(im*a+a*cot(c+d*x))^-2*cot(c+d*x)^(1/2)+(1/2)*2^(1/2)*a^-2*d^-1*(9//16+5//16*im)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+(1/2)*2^(1/2)*a^-2*d^-1*(9//32+-5//32*im)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+-1//2*2^(1/2)*a^-2*d^-1*(9//16+5//16*im)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*a^-2*d^-1*(9//32+-5//32*im)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+5//8*im*a^-2*d^-1*(im+cot(c+d*x))^-1*cot(c+d*x)^(1/2))
@test integrate((a+im*a*tan(c+d*x))^-2*cot(c+d*x)^-7//2, x) == :(-25//8*a^-2*d^-1*cot(c+d*x)^-1//2+-1//4*d^-1*(im*a+a*cot(c+d*x))^-2*cot(c+d*x)^-1//2+(1/2)*2^(1/2)*a^-2*d^-1*(25//16+-21//16*im)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+(1/2)*2^(1/2)*a^-2*d^-1*(25//32+21//32*im)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+-1//2*2^(1/2)*a^-2*d^-1*(25//16+-21//16*im)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*a^-2*d^-1*(25//32+21//32*im)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+7//8*im*a^-2*d^-1*(im+cot(c+d*x))^-1*cot(c+d*x)^-1//2)
@test integrate((a+im*a*tan(c+d*x))^-3*cot(c+d*x)^(1/2), x) == :(1//6*d^-1*(im*a+a*cot(c+d*x))^-3*cot(c+d*x)^5//2+5//8*d^-1*(im*a^3+a^3*cot(c+d*x))^-1*cot(c+d*x)^(1/2)+1//3*a^-1*d^-1*(im*a+a*cot(c+d*x))^-2*cot(c+d*x)^3//2+(1/2)*2^(1/2)*a^-3*d^-1*(7//16+-5//16*im)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+(1/2)*2^(1/2)*a^-3*d^-1*(7//32+5//32*im)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+-1//2*2^(1/2)*a^-3*d^-1*(7//16+-5//16*im)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*a^-3*d^-1*(7//32+5//32*im)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+im*a*tan(c+d*x))^-3*cot(c+d*x)^-1//2, x) == :(1//6*d^-1*(im*a+a*cot(c+d*x))^-3*cot(c+d*x)^3//2+1//4*im*d^-1*(im*a^3+a^3*cot(c+d*x))^-1*cot(c+d*x)^(1/2)+1//4*a^-1*d^-1*(im*a+a*cot(c+d*x))^-2*cot(c+d*x)^(1/2)+-1//16*im*2^(1/2)*a^-3*d^-1*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//32*im*2^(1/2)*a^-3*d^-1*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//16*im*2^(1/2)*a^-3*d^-1*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+1//32*im*2^(1/2)*a^-3*d^-1*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+im*a*tan(c+d*x))^-3*cot(c+d*x)^-3//2, x) == :(1//6*d^-1*(im*a+a*cot(c+d*x))^-3*cot(c+d*x)^(1/2)+1//8*d^-1*(im*a^3+a^3*cot(c+d*x))^-1*cot(c+d*x)^(1/2)+-1//8*(-1)^3//4*a^-3*d^-1*arctanh((-1)^3//4*cot(c+d*x)^(1/2))+1//6*im*a^-1*d^-1*(im*a+a*cot(c+d*x))^-2*cot(c+d*x)^(1/2))
@test integrate((a+im*a*tan(c+d*x))^-3*cot(c+d*x)^-5//2, x) == :(-1//16*2^(1/2)*a^-3*d^-1*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//32*2^(1/2)*a^-3*d^-1*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//6*im*d^-1*(im*a+a*cot(c+d*x))^-3*cot(c+d*x)^(1/2)+1//12*a^-1*d^-1*(im*a+a*cot(c+d*x))^-2*cot(c+d*x)^(1/2)+1//16*2^(1/2)*a^-3*d^-1*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+1//32*2^(1/2)*a^-3*d^-1*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+im*a*tan(c+d*x))^-3*cot(c+d*x)^-7//2, x) == :(-1//6*d^-1*(im*a+a*cot(c+d*x))^-3*cot(c+d*x)^(1/2)+5//8*d^-1*(im*a^3+a^3*cot(c+d*x))^-1*cot(c+d*x)^(1/2)+(1/2)*2^(1/2)*a^-3*d^-1*(5//16+-7//16*im)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+(1/2)*2^(1/2)*a^-3*d^-1*(5//32+7//32*im)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+-1//2*2^(1/2)*a^-3*d^-1*(5//16+-7//16*im)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*a^-3*d^-1*(5//32+7//32*im)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//3*im*a^-1*d^-1*(im*a+a*cot(c+d*x))^-2*cot(c+d*x)^(1/2))
@test integrate((a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^7//2, x) == :(-2//5*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^5//2+26//15*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)+-2//15*im*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^3//2+a^(1/2)*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(-1+-1im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^5//2, x) == :(-2//3*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^3//2+-2//3*im*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)+a^(1/2)*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(-1+im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^3//2, x) == :(-2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)+a^(1/2)*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(1+im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2), x) == :(a^(1/2)*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(1+-1im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^-1//2, x) == :(-1*a^(1/2)*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(1+im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-2*(-1)^3//4*a^(1/2)*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^-3//2, x) == :(d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^-1//2+-1*(-1)^1//4*a^(1/2)*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+-1*a^(1/2)*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(1+-1im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^3//2*cot(c+d*x)^7//2, x) == :(-2//5*a^2*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^5//2+12//5*a*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)+-4//5*im*a*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^3//2+-2//5*im*a^2*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^3//2+a^3//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(-2+-2im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^3//2*cot(c+d*x)^5//2, x) == :(-2//3*d^-1*(a+im*a*tan(c+d*x))^3//2*cot(c+d*x)^3//2+-2*im*a*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)+a^3//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(-2+2im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^3//2*cot(c+d*x)^3//2, x) == :(-2*a*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)+a^3//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(2+2im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^3//2*cot(c+d*x)^(1/2), x) == :(a^3//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(2+-2im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+2*(-1)^1//4*a^3//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^3//2*cot(c+d*x)^-1//2, x) == :(-1*a^2*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^-3//2+im*a^2*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^-1//2+-1*a^3//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(2+2im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-3*(-1)^3//4*a^3//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^5//2*cot(c+d*x)^9//2, x) == :(-2//7*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^7//2+32//21*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^3//2+-6//7*im*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^5//2+104//21*im*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)+a^5//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(4+-4im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^5//2*cot(c+d*x)^7//2, x) == :(-2//5*d^-1*(a+im*a*tan(c+d*x))^5//2*cot(c+d*x)^5//2+4*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)+-2//3*im*a*d^-1*(a+im*a*tan(c+d*x))^3//2*cot(c+d*x)^3//2+a^5//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(-4+-4im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^5//2*cot(c+d*x)^5//2, x) == :(-2//3*a*d^-1*(a+im*a*tan(c+d*x))^3//2*cot(c+d*x)^3//2+-4*im*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)+a^5//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(-4+4im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^5//2*cot(c+d*x)^3//2, x) == :(-2*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)+a^5//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(4+4im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+2*(-1)^3//4*a^5//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^5//2*cot(c+d*x)^(1/2), x) == :(-1*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^-1//2+a^5//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(4+-4im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+5*(-1)^1//4*a^5//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^5//2*cot(c+d*x)^-1//2, x) == :(-1//2*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^-3//2+9//4*im*a^2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^-1//2+-1*a^5//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(4+4im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-23//4*(-1)^3//4*a^5//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^5//2, x) == :(d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^3//2+-5//3*a^-1*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^3//2+7//3*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)+-1*a^-1//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(1/2+-1//2*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^3//2, x) == :(d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^(1/2)+-3*a^-1*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)+a^-1//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(1/2+(1/2)*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^(1/2), x) == :(d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^-1//2+a^-1//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(1/2+-1//2*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^-1//2, x) == :(im*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^-1//2+a^-1//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(-1//2+-1//2*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^-3//2, x) == :(-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^-1//2+-1*a^-1//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(1/2+-1//2*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-2*(-1)^1//4*a^-1//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^-5//2, x) == :(-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^-3//2+-2*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^-1//2+a^-1//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(1/2+(1/2)*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-1*(-1)^3//4*a^-1//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)^5//2, x) == :(1//3*d^-1*(a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)^3//2+-7//2*a^-2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^3//2+5//2*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^3//2+13//2*im*a^-2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)+a^-3//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(-1//4+1//4*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)^3//2, x) == :(1//3*d^-1*(a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)^(1/2)+-25//6*a^-2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)+11//6*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^(1/2)+a^-3//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(1//4+1//4*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)^(1/2), x) == :(1//3*d^-1*(a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)^-1//2+7//6*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^-1//2+a^-3//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(1//4+-1//4*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)^-1//2, x) == :(1//3*d^-1*(a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)^-3//2+(1/2)*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^-1//2+-1*a^-3//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(1//4+1//4*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)^-3//2, x) == :((1/2)*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^-1//2+1//3*im*d^-1*(a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)^-3//2+a^-3//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(-1//4+1//4*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)^-5//2, x) == :(-1//3*d^-1*(a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)^-3//2+3//2*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^-1//2+a^-3//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(1//4+1//4*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+2*(-1)^3//4*a^-3//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)^-7//2, x) == :(-1//3*d^-1*(a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)^-5//2+-7//2*a^-2*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^-1//2+13//6*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^-3//2+a^-3//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(1//4+-1//4*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+-3*(-1)^1//4*a^-3//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+im*a*tan(c+d*x))^-5//2*cot(c+d*x)^5//2, x) == :(1//5*d^-1*(a+im*a*tan(c+d*x))^-5//2*cot(c+d*x)^3//2+-361//60*a^-3*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^3//2+7//10*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)^3//2+89//20*a^-2*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^3//2+707//60*im*a^-3*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)+a^-5//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(-1//8+1//8*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^-5//2*cot(c+d*x)^3//2, x) == :(1//5*d^-1*(a+im*a*tan(c+d*x))^-5//2*cot(c+d*x)^(1/2)+-317//60*a^-3*d^-1*(a+im*a*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)+17//30*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)^(1/2)+151//60*a^-2*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^(1/2)+a^-5//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(1//8+1//8*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^-5//2*cot(c+d*x)^(1/2), x) == :(1//5*d^-1*(a+im*a*tan(c+d*x))^-5//2*cot(c+d*x)^-1//2+13//30*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)^-1//2+67//60*a^-2*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^-1//2+a^-5//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(1//8+-1//8*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^-5//2*cot(c+d*x)^-1//2, x) == :(1//5*im*d^-1*(a+im*a*tan(c+d*x))^-5//2*cot(c+d*x)^-1//2+-1//20*im*a^-2*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^-1//2+1//10*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)^-1//2+a^-5//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(-1//8+-1//8*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^-5//2*cot(c+d*x)^-3//2, x) == :(1//5*d^-1*(a+im*a*tan(c+d*x))^-5//2*cot(c+d*x)^-5//2+1//4*a^-2*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^-1//2+1//6*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)^-3//2+a^-5//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(-1//8+1//8*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^-5//2*cot(c+d*x)^-5//2, x) == :(1//5*im*d^-1*(a+im*a*tan(c+d*x))^-5//2*cot(c+d*x)^-5//2+1//6*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)^-3//2+-1//4*im*a^-2*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^-1//2+a^-5//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(1//8+1//8*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im)))
@test integrate((a+im*a*tan(c+d*x))^-5//2*cot(c+d*x)^-7//2, x) == :(-1//5*d^-1*(a+im*a*tan(c+d*x))^-5//2*cot(c+d*x)^-5//2+7//4*a^-2*d^-1*(a+im*a*tan(c+d*x))^-1//2*cot(c+d*x)^-1//2+(1/2)*im*a^-1*d^-1*(a+im*a*tan(c+d*x))^-3//2*cot(c+d*x)^-3//2+a^-5//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(1//8+-1//8*im)*arctanh(a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)*(1+im))+2*(-1)^1//4*a^-5//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((-1)^3//4*a^(1/2)*(a+im*a*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate(cot(c+d*x)^7//2*(a+b*tan(c+d*x)), x) == :(2*a*d^-1*cot(c+d*x)^(1/2)+-2//3*b*d^-1*cot(c+d*x)^3//2+-2//5*a*d^-1*cot(c+d*x)^5//2+(1/2)*2^(1/2)*d^-1*(a+-1b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+-1b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a+b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate(cot(c+d*x)^5//2*(a+b*tan(c+d*x)), x) == :(-2*b*d^-1*cot(c+d*x)^(1/2)+-2//3*a*d^-1*cot(c+d*x)^3//2+(1/2)*2^(1/2)*d^-1*(a+b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+-1b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a+-1b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate(cot(c+d*x)^3//2*(a+b*tan(c+d*x)), x) == :(-2*a*d^-1*cot(c+d*x)^(1/2)+(1/2)*2^(1/2)*d^-1*(a+-1b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+-1b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a+b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate(cot(c+d*x)^(1/2)*(a+b*tan(c+d*x)), x) == :((1/2)*2^(1/2)*d^-1*(a+b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+-1b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a+-1b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate(cot(c+d*x)^-1//2*(a+b*tan(c+d*x)), x) == :(2*b*d^-1*cot(c+d*x)^-1//2+(1/2)*2^(1/2)*d^-1*(a+-1b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+-1b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a+b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate(cot(c+d*x)^-3//2*(a+b*tan(c+d*x)), x) == :(2*a*d^-1*cot(c+d*x)^-1//2+2//3*b*d^-1*cot(c+d*x)^-3//2+(1/2)*2^(1/2)*d^-1*(a+b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+-1b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a+-1b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate(cot(c+d*x)^-5//2*(a+b*tan(c+d*x)), x) == :(-2*b*d^-1*cot(c+d*x)^-1//2+2//3*a*d^-1*cot(c+d*x)^-3//2+2//5*b*d^-1*cot(c+d*x)^-5//2+(1/2)*2^(1/2)*d^-1*(a+-1b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+-1b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a+b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+b*tan(c+d*x))^2*cot(c+d*x)^9//2, x) == :(-2//7*a^2*d^-1*cot(c+d*x)^7//2+1//3*d^-1*cot(c+d*x)^3//2*(-2*b^2+2*a^2)+(1/2)*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+4*a*b*d^-1*cot(c+d*x)^(1/2)+-4//5*a*b*d^-1*cot(c+d*x)^5//2+-1//2*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+b*tan(c+d*x))^2*cot(c+d*x)^7//2, x) == :(d^-1*cot(c+d*x)^(1/2)*(-2*b^2+2*a^2)+-2//5*a^2*d^-1*cot(c+d*x)^5//2+(1/2)*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-4//3*a*b*d^-1*cot(c+d*x)^3//2+-1//2*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+b*tan(c+d*x))^2*cot(c+d*x)^5//2, x) == :(-2//3*a^2*d^-1*cot(c+d*x)^3//2+(1/2)*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-4*a*b*d^-1*cot(c+d*x)^(1/2)+-1//2*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+b*tan(c+d*x))^2*cot(c+d*x)^3//2, x) == :(-2*a^2*d^-1*cot(c+d*x)^(1/2)+(1/2)*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+b*tan(c+d*x))^2*cot(c+d*x)^(1/2), x) == :(2*b^2*d^-1*cot(c+d*x)^-1//2+(1/2)*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+b*tan(c+d*x))^2*cot(c+d*x)^-1//2, x) == :(2//3*b^2*d^-1*cot(c+d*x)^-3//2+(1/2)*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+4*a*b*d^-1*cot(c+d*x)^-1//2+-1//2*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+b*tan(c+d*x))^2*cot(c+d*x)^-3//2, x) == :(d^-1*cot(c+d*x)^-1//2*(-2*b^2+2*a^2)+2//5*b^2*d^-1*cot(c+d*x)^-5//2+(1/2)*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+4//3*a*b*d^-1*cot(c+d*x)^-3//2)
@test integrate((a+b*tan(c+d*x))^2*cot(c+d*x)^-5//2, x) == :(1//3*d^-1*cot(c+d*x)^-3//2*(-2*b^2+2*a^2)+2//7*b^2*d^-1*cot(c+d*x)^-7//2+(1/2)*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-4*a*b*d^-1*cot(c+d*x)^-1//2+-1//2*2^(1/2)*d^-1*(a^2+-1*b^2+-2*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+-1*b^2+2*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+4//5*a*b*d^-1*cot(c+d*x)^-5//2)
@test integrate((a+b*tan(c+d*x))^3*cot(c+d*x)^9//2, x) == :(2*b*d^-1*cot(c+d*x)^(1/2)*(-1*b^2+3*a^2)+-32//35*b*a^2*d^-1*cot(c+d*x)^5//2+-2//7*a^2*d^-1*cot(c+d*x)^5//2*(b+a*cot(c+d*x))+2//3*a*d^-1*cot(c+d*x)^3//2*(a^2+-3*b^2)+(1/2)*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+b*tan(c+d*x))^3*cot(c+d*x)^7//2, x) == :(2*a*d^-1*cot(c+d*x)^(1/2)*(a^2+-3*b^2)+-8//5*b*a^2*d^-1*cot(c+d*x)^3//2+-2//5*a^2*d^-1*cot(c+d*x)^3//2*(b+a*cot(c+d*x))+(1/2)*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+b*tan(c+d*x))^3*cot(c+d*x)^5//2, x) == :(-16//3*b*a^2*d^-1*cot(c+d*x)^(1/2)+-2//3*a^2*d^-1*cot(c+d*x)^(1/2)*(b+a*cot(c+d*x))+(1/2)*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+b*tan(c+d*x))^3*cot(c+d*x)^3//2, x) == :(-2*a*d^-1*cot(c+d*x)^(1/2)*(a^2+b^2)+2*b^2*d^-1*cot(c+d*x)^-1//2*(b+a*cot(c+d*x))+(1/2)*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+b*tan(c+d*x))^3*cot(c+d*x)^(1/2), x) == :(2//3*b^2*d^-1*cot(c+d*x)^-3//2*(b+a*cot(c+d*x))+16//3*a*b^2*d^-1*cot(c+d*x)^-1//2+(1/2)*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+b*tan(c+d*x))^3*cot(c+d*x)^-1//2, x) == :(2*b*d^-1*cot(c+d*x)^-1//2*(-1*b^2+3*a^2)+2//5*b^2*d^-1*cot(c+d*x)^-5//2*(b+a*cot(c+d*x))+8//5*a*b^2*d^-1*cot(c+d*x)^-3//2+(1/2)*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+b*tan(c+d*x))^3*cot(c+d*x)^-3//2, x) == :(2*a*d^-1*cot(c+d*x)^-1//2*(a^2+-3*b^2)+2//3*b*d^-1*cot(c+d*x)^-3//2*(-1*b^2+3*a^2)+2//7*b^2*d^-1*cot(c+d*x)^-7//2*(b+a*cot(c+d*x))+32//35*a*b^2*d^-1*cot(c+d*x)^-5//2+(1/2)*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a+b)*(a^2+b^2+-4*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-1*cot(c+d*x)^5//2, x) == :(-2//3*a^-1*d^-1*cot(c+d*x)^3//2+2*b*a^-2*d^-1*cot(c+d*x)^(1/2)+(1/2)*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-2*a^-5//2*b^7//2*d^-1*(a^2+b^2)^-1*arctan(a^(1/2)*b^-1//2*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-1*cot(c+d*x)^3//2, x) == :(-2*a^-1*d^-1*cot(c+d*x)^(1/2)+(1/2)*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+2*a^-3//2*b^5//2*d^-1*(a^2+b^2)^-1*arctan(a^(1/2)*b^-1//2*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-1*cot(c+d*x)^(1/2), x) == :((1/2)*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-2*a^-1//2*b^3//2*d^-1*(a^2+b^2)^-1*arctan(a^(1/2)*b^-1//2*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-1*cot(c+d*x)^-1//2, x) == :((1/2)*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+2*a^(1/2)*b^(1/2)*d^-1*(a^2+b^2)^-1*arctan(a^(1/2)*b^-1//2*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-1*cot(c+d*x)^-3//2, x) == :((1/2)*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-2*a^3//2*b^-1//2*d^-1*(a^2+b^2)^-1*arctan(a^(1/2)*b^-1//2*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-1*cot(c+d*x)^-5//2, x) == :(2*b^-1*d^-1*cot(c+d*x)^-1//2+(1/2)*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+2*a^5//2*b^-3//2*d^-1*(a^2+b^2)^-1*arctan(a^(1/2)*b^-1//2*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-1*(a+-1b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-2*cot(c+d*x)^5//2, x) == :((1/2)*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//3*a^-2*d^-1*(a^2+b^2)^-1*cot(c+d*x)^3//2*(2*a^2+5*b^2)+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+b*a^-3*d^-1*(a^2+b^2)^-1*cot(c+d*x)^(1/2)*(4*a^2+5*b^2)+a^-1*b^2*d^-1*(b+a*cot(c+d*x))^-1*(a^2+b^2)^-1*cot(c+d*x)^5//2+-1*a^-7//2*b^7//2*d^-1*(a^2+b^2)^-2*(5*b^2+9*a^2)*arctan(a^(1/2)*b^-1//2*cot(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^-2*cot(c+d*x)^3//2, x) == :((1/2)*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1*a^-2*d^-1*(a^2+b^2)^-1*cot(c+d*x)^(1/2)*(2*a^2+3*b^2)+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+a^-1*b^2*d^-1*(b+a*cot(c+d*x))^-1*(a^2+b^2)^-1*cot(c+d*x)^3//2+a^-5//2*b^5//2*d^-1*(a^2+b^2)^-2*(3*b^2+7*a^2)*arctan(a^(1/2)*b^-1//2*cot(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^-2*cot(c+d*x)^(1/2), x) == :((1/2)*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+a^-1*b^2*d^-1*(b+a*cot(c+d*x))^-1*(a^2+b^2)^-1*cot(c+d*x)^(1/2)+-1*a^-3//2*b^3//2*d^-1*(a^2+b^2)^-2*(b^2+5*a^2)*arctan(a^(1/2)*b^-1//2*cot(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^-2*cot(c+d*x)^-1//2, x) == :((1/2)*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1*b*d^-1*(b+a*cot(c+d*x))^-1*(a^2+b^2)^-1*cot(c+d*x)^(1/2)+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+a^-1//2*b^(1/2)*d^-1*(a^2+b^2)^-2*(-1*b^2+3*a^2)*arctan(a^(1/2)*b^-1//2*cot(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^-2*cot(c+d*x)^-3//2, x) == :(a*d^-1*(b+a*cot(c+d*x))^-1*(a^2+b^2)^-1*cot(c+d*x)^(1/2)+(1/2)*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+-1*a^(1/2)*b^-1//2*d^-1*(a^2+b^2)^-2*(a^2+-3*b^2)*arctan(a^(1/2)*b^-1//2*cot(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^-2*cot(c+d*x)^-5//2, x) == :((1/2)*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+-1*a^2*b^-1*d^-1*(b+a*cot(c+d*x))^-1*(a^2+b^2)^-1*cot(c+d*x)^(1/2)+-1*a^3//2*b^-3//2*d^-1*(a^2+b^2)^-2*(a^2+5*b^2)*arctan(a^(1/2)*b^-1//2*cot(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^-2*cot(c+d*x)^-7//2, x) == :(b^-2*d^-1*(a^2+b^2)^-1*cot(c+d*x)^-1//2*(2*b^2+3*a^2)+(1/2)*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+-2*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-2*(a^2+-1*b^2+2*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+a^5//2*b^-5//2*d^-1*(a^2+b^2)^-2*(3*a^2+7*b^2)*arctan(a^(1/2)*b^-1//2*cot(c+d*x)^(1/2))+-1*a^2*b^-1*d^-1*(b+a*cot(c+d*x))^-1*(a^2+b^2)^-1*cot(c+d*x)^-1//2)
@test integrate((a+b*tan(c+d*x))^-3*cot(c+d*x)^5//2, x) == :(-1//12*a^-3*d^-1*(a^2+b^2)^-2*cot(c+d*x)^3//2*(8*a^4+35*b^4+67*a^2*b^2)+(1/2)*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+(1/2)*a^-1*b^2*d^-1*(b+a*cot(c+d*x))^-2*(a^2+b^2)^-1*cot(c+d*x)^7//2+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+-1//4*a^-9//2*b^7//2*d^-1*(a^2+b^2)^-3*(35*b^4+99*a^4+102*a^2*b^2)*arctan(a^(1/2)*b^-1//2*cot(c+d*x)^(1/2))+1//4*b*a^-4*d^-1*(a^2+b^2)^-2*cot(c+d*x)^(1/2)*(24*a^4+35*b^4+67*a^2*b^2)+1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*a^-2*b^2*d^-1*(b+a*cot(c+d*x))^-1*(a^2+b^2)^-2*cot(c+d*x)^5//2*(7*b^2+15*a^2))
@test integrate((a+b*tan(c+d*x))^-3*cot(c+d*x)^3//2, x) == :(-1//4*a^-3*d^-1*(a^2+b^2)^-2*cot(c+d*x)^(1/2)*(8*a^4+15*b^4+31*a^2*b^2)+(1/2)*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+(1/2)*a^-1*b^2*d^-1*(b+a*cot(c+d*x))^-2*(a^2+b^2)^-1*cot(c+d*x)^5//2+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*a^-7//2*b^5//2*d^-1*(a^2+b^2)^-3*(15*b^4+63*a^4+46*a^2*b^2)*arctan(a^(1/2)*b^-1//2*cot(c+d*x)^(1/2))+1//4*a^-2*b^2*d^-1*(b+a*cot(c+d*x))^-1*(a^2+b^2)^-2*cot(c+d*x)^3//2*(5*b^2+13*a^2))
@test integrate((a+b*tan(c+d*x))^-3*cot(c+d*x)^(1/2), x) == :((1/2)*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+(1/2)*a^-1*b^2*d^-1*(b+a*cot(c+d*x))^-2*(a^2+b^2)^-1*cot(c+d*x)^3//2+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+-1//4*a^-5//2*b^3//2*d^-1*(a^2+b^2)^-3*(3*b^4+35*a^4+6*a^2*b^2)*arctan(a^(1/2)*b^-1//2*cot(c+d*x)^(1/2))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*a^-2*b^2*d^-1*(b+a*cot(c+d*x))^-1*(a^2+b^2)^-2*cot(c+d*x)^(1/2)*(3*b^2+11*a^2))
@test integrate((a+b*tan(c+d*x))^-3*cot(c+d*x)^-1//2, x) == :((1/2)*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+(1/2)*a^-1*b^2*d^-1*(b+a*cot(c+d*x))^-2*(a^2+b^2)^-1*cot(c+d*x)^(1/2)+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+1//4*a^-3//2*b^(1/2)*d^-1*(a^2+b^2)^-3*(-1*b^4+15*a^4+-18*a^2*b^2)*arctan(a^(1/2)*b^-1//2*cot(c+d*x)^(1/2))+-1//4*b*a^-1*d^-1*(b+a*cot(c+d*x))^-1*(a^2+b^2)^-2*cot(c+d*x)^(1/2)*(b^2+9*a^2))
@test integrate((a+b*tan(c+d*x))^-3*cot(c+d*x)^-3//2, x) == :(-1*b*d^-1*(b+a*cot(c+d*x))^-2*(2*a^2+2*b^2)^-1*cot(c+d*x)^(1/2)+1//4*d^-1*(b+a*cot(c+d*x))^-1*(a^2+b^2)^-2*cot(c+d*x)^(1/2)*(-3*b^2+5*a^2)+(1/2)*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+-1//4*a^-1//2*b^-1//2*d^-1*(a^2+b^2)^-3*(3*a^4+3*b^4+-26*a^2*b^2)*arctan(a^(1/2)*b^-1//2*cot(c+d*x)^(1/2))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x)))
@test integrate((a+b*tan(c+d*x))^-3*cot(c+d*x)^-5//2, x) == :(a*d^-1*(b+a*cot(c+d*x))^-2*(2*a^2+2*b^2)^-1*cot(c+d*x)^(1/2)+(1/2)*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+-1//4*a^(1/2)*b^-3//2*d^-1*(a^2+b^2)^-3*(a^4+-15*b^4+18*a^2*b^2)*arctan(a^(1/2)*b^-1//2*cot(c+d*x)^(1/2))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+-1//4*a*b^-1*d^-1*(b+a*cot(c+d*x))^-1*(a^2+b^2)^-2*cot(c+d*x)^(1/2)*(a^2+-7*b^2))
@test integrate((a+b*tan(c+d*x))^-3*cot(c+d*x)^-7//2, x) == :((1/2)*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+-1*2^(1/2)*cot(c+d*x)^(1/2))+-1//2*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+b)*(a^2+b^2+-4*a*b)*arctan(1+2^(1/2)*cot(c+d*x)^(1/2))+-1//2*a^2*b^-1*d^-1*(b+a*cot(c+d*x))^-2*(a^2+b^2)^-1*cot(c+d*x)^(1/2)+-1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*log(1+-1*2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+-1//4*a^3//2*b^-5//2*d^-1*(a^2+b^2)^-3*(3*a^4+35*b^4+6*a^2*b^2)*arctan(a^(1/2)*b^-1//2*cot(c+d*x)^(1/2))+1//4*2^(1/2)*d^-1*(a^2+b^2)^-3*(a+-1b)*(a^2+b^2+4*a*b)*log(1+2^(1/2)*cot(c+d*x)^(1/2)+cot(c+d*x))+-1//4*a^2*b^-2*d^-1*(b+a*cot(c+d*x))^-1*(a^2+b^2)^-2*cot(c+d*x)^(1/2)*(3*a^2+11*b^2))
@test integrate((a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^7//2, x) == :(-2//5*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^5//2+d^-1*(-1b+im*a)^(1/2)*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(b+im*a)^(1/2)*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-2//15*b*a^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^3//2+1//15*a^-2*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)*(4*b^2+30*a^2))
@test integrate((a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^5//2, x) == :(-2//3*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^3//2+-2//3*b*a^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)+im*d^-1*(b+im*a)^(1/2)*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+im*d^-1*(-1b+im*a)^(1/2)*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^3//2, x) == :(-2*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)+d^-1*(b+im*a)^(1/2)*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(-1b+im*a)^(1/2)*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2), x) == :(-1*im*d^-1*(b+im*a)^(1/2)*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(-1b+im*a)^(1/2)*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^-1//2, x) == :(d^-1*(-1b+im*a)^(1/2)*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(b+im*a)^(1/2)*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+2*b^(1/2)*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^-3//2, x) == :(d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^-1//2+im*d^-1*(b+im*a)^(1/2)*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+im*d^-1*(-1b+im*a)^(1/2)*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+a*b^-1//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^3//2*cot(c+d*x)^9//2, x) == :(-16//35*b*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^5//2+-2//7*a*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^7//2+-1*d^-1*(b+im*a)^3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(-1b+im*a)^3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+1//105*a^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^3//2*(-6*b^2+70*a^2)+4//105*b*a^-2*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)*(3*b^2+70*a^2))
@test integrate((a+b*tan(c+d*x))^3//2*cot(c+d*x)^7//2, x) == :(-4//5*b*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^3//2+-2//5*a*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^5//2+1//5*a^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)*(-2*b^2+10*a^2)+im*d^-1*(b+im*a)^3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(-1b+im*a)^3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^3//2*cot(c+d*x)^5//2, x) == :(-8//3*b*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)+-2//3*a*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^3//2+d^-1*(b+im*a)^3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+d^-1*(-1b+im*a)^3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^3//2*cot(c+d*x)^3//2, x) == :(-2*a*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)+im*d^-1*(-1b+im*a)^3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(b+im*a)^3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^3//2*cot(c+d*x)^(1/2), x) == :(-1*d^-1*(b+im*a)^3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(-1b+im*a)^3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+2*b^3//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^3//2*cot(c+d*x)^-1//2, x) == :(b*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^-1//2+im*d^-1*(b+im*a)^3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(-1b+im*a)^3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+3*a*b^(1/2)*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^3//2*cot(c+d*x)^-3//2, x) == :((1/2)*d^-1*(a+b*tan(c+d*x))^3//2*cot(c+d*x)^-1//2+3//4*a*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^-1//2+d^-1*(b+im*a)^3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+d^-1*(-1b+im*a)^3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+1//4*b^-1//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(-8*b^2+3*a^2)*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^5//2*cot(c+d*x)^11//2, x) == :(-2//9*a^2*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^9//2+1//105*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^5//2*(-50*b^2+42*a^2)+d^-1*(-1b+im*a)^5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(b+im*a)^5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-38//63*a*b*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^7//2+-1//315*a^-2*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)*(-20*b^4+630*a^4+-966*a^2*b^2)+2//315*b*a^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^3//2*(-5*b^2+231*a^2))
@test integrate((a+b*tan(c+d*x))^5//2*cot(c+d*x)^9//2, x) == :(-2//7*a^2*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^7//2+1//21*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^3//2*(-18*b^2+14*a^2)+-6//7*a*b*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^5//2+im*d^-1*(b+im*a)^5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+im*d^-1*(-1b+im*a)^5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+2//21*b*a^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)*(-3*b^2+49*a^2))
@test integrate((a+b*tan(c+d*x))^5//2*cot(c+d*x)^7//2, x) == :(-2//5*a^2*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^5//2+1//15*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)*(-46*b^2+30*a^2)+d^-1*(b+im*a)^5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(-1b+im*a)^5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-22//15*a*b*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^3//2)
@test integrate((a+b*tan(c+d*x))^5//2*cot(c+d*x)^5//2, x) == :(-2//3*a^2*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^3//2+-14//3*a*b*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)+-1*im*d^-1*(b+im*a)^5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(-1b+im*a)^5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^5//2*cot(c+d*x)^3//2, x) == :(-2*a^2*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)+d^-1*(-1b+im*a)^5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(b+im*a)^5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+2*b^5//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^5//2*cot(c+d*x)^(1/2), x) == :(b^2*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^-1//2+im*d^-1*(b+im*a)^5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+im*d^-1*(-1b+im*a)^5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+5*a*b^3//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^5//2*cot(c+d*x)^-1//2, x) == :((1/2)*b^2*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^-3//2+d^-1*(b+im*a)^5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(-1b+im*a)^5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+9//4*a*b*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^-1//2+1//4*b^(1/2)*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(-8*b^2+15*a^2)*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^5//2*cot(c+d*x)^-3//2, x) == :(1//3*b^2*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^-5//2+1//8*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^-1//2*(-8*b^2+11*a^2)+13//12*a*b*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^-3//2+-1*im*d^-1*(b+im*a)^5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(-1b+im*a)^5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+5//8*a*b^-1//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*(a^2+-8*b^2)*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^-1//2*cot(c+d*x)^5//2, x) == :(-2//3*a^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^3//2+-1*d^-1*(b+im*a)^-1//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(-1b+im*a)^-1//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+4//3*b*a^-2*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2))
@test integrate((a+b*tan(c+d*x))^-1//2*cot(c+d*x)^3//2, x) == :(-2*a^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^(1/2)+im*d^-1*(b+im*a)^-1//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(-1b+im*a)^-1//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^-1//2*cot(c+d*x)^(1/2), x) == :(d^-1*(b+im*a)^-1//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+d^-1*(-1b+im*a)^-1//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^-1//2*cot(c+d*x)^-1//2, x) == :(im*d^-1*(-1b+im*a)^-1//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(b+im*a)^-1//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^-1//2*cot(c+d*x)^-3//2, x) == :(-1*d^-1*(b+im*a)^-1//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(-1b+im*a)^-1//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+2*b^-1//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^-1//2*cot(c+d*x)^-5//2, x) == :(b^-1*d^-1*(a+b*tan(c+d*x))^(1/2)*cot(c+d*x)^-1//2+im*d^-1*(b+im*a)^-1//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(-1b+im*a)^-1//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*a*b^-3//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^-3//2*cot(c+d*x)^5//2, x) == :(-2//3*a^-1*d^-1*(a+b*tan(c+d*x))^-1//2*cot(c+d*x)^3//2+8//3*b*a^-2*d^-1*(a+b*tan(c+d*x))^-1//2*cot(c+d*x)^(1/2)+-1*im*d^-1*(b+im*a)^-3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(-1b+im*a)^-3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+2//3*a^-3*b^2*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-1*cot(c+d*x)^-1//2*(5*a^2+8*b^2))
@test integrate((a+b*tan(c+d*x))^-3//2*cot(c+d*x)^3//2, x) == :(-2*a^-1*d^-1*(a+b*tan(c+d*x))^-1//2*cot(c+d*x)^(1/2)+d^-1*(-1b+im*a)^-3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(b+im*a)^-3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-2*b*a^-2*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-1*cot(c+d*x)^-1//2*(a^2+2*b^2))
@test integrate((a+b*tan(c+d*x))^-3//2*cot(c+d*x)^(1/2), x) == :(im*d^-1*(b+im*a)^-3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+im*d^-1*(-1b+im*a)^-3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+2*a^-1*b^2*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-1*cot(c+d*x)^-1//2)
@test integrate((a+b*tan(c+d*x))^-3//2*cot(c+d*x)^-1//2, x) == :(d^-1*(b+im*a)^-3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(-1b+im*a)^-3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-2*b*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-1*cot(c+d*x)^-1//2)
@test integrate((a+b*tan(c+d*x))^-3//2*cot(c+d*x)^-3//2, x) == :(2*a*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-1*cot(c+d*x)^-1//2+-1*im*d^-1*(b+im*a)^-3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(-1b+im*a)^-3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2)))
@test integrate((a+b*tan(c+d*x))^-3//2*cot(c+d*x)^-5//2, x) == :(d^-1*(-1b+im*a)^-3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(b+im*a)^-3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+2*b^-3//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+-2*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-1*cot(c+d*x)^-1//2)
@test integrate((a+b*tan(c+d*x))^-3//2*cot(c+d*x)^-7//2, x) == :(im*d^-1*(b+im*a)^-3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+im*d^-1*(-1b+im*a)^-3//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+b^-2*d^-1*(a+b*tan(c+d*x))^(1/2)*(a^2+b^2)^-1*cot(c+d*x)^-1//2*(b^2+3*a^2)+-3*a*b^-5//2*d^-1*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh(b^(1/2)*(a+b*tan(c+d*x))^-1//2*tan(c+d*x)^(1/2))+-2*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-1*cot(c+d*x)^-3//2)
@test integrate((a+b*tan(c+d*x))^-5//2*cot(c+d*x)^5//2, x) == :(-2//3*a^-1*d^-1*(a+b*tan(c+d*x))^-3//2*cot(c+d*x)^3//2+d^-1*(b+im*a)^-5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+d^-1*(-1b+im*a)^-5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+4*b*a^-2*d^-1*(a+b*tan(c+d*x))^-3//2*cot(c+d*x)^(1/2)+2//3*a^-3*b^2*d^-1*(a+b*tan(c+d*x))^-3//2*(a^2+b^2)^-1*cot(c+d*x)^-1//2*(7*a^2+8*b^2)+4//3*a^-4*b^2*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-2*cot(c+d*x)^-1//2*(4*a^4+8*b^4+15*a^2*b^2))
@test integrate((a+b*tan(c+d*x))^-5//2*cot(c+d*x)^3//2, x) == :(-2*a^-1*d^-1*(a+b*tan(c+d*x))^-3//2*cot(c+d*x)^(1/2)+im*d^-1*(-1b+im*a)^-5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(b+im*a)^-5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-2//3*b*a^-3*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-2*cot(c+d*x)^-1//2*(3*a^4+8*b^4+17*a^2*b^2)+-2//3*b*a^-2*d^-1*(a+b*tan(c+d*x))^-3//2*(a^2+b^2)^-1*cot(c+d*x)^-1//2*(3*a^2+4*b^2))
@test integrate((a+b*tan(c+d*x))^-5//2*cot(c+d*x)^(1/2), x) == :(-1*d^-1*(b+im*a)^-5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*d^-1*(-1b+im*a)^-5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+2//3*a^-1*b^2*d^-1*(a+b*tan(c+d*x))^-3//2*(a^2+b^2)^-1*cot(c+d*x)^-1//2+4//3*a^-2*b^2*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-2*cot(c+d*x)^-1//2*(b^2+4*a^2))
@test integrate((a+b*tan(c+d*x))^-5//2*cot(c+d*x)^-1//2, x) == :(-2*b*d^-1*(a+b*tan(c+d*x))^-3//2*(3*a^2+3*b^2)^-1*cot(c+d*x)^-1//2+im*d^-1*(b+im*a)^-5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(-1b+im*a)^-5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-2//3*b*a^-1*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-2*cot(c+d*x)^-1//2*(-1*b^2+5*a^2))
@test integrate((a+b*tan(c+d*x))^-5//2*cot(c+d*x)^-3//2, x) == :(d^-1*(b+im*a)^-5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+d^-1*(-1b+im*a)^-5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+2*a*d^-1*(a+b*tan(c+d*x))^-3//2*(3*a^2+3*b^2)^-1*cot(c+d*x)^-1//2+1//3*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-2*cot(c+d*x)^-1//2*(-8*b^2+4*a^2))
@test integrate((a+b*tan(c+d*x))^-5//2*cot(c+d*x)^-5//2, x) == :(im*d^-1*(-1b+im*a)^-5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctan((a+b*tan(c+d*x))^-1//2*(-1b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-1*im*d^-1*(b+im*a)^-5//2*cot(c+d*x)^(1/2)*tan(c+d*x)^(1/2)*arctanh((a+b*tan(c+d*x))^-1//2*(b+im*a)^(1/2)*tan(c+d*x)^(1/2))+-2//3*a^2*b^-1*d^-1*(a+b*tan(c+d*x))^-3//2*(a^2+b^2)^-1*cot(c+d*x)^-1//2+2//3*a*b^-1*d^-1*(a+b*tan(c+d*x))^-1//2*(a^2+b^2)^-2*cot(c+d*x)^-1//2*(a^2+7*b^2))
@test integrate((a+im*a*tan(e+f*x))^3*(c+-1*im*c*tan(e+f*x)), x) == :(-1//3*im*c*f^-1*(a+im*a*tan(e+f*x))^3)
@test integrate((a+im*a*tan(e+f*x))*(c+-1*im*c*tan(e+f*x)), x) == :(a*c*f^-1*tan(e+f*x))
@test integrate((a+im*a*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x)), x) == :(im*c*f^-1*(a+im*a*tan(e+f*x))^-1)
@test integrate((a+im*a*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x)), x) == :((1/2)*im*c*f^-1*(a+im*a*tan(e+f*x))^-2)
@test integrate((a+im*a*tan(e+f*x))^-3*(c+-1*im*c*tan(e+f*x)), x) == :(1//3*im*c*f^-1*(a+im*a*tan(e+f*x))^-3)
@test integrate((a+im*a*tan(e+f*x))^4*(c+-1*im*c*tan(e+f*x))^2, x) == :(-1//2*im*c^2*f^-1*(a+im*a*tan(e+f*x))^4+1//5*im*a^-1*c^2*f^-1*(a+im*a*tan(e+f*x))^5)
@test integrate((a+im*a*tan(e+f*x))^3*(c+-1*im*c*tan(e+f*x))^2, x) == :(a^3*c^2*f^-1*tan(e+f*x)+1//3*a^3*c^2*f^-1*tan(e+f*x)^3+1//4*im*a^3*c^2*f^-1*sec(e+f*x)^4)
@test integrate((a+im*a*tan(e+f*x))^2*(c+-1*im*c*tan(e+f*x))^2, x) == :(a^2*c^2*f^-1*tan(e+f*x)+1//3*a^2*c^2*f^-1*tan(e+f*x)^3)
@test integrate((a+im*a*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^2, x) == :(-1*x*a^-1*c^2+2*im*c^2*f^-1*(a+im*a*tan(e+f*x))^-1+-1*im*a^-1*c^2*f^-1*log(cos(e+f*x)))
@test integrate((a+im*a*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x))^2, x) == :(c^2*f^-1*(a+im*a*tan(e+f*x))^-2*tan(e+f*x))
@test integrate((a+im*a*tan(e+f*x))^-3*(c+-1*im*c*tan(e+f*x))^2, x) == :(2//3*im*c^2*f^-1*(a+im*a*tan(e+f*x))^-3+-1//2*im*a^-1*c^2*f^-1*(a+im*a*tan(e+f*x))^-2)
@test integrate((a+im*a*tan(e+f*x))^-4*(c+-1*im*c*tan(e+f*x))^2, x) == :((1/2)*im*c^2*f^-1*(a+im*a*tan(e+f*x))^-4+-1//3*im*a^2*c^2*f^-1*(a^2+im*a^2*tan(e+f*x))^-3)
@test integrate((a+im*a*tan(e+f*x))^5*(c+-1*im*c*tan(e+f*x))^3, x) == :(-4//5*im*c^3*f^-1*(a+im*a*tan(e+f*x))^5+-1//7*im*a^-2*c^3*f^-1*(a+im*a*tan(e+f*x))^7+2//3*im*a^-1*c^3*f^-1*(a+im*a*tan(e+f*x))^6)
@test integrate((a+im*a*tan(e+f*x))^4*(c+-1*im*c*tan(e+f*x))^3, x) == :(a^4*c^3*f^-1*tan(e+f*x)+1//5*a^4*c^3*f^-1*tan(e+f*x)^5+2//3*a^4*c^3*f^-1*tan(e+f*x)^3+1//6*im*a^4*c^3*f^-1*sec(e+f*x)^6)
@test integrate((a+im*a*tan(e+f*x))^3*(c+-1*im*c*tan(e+f*x))^3, x) == :(a^3*c^3*f^-1*tan(e+f*x)+1//5*a^3*c^3*f^-1*tan(e+f*x)^5+2//3*a^3*c^3*f^-1*tan(e+f*x)^3)
@test integrate((a+im*a*tan(e+f*x))^2*(c+-1*im*c*tan(e+f*x))^3, x) == :(a^2*c^3*f^-1*tan(e+f*x)+1//3*a^2*c^3*f^-1*tan(e+f*x)^3+-1//4*im*a^2*c^3*f^-1*sec(e+f*x)^4)
@test integrate((c+-1*im*c*tan(e+f*x))^3*(a+im*a*tan(e+f*x)), x) == :(1//3*im*a*f^-1*(c+-1*im*c*tan(e+f*x))^3)
@test integrate((a+im*a*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^3, x) == :(-4*x*a^-1*c^3+a^-1*c^3*f^-1*tan(e+f*x)+4*im*c^3*f^-1*(a+im*a*tan(e+f*x))^-1+-4*im*a^-1*c^3*f^-1*log(cos(e+f*x)))
@test integrate((a+im*a*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x))^3, x) == :(x*a^-2*c^3+-4*im*c^3*f^-1*(a^2+im*a^2*tan(e+f*x))^-1+2*im*c^3*f^-1*(a+im*a*tan(e+f*x))^-2+im*a^-2*c^3*f^-1*log(cos(e+f*x)))
@test integrate((a+im*a*tan(e+f*x))^-3*(c+-1*im*c*tan(e+f*x))^3, x) == :(1//6*im*c^3*f^-1*(a^2+-1*im*a^2*tan(e+f*x))^3*(a^3+im*a^3*tan(e+f*x))^-3)
@test integrate((a+im*a*tan(e+f*x))^-4*(c+-1*im*c*tan(e+f*x))^3, x) == :(im*c^3*f^-1*(a+im*a*tan(e+f*x))^-4+(1/2)*im*c^3*f^-1*(a^2+im*a^2*tan(e+f*x))^-2+-4//3*im*a^-1*c^3*f^-1*(a+im*a*tan(e+f*x))^-3)
@test integrate((a+im*a*tan(e+f*x))^-5*(c+-1*im*c*tan(e+f*x))^3, x) == :(4//5*im*c^3*f^-1*(a+im*a*tan(e+f*x))^-5+-1*im*a^3*c^3*f^-1*(a^2+im*a^2*tan(e+f*x))^-4+1//3*im*a^-2*c^3*f^-1*(a+im*a*tan(e+f*x))^-3)
@test integrate((a+im*a*tan(e+f*x))^5*(c+-1*im*c*tan(e+f*x))^4, x) == :(a^5*c^4*f^-1*tan(e+f*x)^3+a^5*c^4*f^-1*tan(e+f*x)+1//7*a^5*c^4*f^-1*tan(e+f*x)^7+3//5*a^5*c^4*f^-1*tan(e+f*x)^5+1//8*im*a^5*c^4*f^-1*sec(e+f*x)^8)
@test integrate((a+im*a*tan(e+f*x))^4*(c+-1*im*c*tan(e+f*x))^4, x) == :(a^4*c^4*f^-1*tan(e+f*x)^3+a^4*c^4*f^-1*tan(e+f*x)+1//7*a^4*c^4*f^-1*tan(e+f*x)^7+3//5*a^4*c^4*f^-1*tan(e+f*x)^5)
@test integrate((a+im*a*tan(e+f*x))^3*(c+-1*im*c*tan(e+f*x))^4, x) == :(a^3*c^4*f^-1*tan(e+f*x)+1//5*a^3*c^4*f^-1*tan(e+f*x)^5+2//3*a^3*c^4*f^-1*tan(e+f*x)^3+-1//6*im*a^3*c^4*f^-1*sec(e+f*x)^6)
@test integrate((a+im*a*tan(e+f*x))^2*(c+-1*im*c*tan(e+f*x))^4, x) == :((1/2)*im*a^2*f^-1*(c+-1*im*c*tan(e+f*x))^4+-1//5*im*a^2*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^5)
@test integrate((c+-1*im*c*tan(e+f*x))^4*(a+im*a*tan(e+f*x)), x) == :(1//4*im*a*f^-1*(c+-1*im*c*tan(e+f*x))^4)
@test integrate((a+im*a*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^4, x) == :(-12*x*a^-1*c^4+5*a^-1*c^4*f^-1*tan(e+f*x)+8*im*c^4*f^-1*(a+im*a*tan(e+f*x))^-1+-12*im*a^-1*c^4*f^-1*log(cos(e+f*x))+-1//2*im*a^-1*c^4*f^-1*tan(e+f*x)^2)
@test integrate((a+im*a*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x))^4, x) == :(6*x*a^-2*c^4+-1*a^-2*c^4*f^-1*tan(e+f*x)+-12*im*c^4*f^-1*(a^2+im*a^2*tan(e+f*x))^-1+4*im*c^4*f^-1*(a+im*a*tan(e+f*x))^-2+6*im*a^-2*c^4*f^-1*log(cos(e+f*x)))
@test integrate((a+im*a*tan(e+f*x))^-3*(c+-1*im*c*tan(e+f*x))^4, x) == :(-1*x*a^-3*c^4+6*im*c^4*f^-1*(a^3+im*a^3*tan(e+f*x))^-1+8//3*im*c^4*f^-1*(a+im*a*tan(e+f*x))^-3+-1*im*a^-3*c^4*f^-1*log(cos(e+f*x))+-6*im*a^-1*c^4*f^-1*(a+im*a*tan(e+f*x))^-2)
@test integrate((a+im*a*tan(e+f*x))^-4*(c+-1*im*c*tan(e+f*x))^4, x) == :(1//8*im*c^4*f^-1*(a^2+-1*im*a^2*tan(e+f*x))^4*(a^3+im*a^3*tan(e+f*x))^-4)
@test integrate((a+im*a*tan(e+f*x))^-5*(c+-1*im*c*tan(e+f*x))^4, x) == :(1//10*im*c^4*f^-1*(1+-1*im*tan(e+f*x))^4*(a+im*a*tan(e+f*x))^-5+1//80*im*a^-5*c^4*f^-1*(a+im*a*tan(e+f*x))^-4*(a+-1*im*a*tan(e+f*x))^4)
@test integrate((a+im*a*tan(e+f*x))^4*(c+-1*im*c*tan(e+f*x))^-1, x) == :(-12*x*a^4*c^-1+-8*im*a^4*f^-1*(c+-1*im*c*tan(e+f*x))^-1+5*a^4*c^-1*f^-1*tan(e+f*x)+(1/2)*im*a^4*c^-1*f^-1*tan(e+f*x)^2+12*im*a^4*c^-1*f^-1*log(cos(e+f*x)))
@test integrate((a+im*a*tan(e+f*x))^3*(c+-1*im*c*tan(e+f*x))^-1, x) == :(-4*x*a^3*c^-1+a^3*c^-1*f^-1*tan(e+f*x)+-4*im*a^3*f^-1*(c+-1*im*c*tan(e+f*x))^-1+4*im*a^3*c^-1*f^-1*log(cos(e+f*x)))
@test integrate((a+im*a*tan(e+f*x))^2*(c+-1*im*c*tan(e+f*x))^-1, x) == :(-1*x*a^2*c^-1+-2*im*a^2*f^-1*(c+-1*im*c*tan(e+f*x))^-1+im*a^2*c^-1*f^-1*log(cos(e+f*x)))
@test integrate((c+-1*im*c*tan(e+f*x))^-1*(a+im*a*tan(e+f*x)), x) == :(-1*im*a*f^-1*(c+-1*im*c*tan(e+f*x))^-1)
@test integrate((a+im*a*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^-1, x) == :((1/2)*x*a^-1*c^-1+(1/2)*a^-1*c^-1*f^-1*cos(e+f*x)*sin(e+f*x))
@test integrate((a+im*a*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x))^-1, x) == :(3//8*x*a^-2*c^-1+1//4*im*a^-2*c^-1*f^-1*cos(e+f*x)^4+1//4*a^-2*c^-1*f^-1*cos(e+f*x)^3*sin(e+f*x)+3//8*a^-2*c^-1*f^-1*cos(e+f*x)*sin(e+f*x))
@test integrate((a+im*a*tan(e+f*x))^-3*(c+-1*im*c*tan(e+f*x))^-1, x) == :(1//4*x*a^-3*c^-1+-1//16*im*a^-3*f^-1*(c+-1*im*c*tan(e+f*x))^-1+3//16*im*a^-3*f^-1*(c+im*c*tan(e+f*x))^-1+1//8*im*c*a^-3*f^-1*(c+im*c*tan(e+f*x))^-2+1//12*im*a^-3*c^2*f^-1*(c+im*c*tan(e+f*x))^-3)
@test integrate((a+im*a*tan(e+f*x))^4*(c+-1*im*c*tan(e+f*x))^-2, x) == :(6*x*a^4*c^-2+-1*a^4*c^-2*f^-1*tan(e+f*x)+-4*im*a^4*f^-1*(c+-1*im*c*tan(e+f*x))^-2+12*im*a^4*f^-1*(c^2+-1*im*c^2*tan(e+f*x))^-1+-6*im*a^4*c^-2*f^-1*log(cos(e+f*x)))
@test integrate((a+im*a*tan(e+f*x))^3*(c+-1*im*c*tan(e+f*x))^-2, x) == :(x*a^3*c^-2+-2*im*a^3*f^-1*(c+-1*im*c*tan(e+f*x))^-2+4*im*a^3*f^-1*(c^2+-1*im*c^2*tan(e+f*x))^-1+-1*im*a^3*c^-2*f^-1*log(cos(e+f*x)))
@test integrate((a+im*a*tan(e+f*x))^2*(c+-1*im*c*tan(e+f*x))^-2, x) == :(a^2*f^-1*(c+-1*im*c*tan(e+f*x))^-2*tan(e+f*x))
@test integrate((c+-1*im*c*tan(e+f*x))^-2*(a+im*a*tan(e+f*x)), x) == :(-1//2*im*a*f^-1*(c+-1*im*c*tan(e+f*x))^-2)
@test integrate((a+im*a*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^-2, x) == :(3//8*x*a^-1*c^-2+-1//4*im*a^-1*f^-1*(c^2+-1*im*c^2*tan(e+f*x))^-1+-1//8*im*a^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-2+1//8*im*a^-1*f^-1*(c^2+im*c^2*tan(e+f*x))^-1)
@test integrate((a+im*a*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x))^-2, x) == :(3//8*x*a^-2*c^-2+1//4*a^-2*c^-2*f^-1*cos(e+f*x)^3*sin(e+f*x)+3//8*a^-2*c^-2*f^-1*cos(e+f*x)*sin(e+f*x))
@test integrate((a+im*a*tan(e+f*x))^-3*(c+-1*im*c*tan(e+f*x))^-2, x) == :(5//16*x*a^-3*c^-2+1//6*im*a^-3*c^-2*f^-1*cos(e+f*x)^6+1//6*a^-3*c^-2*f^-1*cos(e+f*x)^5*sin(e+f*x)+5//16*a^-3*c^-2*f^-1*cos(e+f*x)*sin(e+f*x)+5//24*a^-3*c^-2*f^-1*cos(e+f*x)^3*sin(e+f*x))
@test integrate((a+im*a*tan(e+f*x))^6*(c+-1*im*c*tan(e+f*x))^-3, x) == :(-40*x*a^6*c^-3+-80*im*a^6*f^-1*(c^3+-1*im*c^3*tan(e+f*x))^-1+9*a^6*c^-3*f^-1*tan(e+f*x)+-32//3*im*a^6*f^-1*(c+-1*im*c*tan(e+f*x))^-3+(1/2)*im*a^6*c^-3*f^-1*tan(e+f*x)^2+40*im*a^6*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-2+40*im*a^6*c^-3*f^-1*log(cos(e+f*x)))
@test integrate((a+im*a*tan(e+f*x))^5*(c+-1*im*c*tan(e+f*x))^-3, x) == :(-8*x*a^5*c^-3+a^5*c^-3*f^-1*tan(e+f*x)+-24*im*a^5*f^-1*(c^3+-1*im*c^3*tan(e+f*x))^-1+-16//3*im*a^5*f^-1*(c+-1*im*c*tan(e+f*x))^-3+8*im*a^5*c^-3*f^-1*log(cos(e+f*x))+16*im*a^5*c^5*f^-1*(c^4+-1*im*c^4*tan(e+f*x))^-2)
@test integrate((a+im*a*tan(e+f*x))^4*(c+-1*im*c*tan(e+f*x))^-3, x) == :(-1*x*a^4*c^-3+-6*im*a^4*f^-1*(c^3+-1*im*c^3*tan(e+f*x))^-1+-8//3*im*a^4*f^-1*(c+-1*im*c*tan(e+f*x))^-3+im*a^4*c^-3*f^-1*log(cos(e+f*x))+6*im*a^4*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-2)
@test integrate((a+im*a*tan(e+f*x))^3*(c+-1*im*c*tan(e+f*x))^-3, x) == :(-1//6*im*a^3*f^-1*(c^2+im*c^2*tan(e+f*x))^3*(c^3+-1*im*c^3*tan(e+f*x))^-3)
@test integrate((a+im*a*tan(e+f*x))^2*(c+-1*im*c*tan(e+f*x))^-3, x) == :(-2//3*im*a^2*f^-1*(c+-1*im*c*tan(e+f*x))^-3+(1/2)*im*a^2*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-2)
@test integrate((c+-1*im*c*tan(e+f*x))^-3*(a+im*a*tan(e+f*x)), x) == :(-1//3*im*a*f^-1*(c+-1*im*c*tan(e+f*x))^-3)
@test integrate((a+im*a*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^-3, x) == :(1//4*x*a^-1*c^-3+-3//16*im*a^-1*f^-1*(c^3+-1*im*c^3*tan(e+f*x))^-1+-1//12*im*a^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-3+1//16*im*a^-1*f^-1*(c^3+im*c^3*tan(e+f*x))^-1+-1//8*im*a^-1*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-2)
@test integrate((a+im*a*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x))^-3, x) == :(5//16*x*a^-2*c^-3+-3//16*im*a^-2*f^-1*(c^3+-1*im*c^3*tan(e+f*x))^-1+-1//24*im*a^-2*f^-1*(c+-1*im*c*tan(e+f*x))^-3+1//8*im*a^-2*f^-1*(c^3+im*c^3*tan(e+f*x))^-1+-3//32*im*a^-2*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-2+1//32*im*a^-2*c^-1*f^-1*(c+im*c*tan(e+f*x))^-2)
@test integrate((a+im*a*tan(e+f*x))^-3*(c+-1*im*c*tan(e+f*x))^-3, x) == :(5//16*x*a^-3*c^-3+1//6*a^-3*c^-3*f^-1*cos(e+f*x)^5*sin(e+f*x)+5//16*a^-3*c^-3*f^-1*cos(e+f*x)*sin(e+f*x)+5//24*a^-3*c^-3*f^-1*cos(e+f*x)^3*sin(e+f*x))
@test integrate((a+im*a*tan(e+f*x))^6*(c+-1*im*c*tan(e+f*x))^-4, x) == :(10*x*a^6*c^-4+-1*a^6*c^-4*f^-1*tan(e+f*x)+-40*im*a^6*f^-1*(c^2+-1*im*c^2*tan(e+f*x))^-2+-8*im*a^6*f^-1*(c+-1*im*c*tan(e+f*x))^-4+40*im*a^6*f^-1*(c^4+-1*im*c^4*tan(e+f*x))^-1+-10*im*a^6*c^-4*f^-1*log(cos(e+f*x))+80//3*im*a^6*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-3)
@test integrate((a+im*a*tan(e+f*x))^5*(c+-1*im*c*tan(e+f*x))^-4, x) == :(x*a^5*c^-4+-12*im*a^5*f^-1*(c^2+-1*im*c^2*tan(e+f*x))^-2+-4*im*a^5*f^-1*(c+-1*im*c*tan(e+f*x))^-4+8*im*a^5*f^-1*(c^4+-1*im*c^4*tan(e+f*x))^-1+-1*im*a^5*c^-4*f^-1*log(cos(e+f*x))+32//3*im*a^5*c^5*f^-1*(c^3+-1*im*c^3*tan(e+f*x))^-3)
@test integrate((a+im*a*tan(e+f*x))^4*(c+-1*im*c*tan(e+f*x))^-4, x) == :(-1//8*im*a^4*f^-1*(c^2+im*c^2*tan(e+f*x))^4*(c^3+-1*im*c^3*tan(e+f*x))^-4)
@test integrate((a+im*a*tan(e+f*x))^3*(c+-1*im*c*tan(e+f*x))^-4, x) == :(-1*im*a^3*f^-1*(c+-1*im*c*tan(e+f*x))^-4+-1//2*im*a^3*f^-1*(c^2+-1*im*c^2*tan(e+f*x))^-2+4//3*im*a^3*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-3)
@test integrate((a+im*a*tan(e+f*x))^2*(c+-1*im*c*tan(e+f*x))^-4, x) == :(-1//2*im*a^2*f^-1*(c+-1*im*c*tan(e+f*x))^-4+1//3*im*a^2*c^2*f^-1*(c^2+-1*im*c^2*tan(e+f*x))^-3)
@test integrate((c+-1*im*c*tan(e+f*x))^-4*(a+im*a*tan(e+f*x)), x) == :(-1//4*im*a*f^-1*(c+-1*im*c*tan(e+f*x))^-4)
@test integrate((a+im*a*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^-4, x) == :(5//32*x*a^-1*c^-4+-3//32*im*a^-1*f^-1*(c^2+-1*im*c^2*tan(e+f*x))^-2+-1//8*im*a^-1*f^-1*(c^4+-1*im*c^4*tan(e+f*x))^-1+-1//16*im*a^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-4+1//32*im*a^-1*f^-1*(c^4+im*c^4*tan(e+f*x))^-1+-1//12*im*a^-1*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-3)
@test integrate((a+im*a*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x))^-4, x) == :(15//64*x*a^-2*c^-4+-5//32*im*a^-2*f^-1*(c^4+-1*im*c^4*tan(e+f*x))^-1+-3//32*im*a^-2*f^-1*(c^2+-1*im*c^2*tan(e+f*x))^-2+-1//32*im*a^-2*f^-1*(c+-1*im*c*tan(e+f*x))^-4+1//64*im*a^-2*f^-1*(c^2+im*c^2*tan(e+f*x))^-2+5//64*im*a^-2*f^-1*(c^4+im*c^4*tan(e+f*x))^-1+-1//16*im*a^-2*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-3)
@test integrate((a+im*a*tan(e+f*x))^-3*(c+-1*im*c*tan(e+f*x))^-4, x) == :(35//128*x*a^-3*c^-4+-5//32*im*a^-3*f^-1*(c^4+-1*im*c^4*tan(e+f*x))^-1+-5//64*im*a^-3*f^-1*(c^2+-1*im*c^2*tan(e+f*x))^-2+-1//64*im*a^-3*f^-1*(c+-1*im*c*tan(e+f*x))^-4+5//128*im*a^-3*f^-1*(c^2+im*c^2*tan(e+f*x))^-2+15//128*im*a^-3*f^-1*(c^4+im*c^4*tan(e+f*x))^-1+-1//24*im*a^-3*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-3+1//96*im*a^-3*c^-1*f^-1*(c+im*c*tan(e+f*x))^-3)
@test integrate((a+im*a*tan(e+f*x))^3*(c+-1*im*c*tan(e+f*x))^(1/2), x) == :(8*im*a^3*f^-1*(c+-1*im*c*tan(e+f*x))^(1/2)+-8//3*im*a^3*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^3//2+2//5*im*a^3*c^-2*f^-1*(c+-1*im*c*tan(e+f*x))^5//2)
@test integrate((a+im*a*tan(e+f*x))^2*(c+-1*im*c*tan(e+f*x))^(1/2), x) == :(4*im*a^2*f^-1*(c+-1*im*c*tan(e+f*x))^(1/2)+-2//3*im*a^2*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^3//2)
@test integrate((c+-1*im*c*tan(e+f*x))^(1/2)*(a+im*a*tan(e+f*x)), x) == :(2*im*a*f^-1*(c+-1*im*c*tan(e+f*x))^(1/2))
@test integrate((a+im*a*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^(1/2), x) == :((1/2)*im*a^-1*f^-1*(1+im*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^(1/2)+1//4*im*2^(1/2)*a^-1*c^(1/2)*f^-1*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*im*c*tan(e+f*x))^(1/2)))
@test integrate((a+im*a*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x))^(1/2), x) == :(1//4*im*a^-2*f^-1*(1+im*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x))^(1/2)+3//16*im*a^-2*f^-1*(1+im*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^(1/2)+3//32*im*2^(1/2)*a^-2*c^(1/2)*f^-1*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*im*c*tan(e+f*x))^(1/2)))
@test integrate((a+im*a*tan(e+f*x))^-3*(c+-1*im*c*tan(e+f*x))^(1/2), x) == :(1//6*im*a^-3*f^-1*(1+im*tan(e+f*x))^-3*(c+-1*im*c*tan(e+f*x))^(1/2)+5//48*im*a^-3*f^-1*(1+im*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x))^(1/2)+5//64*im*a^-3*f^-1*(1+im*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^(1/2)+5//128*im*2^(1/2)*a^-3*c^(1/2)*f^-1*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*im*c*tan(e+f*x))^(1/2)))
@test integrate((a+im*a*tan(e+f*x))^3*(c+-1*im*c*tan(e+f*x))^3//2, x) == :(8//3*im*a^3*f^-1*(c+-1*im*c*tan(e+f*x))^3//2+-8//5*im*a^3*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^5//2+2//7*im*a^3*c^-2*f^-1*(c+-1*im*c*tan(e+f*x))^7//2)
@test integrate((a+im*a*tan(e+f*x))^2*(c+-1*im*c*tan(e+f*x))^3//2, x) == :(4//3*im*a^2*f^-1*(c+-1*im*c*tan(e+f*x))^3//2+-2//5*im*a^2*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^5//2)
@test integrate((c+-1*im*c*tan(e+f*x))^3//2*(a+im*a*tan(e+f*x)), x) == :(2//3*im*a*f^-1*(c+-1*im*c*tan(e+f*x))^3//2)
@test integrate((a+im*a*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^3//2, x) == :(im*a^-1*c^2*f^-1*(c+im*c*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^(1/2)+-1//2*im*2^(1/2)*a^-1*c^3//2*f^-1*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*im*c*tan(e+f*x))^(1/2)))
@test integrate((a+im*a*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x))^3//2, x) == :((1/2)*im*a^-2*c^3*f^-1*(c+im*c*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x))^(1/2)+-1//8*im*a^-2*c^2*f^-1*(c+im*c*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^(1/2)+-1//16*im*2^(1/2)*a^-2*c^3//2*f^-1*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*im*c*tan(e+f*x))^(1/2)))
@test integrate((a+im*a*tan(e+f*x))^-3*(c+-1*im*c*tan(e+f*x))^3//2, x) == :(-1//24*im*a^-3*c^3*f^-1*(c+im*c*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x))^(1/2)+-1//32*im*a^-3*c^2*f^-1*(c+im*c*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^(1/2)+-1//64*im*2^(1/2)*a^-3*c^3//2*f^-1*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*im*c*tan(e+f*x))^(1/2))+1//3*im*a^-3*c^4*f^-1*(c+im*c*tan(e+f*x))^-3*(c+-1*im*c*tan(e+f*x))^(1/2))
@test integrate((a+im*a*tan(e+f*x))^3*(c+-1*im*c*tan(e+f*x))^5//2, x) == :(8//5*im*a^3*f^-1*(c+-1*im*c*tan(e+f*x))^5//2+-8//7*im*a^3*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^7//2+2//9*im*a^3*c^-2*f^-1*(c+-1*im*c*tan(e+f*x))^9//2)
@test integrate((a+im*a*tan(e+f*x))^2*(c+-1*im*c*tan(e+f*x))^5//2, x) == :(4//5*im*a^2*f^-1*(c+-1*im*c*tan(e+f*x))^5//2+-2//7*im*a^2*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^7//2)
@test integrate((c+-1*im*c*tan(e+f*x))^5//2*(a+im*a*tan(e+f*x)), x) == :(2//5*im*a*f^-1*(c+-1*im*c*tan(e+f*x))^5//2)
@test integrate((a+im*a*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^5//2, x) == :(3*im*a^-1*c^2*f^-1*(c+-1*im*c*tan(e+f*x))^(1/2)+im*a^-1*c^2*f^-1*(c+im*c*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^3//2+-3*im*2^(1/2)*a^-1*c^5//2*f^-1*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*im*c*tan(e+f*x))^(1/2)))
@test integrate((a+im*a*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x))^5//2, x) == :((1/2)*im*a^-2*c^3*f^-1*(c+im*c*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x))^3//2+-3//4*im*a^-2*c^3*f^-1*(c+im*c*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^(1/2)+3//8*im*2^(1/2)*a^-2*c^5//2*f^-1*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*im*c*tan(e+f*x))^(1/2)))
@test integrate((a+im*a*tan(e+f*x))^-3*(c+-1*im*c*tan(e+f*x))^5//2, x) == :(-1//4*im*a^-3*c^4*f^-1*(c+im*c*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x))^(1/2)+1//3*im*a^-3*c^4*f^-1*(c+im*c*tan(e+f*x))^-3*(c+-1*im*c*tan(e+f*x))^3//2+1//16*im*a^-3*c^3*f^-1*(c+im*c*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^(1/2)+1//32*im*2^(1/2)*a^-3*c^5//2*f^-1*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*im*c*tan(e+f*x))^(1/2)))
@test integrate((a+im*a*tan(e+f*x))^3*(c+-1*im*c*tan(e+f*x))^-1//2, x) == :(-8*im*a^3*f^-1*(c+-1*im*c*tan(e+f*x))^-1//2+-8*im*a^3*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^(1/2)+2//3*im*a^3*c^-2*f^-1*(c+-1*im*c*tan(e+f*x))^3//2)
@test integrate((a+im*a*tan(e+f*x))^2*(c+-1*im*c*tan(e+f*x))^-1//2, x) == :(-4*im*a^2*f^-1*(c+-1*im*c*tan(e+f*x))^-1//2+-2*im*a^2*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^(1/2))
@test integrate((c+-1*im*c*tan(e+f*x))^-1//2*(a+im*a*tan(e+f*x)), x) == :(-2*im*a*f^-1*(c+-1*im*c*tan(e+f*x))^-1//2)
@test integrate((a+im*a*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^-1//2, x) == :(-3//4*im*a^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-1//2+(1/2)*im*a^-1*f^-1*(1+im*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^-1//2+3//8*im*2^(1/2)*a^-1*c^-1//2*f^-1*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*im*c*tan(e+f*x))^(1/2)))
@test integrate((a+im*a*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x))^-1//2, x) == :(-15//32*im*a^-2*f^-1*(c+-1*im*c*tan(e+f*x))^-1//2+1//4*im*a^-2*f^-1*(1+im*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x))^-1//2+5//16*im*a^-2*f^-1*(1+im*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^-1//2+15//64*im*2^(1/2)*a^-2*c^-1//2*f^-1*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*im*c*tan(e+f*x))^(1/2)))
@test integrate((a+im*a*tan(e+f*x))^-3*(c+-1*im*c*tan(e+f*x))^-1//2, x) == :(-35//128*im*a^-3*f^-1*(c+-1*im*c*tan(e+f*x))^-1//2+1//6*im*a^-3*f^-1*(1+im*tan(e+f*x))^-3*(c+-1*im*c*tan(e+f*x))^-1//2+7//48*im*a^-3*f^-1*(1+im*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x))^-1//2+35//192*im*a^-3*f^-1*(1+im*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^-1//2+35//256*im*2^(1/2)*a^-3*c^-1//2*f^-1*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*im*c*tan(e+f*x))^(1/2)))
@test integrate((a+im*a*tan(e+f*x))^3*(c+-1*im*c*tan(e+f*x))^-3//2, x) == :(-8//3*im*a^3*f^-1*(c+-1*im*c*tan(e+f*x))^-3//2+2*im*a^3*c^-2*f^-1*(c+-1*im*c*tan(e+f*x))^(1/2)+8*im*a^3*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-1//2)
@test integrate((a+im*a*tan(e+f*x))^2*(c+-1*im*c*tan(e+f*x))^-3//2, x) == :(-4//3*im*a^2*f^-1*(c+-1*im*c*tan(e+f*x))^-3//2+2*im*a^2*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-1//2)
@test integrate((c+-1*im*c*tan(e+f*x))^-3//2*(a+im*a*tan(e+f*x)), x) == :(-2//3*im*a*f^-1*(c+-1*im*c*tan(e+f*x))^-3//2)
@test integrate((a+im*a*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^-3//2, x) == :(-5//12*im*a^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-3//2+(1/2)*im*a^-1*f^-1*(1+im*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^-3//2+-5//8*im*a^-1*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-1//2+5//16*im*2^(1/2)*a^-1*c^-3//2*f^-1*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*im*c*tan(e+f*x))^(1/2)))
@test integrate((a+im*a*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x))^-3//2, x) == :(-35//96*im*a^-2*f^-1*(c+-1*im*c*tan(e+f*x))^-3//2+-35//64*im*a^-2*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-1//2+1//4*im*a^-2*f^-1*(1+im*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x))^-3//2+7//16*im*a^-2*f^-1*(1+im*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^-3//2+35//128*im*2^(1/2)*a^-2*c^-3//2*f^-1*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*im*c*tan(e+f*x))^(1/2)))
@test integrate((a+im*a*tan(e+f*x))^-3*(c+-1*im*c*tan(e+f*x))^-3//2, x) == :(-35//128*im*a^-3*f^-1*(c+-1*im*c*tan(e+f*x))^-3//2+-105//256*im*a^-3*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-1//2+1//6*im*a^-3*f^-1*(1+im*tan(e+f*x))^-3*(c+-1*im*c*tan(e+f*x))^-3//2+3//16*im*a^-3*f^-1*(1+im*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x))^-3//2+21//64*im*a^-3*f^-1*(1+im*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^-3//2+105//512*im*2^(1/2)*a^-3*c^-3//2*f^-1*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*im*c*tan(e+f*x))^(1/2)))
@test integrate((a+im*a*tan(e+f*x))^3*(c+-1*im*c*tan(e+f*x))^-5//2, x) == :(-8//5*im*a^3*f^-1*(c+-1*im*c*tan(e+f*x))^-5//2+-2*im*a^3*c^-2*f^-1*(c+-1*im*c*tan(e+f*x))^-1//2+8//3*im*a^3*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-3//2)
@test integrate((a+im*a*tan(e+f*x))^2*(c+-1*im*c*tan(e+f*x))^-5//2, x) == :(-4//5*im*a^2*f^-1*(c+-1*im*c*tan(e+f*x))^-5//2+2//3*im*a^2*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-3//2)
@test integrate((c+-1*im*c*tan(e+f*x))^-5//2*(a+im*a*tan(e+f*x)), x) == :(-2//5*im*a*f^-1*(c+-1*im*c*tan(e+f*x))^-5//2)
@test integrate((a+im*a*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^-5//2, x) == :(-7//20*im*a^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-5//2+(1/2)*im*a^-1*f^-1*(1+im*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^-5//2+-7//16*im*a^-1*c^-2*f^-1*(c+-1*im*c*tan(e+f*x))^-1//2+-7//24*im*a^-1*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-3//2+7//32*im*2^(1/2)*a^-1*c^-5//2*f^-1*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*im*c*tan(e+f*x))^(1/2)))
@test integrate((a+im*a*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x))^-5//2, x) == :(-63//160*im*a^-2*f^-1*(c+-1*im*c*tan(e+f*x))^-5//2+-63//128*im*a^-2*c^-2*f^-1*(c+-1*im*c*tan(e+f*x))^-1//2+-21//64*im*a^-2*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-3//2+1//4*im*a^-2*f^-1*(1+im*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x))^-5//2+9//16*im*a^-2*f^-1*(1+im*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^-5//2+63//256*im*2^(1/2)*a^-2*c^-5//2*f^-1*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*im*c*tan(e+f*x))^(1/2)))
@test integrate((a+im*a*tan(e+f*x))^-3*(c+-1*im*c*tan(e+f*x))^-5//2, x) == :(-231//640*im*a^-3*f^-1*(c+-1*im*c*tan(e+f*x))^-5//2+-231//512*im*a^-3*c^-2*f^-1*(c+-1*im*c*tan(e+f*x))^-1//2+-77//256*im*a^-3*c^-1*f^-1*(c+-1*im*c*tan(e+f*x))^-3//2+1//6*im*a^-3*f^-1*(1+im*tan(e+f*x))^-3*(c+-1*im*c*tan(e+f*x))^-5//2+11//48*im*a^-3*f^-1*(1+im*tan(e+f*x))^-2*(c+-1*im*c*tan(e+f*x))^-5//2+33//64*im*a^-3*f^-1*(1+im*tan(e+f*x))^-1*(c+-1*im*c*tan(e+f*x))^-5//2+231//1024*im*2^(1/2)*a^-3*c^-5//2*f^-1*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*im*c*tan(e+f*x))^(1/2)))
@test integrate((a+im*a*tan(e+f*x))^5//2*(c+-1*im*c*tan(e+f*x))^(1/2), x) == :((1/2)*im*a*f^-1*(a+im*a*tan(e+f*x))^3//2*(c+-1*im*c*tan(e+f*x))^(1/2)+-3*im*a^5//2*c^(1/2)*f^-1*arctan(a^-1//2*c^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2)+3//2*im*a^2*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^(1/2))
@test integrate((a+im*a*tan(e+f*x))^3//2*(c+-1*im*c*tan(e+f*x))^(1/2), x) == :(im*a*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^(1/2)+-2*im*a^3//2*c^(1/2)*f^-1*arctan(a^-1//2*c^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2))
@test integrate((a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^(1/2), x) == :(-2*im*a^(1/2)*c^(1/2)*f^-1*arctan(a^-1//2*c^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2))
@test integrate((a+im*a*tan(e+f*x))^-1//2*(c+-1*im*c*tan(e+f*x))^(1/2), x) == :(im*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+-1*im*c*tan(e+f*x))^(1/2))
@test integrate((a+im*a*tan(e+f*x))^-3//2*(c+-1*im*c*tan(e+f*x))^(1/2), x) == :(1//3*im*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+-1*im*c*tan(e+f*x))^(1/2)+1//3*im*a^-1*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+-1*im*c*tan(e+f*x))^(1/2))
@test integrate((a+im*a*tan(e+f*x))^-5//2*(c+-1*im*c*tan(e+f*x))^(1/2), x) == :(1//5*im*f^-1*(a+im*a*tan(e+f*x))^-5//2*(c+-1*im*c*tan(e+f*x))^(1/2)+2//15*im*a^-1*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+-1*im*c*tan(e+f*x))^(1/2)+2//15*im*a^-2*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+-1*im*c*tan(e+f*x))^(1/2))
@test integrate((a+im*a*tan(e+f*x))^-7//2*(c+-1*im*c*tan(e+f*x))^(1/2), x) == :(1//7*im*f^-1*(a+im*a*tan(e+f*x))^-7//2*(c+-1*im*c*tan(e+f*x))^(1/2)+2//35*im*a^-3*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+-1*im*c*tan(e+f*x))^(1/2)+2//35*im*a^-2*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+-1*im*c*tan(e+f*x))^(1/2)+3//35*im*a^-1*f^-1*(a+im*a*tan(e+f*x))^-5//2*(c+-1*im*c*tan(e+f*x))^(1/2))
@test integrate((a+im*a*tan(e+f*x))^5//2*(c+-1*im*c*tan(e+f*x))^3//2, x) == :(-1*im*a^5//2*c^3//2*f^-1*arctan(a^-1//2*c^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2)+1//3*im*a*f^-1*(a+im*a*tan(e+f*x))^3//2*(c+-1*im*c*tan(e+f*x))^3//2+(1/2)*c*a^2*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^(1/2)*tan(e+f*x))
@test integrate((a+im*a*tan(e+f*x))^3//2*(c+-1*im*c*tan(e+f*x))^3//2, x) == :(-1*im*a^3//2*c^3//2*f^-1*arctan(a^-1//2*c^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2)+(1/2)*a*c*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^(1/2)*tan(e+f*x))
@test integrate((a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^3//2, x) == :(-1*im*c*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^(1/2)+-2*im*a^(1/2)*c^3//2*f^-1*arctan(a^-1//2*c^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2))
@test integrate((a+im*a*tan(e+f*x))^-1//2*(c+-1*im*c*tan(e+f*x))^3//2, x) == :(2*im*c*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+-1*im*c*tan(e+f*x))^(1/2)+2*im*a^-1//2*c^3//2*f^-1*arctan(a^-1//2*c^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2))
@test integrate((a+im*a*tan(e+f*x))^-3//2*(c+-1*im*c*tan(e+f*x))^3//2, x) == :(1//3*im*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+-1*im*c*tan(e+f*x))^3//2)
@test integrate((a+im*a*tan(e+f*x))^-5//2*(c+-1*im*c*tan(e+f*x))^3//2, x) == :(1//5*im*f^-1*(a+im*a*tan(e+f*x))^-5//2*(c+-1*im*c*tan(e+f*x))^3//2+1//15*im*a^-1*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+-1*im*c*tan(e+f*x))^3//2)
@test integrate((a+im*a*tan(e+f*x))^-7//2*(c+-1*im*c*tan(e+f*x))^3//2, x) == :(1//7*im*f^-1*(a+im*a*tan(e+f*x))^-7//2*(c+-1*im*c*tan(e+f*x))^3//2+2//35*im*a^-1*f^-1*(a+im*a*tan(e+f*x))^-5//2*(c+-1*im*c*tan(e+f*x))^3//2+2//105*im*a^-2*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+-1*im*c*tan(e+f*x))^3//2)
@test integrate((a+im*a*tan(e+f*x))^-9//2*(c+-1*im*c*tan(e+f*x))^3//2, x) == :(1//9*im*f^-1*(a+im*a*tan(e+f*x))^-9//2*(c+-1*im*c*tan(e+f*x))^3//2+1//21*im*a^-1*f^-1*(a+im*a*tan(e+f*x))^-7//2*(c+-1*im*c*tan(e+f*x))^3//2+2//105*im*a^-2*f^-1*(a+im*a*tan(e+f*x))^-5//2*(c+-1*im*c*tan(e+f*x))^3//2+2//315*im*a^-3*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+-1*im*c*tan(e+f*x))^3//2)
@test integrate((a+im*a*tan(e+f*x))^5//2*(c+-1*im*c*tan(e+f*x))^5//2, x) == :(-3//4*im*a^5//2*c^5//2*f^-1*arctan(a^-1//2*c^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2)+1//4*a*c*f^-1*(a+im*a*tan(e+f*x))^3//2*(c+-1*im*c*tan(e+f*x))^3//2*tan(e+f*x)+3//8*a^2*c^2*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^(1/2)*tan(e+f*x))
@test integrate((a+im*a*tan(e+f*x))^3//2*(c+-1*im*c*tan(e+f*x))^5//2, x) == :(-1*im*a^3//2*c^5//2*f^-1*arctan(a^-1//2*c^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2)+-1//3*im*c*f^-1*(a+im*a*tan(e+f*x))^3//2*(c+-1*im*c*tan(e+f*x))^3//2+(1/2)*a*c^2*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^(1/2)*tan(e+f*x))
@test integrate((a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^5//2, x) == :(-3*im*a^(1/2)*c^5//2*f^-1*arctan(a^-1//2*c^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2)+-3//2*im*c^2*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^(1/2)+-1//2*im*c*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^3//2)
@test integrate((a+im*a*tan(e+f*x))^-1//2*(c+-1*im*c*tan(e+f*x))^5//2, x) == :(2*im*c*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+-1*im*c*tan(e+f*x))^3//2+6*im*a^-1//2*c^5//2*f^-1*arctan(a^-1//2*c^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2)+3*im*a^-1*c^2*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^(1/2))
@test integrate((a+im*a*tan(e+f*x))^-3//2*(c+-1*im*c*tan(e+f*x))^5//2, x) == :(-2*im*a^-3//2*c^5//2*f^-1*arctan(a^-1//2*c^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2)+2//3*im*c*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+-1*im*c*tan(e+f*x))^3//2+-2*im*a^-1*c^2*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+-1*im*c*tan(e+f*x))^(1/2))
@test integrate((a+im*a*tan(e+f*x))^-5//2*(c+-1*im*c*tan(e+f*x))^5//2, x) == :(1//5*im*f^-1*(a+im*a*tan(e+f*x))^-5//2*(c+-1*im*c*tan(e+f*x))^5//2)
@test integrate((a+im*a*tan(e+f*x))^-7//2*(c+-1*im*c*tan(e+f*x))^5//2, x) == :(1//7*im*f^-1*(a+im*a*tan(e+f*x))^-7//2*(c+-1*im*c*tan(e+f*x))^5//2+1//35*im*a^-1*f^-1*(a+im*a*tan(e+f*x))^-5//2*(c+-1*im*c*tan(e+f*x))^5//2)
@test integrate((a+im*a*tan(e+f*x))^-9//2*(c+-1*im*c*tan(e+f*x))^5//2, x) == :(1//9*im*f^-1*(a+im*a*tan(e+f*x))^-9//2*(c+-1*im*c*tan(e+f*x))^5//2+2//63*im*a^-1*f^-1*(a+im*a*tan(e+f*x))^-7//2*(c+-1*im*c*tan(e+f*x))^5//2+2//315*im*a^-2*f^-1*(a+im*a*tan(e+f*x))^-5//2*(c+-1*im*c*tan(e+f*x))^5//2)
@test integrate((a+im*a*tan(e+f*x))^-11//2*(c+-1*im*c*tan(e+f*x))^5//2, x) == :(1//11*im*f^-1*(a+im*a*tan(e+f*x))^-11//2*(c+-1*im*c*tan(e+f*x))^5//2+1//33*im*a^-1*f^-1*(a+im*a*tan(e+f*x))^-9//2*(c+-1*im*c*tan(e+f*x))^5//2+2//231*im*a^-2*f^-1*(a+im*a*tan(e+f*x))^-7//2*(c+-1*im*c*tan(e+f*x))^5//2+2//1155*im*a^-3*f^-1*(a+im*a*tan(e+f*x))^-5//2*(c+-1*im*c*tan(e+f*x))^5//2)
@test integrate((a+im*a*tan(e+f*x))^7//2*(c+-1*im*c*tan(e+f*x))^-1//2, x) == :(-2*im*a*f^-1*(a+im*a*tan(e+f*x))^5//2*(c+-1*im*c*tan(e+f*x))^-1//2+15*im*a^7//2*c^-1//2*f^-1*arctan(a^-1//2*c^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2)+-15//2*im*a^3*c^-1*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^(1/2)+-5//2*im*a^2*c^-1*f^-1*(a+im*a*tan(e+f*x))^3//2*(c+-1*im*c*tan(e+f*x))^(1/2))
@test integrate((a+im*a*tan(e+f*x))^5//2*(c+-1*im*c*tan(e+f*x))^-1//2, x) == :(-2*im*a*f^-1*(a+im*a*tan(e+f*x))^3//2*(c+-1*im*c*tan(e+f*x))^-1//2+6*im*a^5//2*c^-1//2*f^-1*arctan(a^-1//2*c^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2)+-3*im*a^2*c^-1*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^(1/2))
@test integrate((a+im*a*tan(e+f*x))^3//2*(c+-1*im*c*tan(e+f*x))^-1//2, x) == :(-2*im*a*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2+2*im*a^3//2*c^-1//2*f^-1*arctan(a^-1//2*c^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2))
@test integrate((a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2, x) == :(-1*im*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2)
@test integrate((a+im*a*tan(e+f*x))^-1//2*(c+-1*im*c*tan(e+f*x))^-1//2, x) == :(f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+-1*im*c*tan(e+f*x))^-1//2*tan(e+f*x))
@test integrate((a+im*a*tan(e+f*x))^-3//2*(c+-1*im*c*tan(e+f*x))^-1//2, x) == :(1//3*im*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+-1*im*c*tan(e+f*x))^-1//2+2//3*a^-1*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+-1*im*c*tan(e+f*x))^-1//2*tan(e+f*x))
@test integrate((a+im*a*tan(e+f*x))^-5//2*(c+-1*im*c*tan(e+f*x))^-1//2, x) == :(1//5*im*f^-1*(a+im*a*tan(e+f*x))^-5//2*(c+-1*im*c*tan(e+f*x))^-1//2+1//5*im*a^-1*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+-1*im*c*tan(e+f*x))^-1//2+2//5*a^-2*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+-1*im*c*tan(e+f*x))^-1//2*tan(e+f*x))
@test integrate((a+im*a*tan(e+f*x))^-7//2*(c+-1*im*c*tan(e+f*x))^-1//2, x) == :(1//7*im*f^-1*(a+im*a*tan(e+f*x))^-7//2*(c+-1*im*c*tan(e+f*x))^-1//2+4//35*im*a^-1*f^-1*(a+im*a*tan(e+f*x))^-5//2*(c+-1*im*c*tan(e+f*x))^-1//2+4//35*im*a^-2*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+-1*im*c*tan(e+f*x))^-1//2+8//35*a^-3*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+-1*im*c*tan(e+f*x))^-1//2*tan(e+f*x))
@test integrate((a+im*a*tan(e+f*x))^9//2*(c+-1*im*c*tan(e+f*x))^-3//2, x) == :(-35*im*a^9//2*c^-3//2*f^-1*arctan(a^-1//2*c^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2)+-2//3*im*a*f^-1*(a+im*a*tan(e+f*x))^7//2*(c+-1*im*c*tan(e+f*x))^-3//2+14//3*im*a^2*c^-1*f^-1*(a+im*a*tan(e+f*x))^5//2*(c+-1*im*c*tan(e+f*x))^-1//2+35//2*im*a^4*c^-2*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^(1/2)+35//6*im*a^3*c^-2*f^-1*(a+im*a*tan(e+f*x))^3//2*(c+-1*im*c*tan(e+f*x))^(1/2))
@test integrate((a+im*a*tan(e+f*x))^7//2*(c+-1*im*c*tan(e+f*x))^-3//2, x) == :(-10*im*a^7//2*c^-3//2*f^-1*arctan(a^-1//2*c^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2)+-2//3*im*a*f^-1*(a+im*a*tan(e+f*x))^5//2*(c+-1*im*c*tan(e+f*x))^-3//2+5*im*a^3*c^-2*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^(1/2)+10//3*im*a^2*c^-1*f^-1*(a+im*a*tan(e+f*x))^3//2*(c+-1*im*c*tan(e+f*x))^-1//2)
@test integrate((a+im*a*tan(e+f*x))^5//2*(c+-1*im*c*tan(e+f*x))^-3//2, x) == :(-2*im*a^5//2*c^-3//2*f^-1*arctan(a^-1//2*c^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2)+-2//3*im*a*f^-1*(a+im*a*tan(e+f*x))^3//2*(c+-1*im*c*tan(e+f*x))^-3//2+2*im*a^2*c^-1*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2)
@test integrate((a+im*a*tan(e+f*x))^3//2*(c+-1*im*c*tan(e+f*x))^-3//2, x) == :(-1//3*im*f^-1*(a+im*a*tan(e+f*x))^3//2*(c+-1*im*c*tan(e+f*x))^-3//2)
@test integrate((a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-3//2, x) == :(-1//3*im*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-3//2+-1//3*im*c^-1*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2)
@test integrate((a+im*a*tan(e+f*x))^-1//2*(c+-1*im*c*tan(e+f*x))^-3//2, x) == :(im*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+-1*im*c*tan(e+f*x))^-3//2+-2//3*im*a^-1*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-3//2+-2//3*im*a^-1*c^-1*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2)
@test integrate((a+im*a*tan(e+f*x))^-3//2*(c+-1*im*c*tan(e+f*x))^-3//2, x) == :(1//3*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+-1*im*c*tan(e+f*x))^-3//2*tan(e+f*x)+2//3*a^-1*c^-1*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+-1*im*c*tan(e+f*x))^-1//2*tan(e+f*x))
@test integrate((a+im*a*tan(e+f*x))^-5//2*(c+-1*im*c*tan(e+f*x))^-3//2, x) == :(1//5*im*f^-1*(a+im*a*tan(e+f*x))^-5//2*(c+-1*im*c*tan(e+f*x))^-3//2+4//15*a^-1*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+-1*im*c*tan(e+f*x))^-3//2*tan(e+f*x)+8//15*a^-2*c^-1*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+-1*im*c*tan(e+f*x))^-1//2*tan(e+f*x))
@test integrate((a+im*a*tan(e+f*x))^-7//2*(c+-1*im*c*tan(e+f*x))^-3//2, x) == :(1//7*im*f^-1*(a+im*a*tan(e+f*x))^-7//2*(c+-1*im*c*tan(e+f*x))^-3//2+1//7*im*a^-1*f^-1*(a+im*a*tan(e+f*x))^-5//2*(c+-1*im*c*tan(e+f*x))^-3//2+4//21*a^-2*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+-1*im*c*tan(e+f*x))^-3//2*tan(e+f*x)+8//21*a^-3*c^-1*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+-1*im*c*tan(e+f*x))^-1//2*tan(e+f*x))
@test integrate((a+im*a*tan(e+f*x))^11//2*(c+-1*im*c*tan(e+f*x))^-5//2, x) == :(63*im*a^11//2*c^-5//2*f^-1*arctan(a^-1//2*c^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2)+-2//5*im*a*f^-1*(a+im*a*tan(e+f*x))^9//2*(c+-1*im*c*tan(e+f*x))^-5//2+-63//2*im*a^5*c^-3*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^(1/2)+-42//5*im*a^3*c^-2*f^-1*(a+im*a*tan(e+f*x))^5//2*(c+-1*im*c*tan(e+f*x))^-1//2+-21//2*im*a^4*c^-3*f^-1*(a+im*a*tan(e+f*x))^3//2*(c+-1*im*c*tan(e+f*x))^(1/2)+6//5*im*a^2*c^-1*f^-1*(a+im*a*tan(e+f*x))^7//2*(c+-1*im*c*tan(e+f*x))^-3//2)
@test integrate((a+im*a*tan(e+f*x))^9//2*(c+-1*im*c*tan(e+f*x))^-5//2, x) == :(14*im*a^9//2*c^-5//2*f^-1*arctan(a^-1//2*c^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2)+-2//5*im*a*f^-1*(a+im*a*tan(e+f*x))^7//2*(c+-1*im*c*tan(e+f*x))^-5//2+-7*im*a^4*c^-3*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^(1/2)+-14//3*im*a^3*c^-2*f^-1*(a+im*a*tan(e+f*x))^3//2*(c+-1*im*c*tan(e+f*x))^-1//2+14//15*im*a^2*c^-1*f^-1*(a+im*a*tan(e+f*x))^5//2*(c+-1*im*c*tan(e+f*x))^-3//2)
@test integrate((a+im*a*tan(e+f*x))^7//2*(c+-1*im*c*tan(e+f*x))^-5//2, x) == :(2*im*a^7//2*c^-5//2*f^-1*arctan(a^-1//2*c^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2)+-2//5*im*a*f^-1*(a+im*a*tan(e+f*x))^5//2*(c+-1*im*c*tan(e+f*x))^-5//2+-2*im*a^3*c^-2*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2+2//3*im*a^2*c^-1*f^-1*(a+im*a*tan(e+f*x))^3//2*(c+-1*im*c*tan(e+f*x))^-3//2)
@test integrate((a+im*a*tan(e+f*x))^5//2*(c+-1*im*c*tan(e+f*x))^-5//2, x) == :(-1//5*im*f^-1*(a+im*a*tan(e+f*x))^5//2*(c+-1*im*c*tan(e+f*x))^-5//2)
@test integrate((a+im*a*tan(e+f*x))^3//2*(c+-1*im*c*tan(e+f*x))^-5//2, x) == :(-1//5*im*f^-1*(a+im*a*tan(e+f*x))^3//2*(c+-1*im*c*tan(e+f*x))^-5//2+-1//15*im*c^-1*f^-1*(a+im*a*tan(e+f*x))^3//2*(c+-1*im*c*tan(e+f*x))^-3//2)
@test integrate((a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-5//2, x) == :(-1//5*im*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-5//2+-2//15*im*c^-1*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-3//2+-2//15*im*c^-2*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2)
@test integrate((a+im*a*tan(e+f*x))^-1//2*(c+-1*im*c*tan(e+f*x))^-5//2, x) == :(im*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+-1*im*c*tan(e+f*x))^-5//2+-3//5*im*a^-1*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-5//2+-2//5*im*a^-1*c^-1*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-3//2+-2//5*im*a^-1*c^-2*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2)
@test integrate((a+im*a*tan(e+f*x))^-3//2*(c+-1*im*c*tan(e+f*x))^-5//2, x) == :(1//3*im*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+-1*im*c*tan(e+f*x))^-5//2+-4//5*im*a^-2*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-5//2+4//3*im*a^-1*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+-1*im*c*tan(e+f*x))^-5//2+-8//15*im*a^-2*c^-1*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-3//2+-8//15*im*a^-2*c^-2*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+-1*im*c*tan(e+f*x))^-1//2)
@test integrate((a+im*a*tan(e+f*x))^-5//2*(c+-1*im*c*tan(e+f*x))^-5//2, x) == :(1//5*f^-1*(a+im*a*tan(e+f*x))^-5//2*(c+-1*im*c*tan(e+f*x))^-5//2*tan(e+f*x)+4//15*a^-1*c^-1*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+-1*im*c*tan(e+f*x))^-3//2*tan(e+f*x)+8//15*a^-2*c^-2*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+-1*im*c*tan(e+f*x))^-1//2*tan(e+f*x))
@test integrate((a+im*a*tan(e+f*x))^-7//2*(c+-1*im*c*tan(e+f*x))^-5//2, x) == :(1//7*im*f^-1*(a+im*a*tan(e+f*x))^-7//2*(c+-1*im*c*tan(e+f*x))^-5//2+6//35*a^-1*f^-1*(a+im*a*tan(e+f*x))^-5//2*(c+-1*im*c*tan(e+f*x))^-5//2*tan(e+f*x)+8//35*a^-2*c^-1*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+-1*im*c*tan(e+f*x))^-3//2*tan(e+f*x)+16//35*a^-3*c^-2*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+-1*im*c*tan(e+f*x))^-1//2*tan(e+f*x))
@test integrate((a+im*a*tan(e+f*x))^4*(c+-1*im*c*tan(e+f*x))^n, x) == :(8*im*a^4*f^-1*n^-1*(c+-1*im*c*tan(e+f*x))^n+-1*im*a^4*c^-3*f^-1*(3+n)^-1*(c+-1*im*c*tan(e+f*x))^(3+n)+-12*im*a^4*c^-1*f^-1*(1+n)^-1*(c+-1*im*c*tan(e+f*x))^(1+n)+6*im*a^4*c^-2*f^-1*(2+n)^-1*(c+-1*im*c*tan(e+f*x))^(2+n))
@test integrate((a+im*a*tan(e+f*x))^3*(c+-1*im*c*tan(e+f*x))^n, x) == :(4*im*a^3*f^-1*n^-1*(c+-1*im*c*tan(e+f*x))^n+im*a^3*c^-2*f^-1*(2+n)^-1*(c+-1*im*c*tan(e+f*x))^(2+n)+-4*im*a^3*c^-1*f^-1*(1+n)^-1*(c+-1*im*c*tan(e+f*x))^(1+n))
@test integrate((a+im*a*tan(e+f*x))^2*(c+-1*im*c*tan(e+f*x))^n, x) == :(2*im*a^2*f^-1*n^-1*(c+-1*im*c*tan(e+f*x))^n+-1*im*a^2*c^-1*f^-1*(1+n)^-1*(c+-1*im*c*tan(e+f*x))^(1+n))
@test integrate((c+-1*im*c*tan(e+f*x))^n*(a+im*a*tan(e+f*x)), x) == :(im*a*f^-1*n^-1*(c+-1*im*c*tan(e+f*x))^n)
@test integrate((a+im*a*tan(e+f*x))^m*(c+-1*im*c*tan(e+f*x))^4, x) == :(-8*im*c^4*f^-1*m^-1*(a+im*a*tan(e+f*x))^m+im*a^-3*c^4*f^-1*(3+m)^-1*(a+im*a*tan(e+f*x))^(3+m)+-6*im*a^-2*c^4*f^-1*(2+m)^-1*(a+im*a*tan(e+f*x))^(2+m)+12*im*a^-1*c^4*f^-1*(1+m)^-1*(a+im*a*tan(e+f*x))^(1+m))
@test integrate((a+im*a*tan(e+f*x))^m*(c+-1*im*c*tan(e+f*x))^3, x) == :(-4*im*c^3*f^-1*m^-1*(a+im*a*tan(e+f*x))^m+-1*im*a^-2*c^3*f^-1*(2+m)^-1*(a+im*a*tan(e+f*x))^(2+m)+4*im*a^-1*c^3*f^-1*(1+m)^-1*(a+im*a*tan(e+f*x))^(1+m))
@test integrate((a+im*a*tan(e+f*x))^m*(c+-1*im*c*tan(e+f*x))^2, x) == :(-2*im*c^2*f^-1*m^-1*(a+im*a*tan(e+f*x))^m+im*a^-1*c^2*f^-1*(1+m)^-1*(a+im*a*tan(e+f*x))^(1+m))
@test integrate((a+im*a*tan(e+f*x))^m*(c+-1*im*c*tan(e+f*x)), x) == :(-1*im*c*f^-1*m^-1*(a+im*a*tan(e+f*x))^m)
@test integrate((a+im*a*tan(e+f*x))^3*(c+d*tan(e+f*x)), x) == :(4*x*a^3*(c+-1*im*d)+1//3*d*f^-1*(a+im*a*tan(e+f*x))^3+(1/2)*a*f^-1*(a+im*a*tan(e+f*x))^2*(d+im*c)+-4*a^3*f^-1*(d+im*c)*log(cos(e+f*x))+-2*a^3*f^-1*(c+-1*im*d)*tan(e+f*x))
@test integrate((a+im*a*tan(e+f*x))^2*(c+d*tan(e+f*x)), x) == :((1/2)*d*f^-1*(a+im*a*tan(e+f*x))^2+2*x*a^2*(c+-1*im*d)+-1*a^2*f^-1*(c+-1*im*d)*tan(e+f*x)+-2*a^2*f^-1*(d+im*c)*log(cos(e+f*x)))
@test integrate((a+im*a*tan(e+f*x))*(c+d*tan(e+f*x)), x) == :(a*x*(c+-1*im*d)+-1*a*f^-1*(d+im*c)*log(cos(e+f*x))+im*a*d*f^-1*tan(e+f*x))
@test integrate((a+im*a*tan(e+f*x))^-1*(c+d*tan(e+f*x)), x) == :((1/2)*x*a^-1*(c+-1*im*d)+(1/2)*f^-1*(a+im*a*tan(e+f*x))^-1*(-1d+im*c))
@test integrate((a+im*a*tan(e+f*x))^-2*(c+d*tan(e+f*x)), x) == :(1//4*x*a^-2*(c+-1*im*d)+1//4*f^-1*(a+im*a*tan(e+f*x))^-2*(-1d+im*c)+1//4*f^-1*(a^2+im*a^2*tan(e+f*x))^-1*(d+im*c))
@test integrate((a+im*a*tan(e+f*x))^-3*(c+d*tan(e+f*x)), x) == :(1//6*f^-1*(a+im*a*tan(e+f*x))^-3*(-1d+im*c)+1//8*x*a^-3*(c+-1*im*d)+1//8*f^-1*(a^3+im*a^3*tan(e+f*x))^-1*(d+im*c)+1//8*a^-1*f^-1*(a+im*a*tan(e+f*x))^-2*(d+im*c))
@test integrate((a+im*a*tan(e+f*x))^3*(c+d*tan(e+f*x))^2, x) == :(4*x*a^3*(c+-1*im*d)^2+-2*a^3*f^-1*(c+-1*im*d)^2*tan(e+f*x)+2//3*c*d*f^-1*(a+im*a*tan(e+f*x))^3+(1/2)*im*a*f^-1*(a+im*a*tan(e+f*x))^2*(c+-1*im*d)^2+-4*im*a^3*f^-1*(c+-1*im*d)^2*log(cos(e+f*x))+-1//4*im*a^-1*d^2*f^-1*(a+im*a*tan(e+f*x))^4)
@test integrate((a+im*a*tan(e+f*x))^2*(c+d*tan(e+f*x))^2, x) == :(2*x*a^2*(c+-1*im*d)^2+c*d*f^-1*(a+im*a*tan(e+f*x))^2+-1*a^2*f^-1*(c+-1*im*d)^2*tan(e+f*x)+-2*im*a^2*f^-1*(c+-1*im*d)^2*log(cos(e+f*x))+-1//3*im*a^-1*d^2*f^-1*(a+im*a*tan(e+f*x))^3)
@test integrate((c+d*tan(e+f*x))^2*(a+im*a*tan(e+f*x)), x) == :(a*x*(c+-1*im*d)^2+(1/2)*im*a*f^-1*(c+d*tan(e+f*x))^2+a*d*f^-1*(d+im*c)*tan(e+f*x)+-1*im*a*f^-1*(c+-1*im*d)^2*log(cos(e+f*x)))
@test integrate((a+im*a*tan(e+f*x))^-1*(c+d*tan(e+f*x))^2, x) == :((1/2)*x*a^-1*(c^2+d^2+-2*im*c*d)+(1/2)*im*f^-1*(a+im*a*tan(e+f*x))^-1*(c+im*d)^2+im*a^-1*d^2*f^-1*log(cos(e+f*x)))
@test integrate((a+im*a*tan(e+f*x))^-2*(c+d*tan(e+f*x))^2, x) == :(1//4*x*a^-2*(c+-1*im*d)^2+1//4*im*f^-1*(a+im*a*tan(e+f*x))^-2*(c+im*d)^2+1//4*a^-2*f^-1*(1+im*tan(e+f*x))^-1*(c+im*d)*(3d+im*c))
@test integrate((a+im*a*tan(e+f*x))^-3*(c+d*tan(e+f*x))^2, x) == :(1//8*x*a^-3*(c+-1*im*d)^2+1//6*im*f^-1*(a+im*a*tan(e+f*x))^-3*(c+im*d)^2+1//8*im*f^-1*(c+-1*im*d)^2*(a^3+im*a^3*tan(e+f*x))^-1+1//8*a^-1*f^-1*(a+im*a*tan(e+f*x))^-2*(c+im*d)*(3d+im*c))
@test integrate((a+im*a*tan(e+f*x))^3*(c+d*tan(e+f*x))^3, x) == :(4*x*a^3*(c+-1*im*d)^3+2*a^3*f^-1*(c+d*tan(e+f*x))^2*(d+im*c)+4*a^3*f^-1*(d+im*c)^3*log(cos(e+f*x))+-1//5*d^-1*f^-1*(c+d*tan(e+f*x))^4*(a^3+im*a^3*tan(e+f*x))+4//3*im*a^3*f^-1*(c+d*tan(e+f*x))^3+1//20*a^3*d^-2*f^-1*(c+d*tan(e+f*x))^4*(-11d+im*c)+4*im*d*a^3*f^-1*(c+-1*im*d)^2*tan(e+f*x))
@test integrate((a+im*a*tan(e+f*x))^2*(c+d*tan(e+f*x))^3, x) == :(2*x*a^2*(c+-1*im*d)^3+a^2*f^-1*(c+d*tan(e+f*x))^2*(d+im*c)+2*a^2*f^-1*(d+im*c)^3*log(cos(e+f*x))+-1//4*a^2*d^-1*f^-1*(c+d*tan(e+f*x))^4+2//3*im*a^2*f^-1*(c+d*tan(e+f*x))^3+2*im*d*a^2*f^-1*(c+-1*im*d)^2*tan(e+f*x))
@test integrate((c+d*tan(e+f*x))^3*(a+im*a*tan(e+f*x)), x) == :(a*x*(c+-1*im*d)^3+a*f^-1*(d+im*c)^3*log(cos(e+f*x))+(1/2)*a*f^-1*(c+d*tan(e+f*x))^2*(d+im*c)+1//3*im*a*f^-1*(c+d*tan(e+f*x))^3+im*a*d*f^-1*(c+-1*im*d)^2*tan(e+f*x))
@test integrate((a+im*a*tan(e+f*x))^-1*(c+d*tan(e+f*x))^3, x) == :((1/2)*x*a^-1*(c^3+3*im*d^3+3*c*d^2+-3*im*d*c^2)+(1/2)*f^-1*(a+im*a*tan(e+f*x))^-1*(c+d*tan(e+f*x))^2*(-1d+im*c)+a^-1*d^2*f^-1*(-1d+3*im*c)*log(cos(e+f*x))+-1//2*a^-1*d^2*f^-1*(c+3*im*d)*tan(e+f*x))
@test integrate((a+im*a*tan(e+f*x))^-2*(c+d*tan(e+f*x))^3, x) == :(1//4*x*a^-2*(c^3+-3*im*d^3+-3*c*d^2+-3*im*d*c^2)+a^-2*d^3*f^-1*log(cos(e+f*x))+1//4*f^-1*(a+im*a*tan(e+f*x))^-2*(c+d*tan(e+f*x))^2*(-1d+im*c)+1//4*a^-2*f^-1*(1+im*tan(e+f*x))^-1*(c+im*d)^2*(3d+im*c))
@test integrate((a+im*a*tan(e+f*x))^-3*(c+d*tan(e+f*x))^3, x) == :(1//8*x*a^-3*(c+-1*im*d)^3+1//6*im*f^-1*(a+im*a*tan(e+f*x))^-3*(c+d*tan(e+f*x))^3+1//8*a^-1*f^-1*(a+im*a*tan(e+f*x))^-2*(c+im*d)^2*(d+im*c)+1//8*a^-3*f^-1*(1+im*tan(e+f*x))^-1*(c+im*d)*(c+-3*im*d)*(d+im*c))
@test integrate((a+im*a*tan(e+f*x))^3*(c+d*tan(e+f*x))^-1, x) == :(-1*d^-1*f^-1*(a^3+im*a^3*tan(e+f*x))+4*x*a^3*(c+-1*im*d)^-1+-1*a^3*d^-2*f^-1*(-3d+im*c)*log(cos(e+f*x))+-1*a^3*d^-2*f^-1*(c+im*d)^2*(d+im*c)^-1*log(c*cos(e+f*x)+d*sin(e+f*x)))
@test integrate((a+im*a*tan(e+f*x))^2*(c+d*tan(e+f*x))^-1, x) == :(x*a^2*d^-2*(c+2*im*d)+a^2*d^-1*f^-1*log(cos(e+f*x))+-1*c*x*a^2*d^-2*(c+-1*im*d)^-1*(c+im*d)+-1*a^2*d^-1*f^-1*(d+im*c)^-1*(-1d+im*c)*log(c*cos(e+f*x)+d*sin(e+f*x)))
@test integrate((c+d*tan(e+f*x))^-1*(a+im*a*tan(e+f*x)), x) == :(a*x*(c+-1*im*d)^-1+a*f^-1*(d+im*c)^-1*log(c*cos(e+f*x)+d*sin(e+f*x)))
@test integrate((a+im*a*tan(e+f*x))^-1*(c+d*tan(e+f*x))^-1, x) == :((1/2)*x*a^-1*(c+im*d)^-1+-1*f^-1*(a+im*a*tan(e+f*x))^-1*(-2d+2*im*c)^-1+-1*c*d*x*a^-1*(c^2+d^2)^-1*(-1d+im*c)^-1+-1*a^-1*d^2*f^-1*(c^2+d^2)^-1*(-1d+im*c)^-1*log(c*cos(e+f*x)+d*sin(e+f*x)))
@test integrate((a+im*a*tan(e+f*x))^-2*(c+d*tan(e+f*x))^-1, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-2*(-4d+4*im*c)^-1+1//4*x*a^-2*(c+im*d)^-3*(c+-1*im*d)^-1*(c^3+-3*c*d^2+3*im*d^3+3*im*d*c^2)+1//4*a^-2*f^-1*(1+im*tan(e+f*x))^-1*(c+im*d)^-2*(-3d+im*c)+-1*a^-2*d^3*f^-1*(c+im*d)^-3*(c+-1*im*d)^-1*log(c*cos(e+f*x)+d*sin(e+f*x)))
@test integrate((a+im*a*tan(e+f*x))^-3*(c+d*tan(e+f*x))^-1, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-3*(-6d+6*im*c)^-1+1//8*f^-1*(a^3+im*a^3*tan(e+f*x))^-1*(-1d+im*c)^-3*(c^2+-7*d^2+4*im*c*d)+1//8*x*a^-3*(c+im*d)^-4*(c+-1*im*d)^-1*(c^4+-7*d^4+-6*c^2*d^2+-4*im*c*d^3+4*im*d*c^3)+1//8*a^-1*f^-1*(a+im*a*tan(e+f*x))^-2*(c+im*d)^-2*(-3d+im*c)+a^-3*d^4*f^-1*(c+im*d)^-4*(d+im*c)^-1*log(c*cos(e+f*x)+d*sin(e+f*x)))
@test integrate((a+im*a*tan(e+f*x))^3*(c+d*tan(e+f*x))^-2, x) == :(4*x*a^3*(c+-1*im*d)^-2+im*a^3*d^-2*f^-1*log(cos(e+f*x))+d^-1*f^-1*(c+d*tan(e+f*x))^-1*(c+-1*im*d)^-1*(c+im*d)*(a^3+im*a^3*tan(e+f*x))+-1*a^3*d^-2*f^-1*(c+-1*im*d)^-2*(c+-3*im*d)*(-1d+im*c)*log(c*cos(e+f*x)+d*sin(e+f*x)))
@test integrate((a+im*a*tan(e+f*x))^2*(c+d*tan(e+f*x))^-2, x) == :(2*x*a^2*(c+-1*im*d)^-2+-2*im*a^2*f^-1*(c+-1*im*d)^-2*log(c*cos(e+f*x)+d*sin(e+f*x))+a^2*d^-1*f^-1*(c+d*tan(e+f*x))^-1*(d+im*c)^-1*(-1d+im*c))
@test integrate((c+d*tan(e+f*x))^-2*(a+im*a*tan(e+f*x)), x) == :(a*x*(c+-1*im*d)^-2+-1*a*f^-1*(c+d*tan(e+f*x))^-1*(d+im*c)^-1+-1*im*a*f^-1*(c+-1*im*d)^-2*log(c*cos(e+f*x)+d*sin(e+f*x)))
@test integrate((a+im*a*tan(e+f*x))^-1*(c+d*tan(e+f*x))^-2, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-1*(c+d*tan(e+f*x))^-1*(-2d+2*im*c)^-1+(1/2)*x*a^-1*(c+im*d)^-3*(c+-1*im*d)^-2*(c^3+-3*im*d^3+3*c*d^2+3*im*d*c^2)+a^-1*d^2*f^-1*(c+-1*im*d)^-2*(-1d+im*c)^-3*(3c+-1*im*d)*log(c*cos(e+f*x)+d*sin(e+f*x))+(1/2)*d*a^-1*f^-1*(c+im*d)^-2*(c+d*tan(e+f*x))^-1*(c+-1*im*d)^-1*(c+-3*im*d))
@test integrate((a+im*a*tan(e+f*x))^-2*(c+d*tan(e+f*x))^-2, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-2*(c+d*tan(e+f*x))^-1*(-4d+4*im*c)^-1+1//4*x*a^-2*(c+im*d)^-4*(c+-1*im*d)^-2*(c^4+9*d^4+-6*c^2*d^2+4*im*d*c^3+12*im*c*d^3)+1//4*a^-2*f^-1*(1+im*tan(e+f*x))^-1*(c+im*d)^-2*(c+d*tan(e+f*x))^-1*(-4d+im*c)+-1*a^-2*d^3*f^-1*(c+im*d)^-4*(c+-1*im*d)^-2*(4c+-2*im*d)*log(c*cos(e+f*x)+d*sin(e+f*x))+1//4*d*a^-2*f^-1*(c+im*d)^-3*(c+d*tan(e+f*x))^-1*(c+-1*im*d)^-1*(c^2+9*d^2+4*im*c*d))
@test integrate((a+im*a*tan(e+f*x))^-3*(c+d*tan(e+f*x))^-2, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-3*(c+d*tan(e+f*x))^-1*(-6d+6*im*c)^-1+1//8*x*a^-3*(c+im*d)^-5*(c+-1*im*d)^-2*(c^5+-35*c*d^4+-10*c^3*d^2+25*im*d^5+-10*im*c^2*d^3+5*im*d*c^4)+1//8*f^-1*(c+d*tan(e+f*x))^-1*(a^3+im*a^3*tan(e+f*x))^-1*(-1d+im*c)^-3*(c^2+-12*d^2+5*im*c*d)+1//24*a^-1*f^-1*(a+im*a*tan(e+f*x))^-2*(c+im*d)^-2*(c+d*tan(e+f*x))^-1*(-11d+3*im*c)+a^-3*d^4*f^-1*(c+-1*im*d)^-2*(-1d+im*c)^-5*(5c+-3*im*d)*log(c*cos(e+f*x)+d*sin(e+f*x))+1//8*d*a^-3*f^-1*(c+im*d)^-4*(c+d*tan(e+f*x))^-1*(c+-1*im*d)^-1*(c^3+-11*c*d^2+25*im*d^3+5*im*d*c^2))
@test integrate((a+im*a*tan(e+f*x))^3*(c+d*tan(e+f*x))^-3, x) == :(4*x*a^3*(c+-1*im*d)^-3+-4*a^3*f^-1*(d+im*c)^-3*log(c*cos(e+f*x)+d*sin(e+f*x))+-1*a*f^-1*(a+im*a*tan(e+f*x))^2*(c+d*tan(e+f*x))^-2*(2d+2*im*c)^-1+2*a^3*d^-1*f^-1*(c+d*tan(e+f*x))^-1*(c+-1*im*d)^-2*(c+im*d))
@test integrate((a+im*a*tan(e+f*x))^2*(c+d*tan(e+f*x))^-3, x) == :(2*x*a^2*(c+-1*im*d)^-3+-2*a^2*f^-1*(d+im*c)^-3*log(c*cos(e+f*x)+d*sin(e+f*x))+2*im*a^2*f^-1*(c+d*tan(e+f*x))^-1*(c+-1*im*d)^-2+(1/2)*a^2*d^-1*f^-1*(c+d*tan(e+f*x))^-2*(d+im*c)^-1*(-1d+im*c))
@test integrate((c+d*tan(e+f*x))^-3*(a+im*a*tan(e+f*x)), x) == :(a*x*(c+-1*im*d)^-3+-1*a*f^-1*(c+d*tan(e+f*x))^-2*(2d+2*im*c)^-1+-1*a*f^-1*(d+im*c)^-3*log(c*cos(e+f*x)+d*sin(e+f*x))+im*a*f^-1*(c+d*tan(e+f*x))^-1*(c+-1*im*d)^-2)
@test integrate((a+im*a*tan(e+f*x))^-1*(c+d*tan(e+f*x))^-3, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-1*(c+d*tan(e+f*x))^-2*(-2d+2*im*c)^-1+(1/2)*x*a^-1*(c+im*d)^-4*(c+-1*im*d)^-3*(c^4+-3*d^4+6*c^2*d^2+-12*im*c*d^3+4*im*d*c^3)+(1/2)*d*a^-1*f^-1*(c+im*d)^-3*(c+d*tan(e+f*x))^-1*(c+-1*im*d)^-2*(c^2+-3*d^2+-8*im*c*d)+(1/2)*d*a^-1*f^-1*(c+im*d)^-2*(c+d*tan(e+f*x))^-2*(c+-1*im*d)^-1*(c+-2*im*d)+2*a^-1*d^2*f^-1*(c+im*d)^-4*(d+im*c)^-3*(-1*d^2+3*c^2+-2*im*c*d)*log(c*cos(e+f*x)+d*sin(e+f*x)))
@test integrate((a+im*a*tan(e+f*x))^-2*(c+d*tan(e+f*x))^-3, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-2*(c+d*tan(e+f*x))^-2*(-4d+4*im*c)^-1+1//4*x*a^-2*(c+im*d)^-5*(c+-1*im*d)^-3*(c^5+-15*im*d^5+-10*c^3*d^2+45*c*d^4+5*im*d*c^4+30*im*c^2*d^3)+1//4*a^-2*f^-1*(1+im*tan(e+f*x))^-1*(c+im*d)^-2*(c+d*tan(e+f*x))^-2*(-5d+im*c)+-2*a^-2*d^3*f^-1*(d+im*c)^-3*(-1d+im*c)^-5*(-2*d^2+5*c^2+-5*im*c*d)*log(c*cos(e+f*x)+d*sin(e+f*x))+1//4*d*a^-2*f^-1*(c+im*d)^-3*(c+d*tan(e+f*x))^-2*(c+-1*im*d)^-1*(c^2+8*d^2+5*im*c*d)+1//4*d*a^-2*f^-1*(c+im*d)^-4*(c+d*tan(e+f*x))^-1*(c+-1*im*d)^-2*(c+-3*im*d)*(c^2+5*d^2+8*im*c*d))
@test integrate((a+im*a*tan(e+f*x))^-3*(c+d*tan(e+f*x))^-3, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-3*(c+d*tan(e+f*x))^-2*(-6d+6*im*c)^-1+1//8*x*a^-3*(c+im*d)^-6*(c+-1*im*d)^-3*(c^6+55*d^6+-105*c^2*d^4+-15*c^4*d^2+-20*im*c^3*d^3+6*im*d*c^5+150*im*c*d^5)+1//24*f^-1*(c+d*tan(e+f*x))^-2*(a^3+im*a^3*tan(e+f*x))^-1*(-1d+im*c)^-3*(-55*d^2+3*c^2+18*im*c*d)+1//24*a^-1*f^-1*(a+im*a*tan(e+f*x))^-2*(c+im*d)^-2*(c+d*tan(e+f*x))^-2*(-13d+3*im*c)+-1*a^-3*d^4*f^-1*(c+im*d)^-6*(d+im*c)^-3*(-7*d^2+15*c^2+-18*im*c*d)*log(c*cos(e+f*x)+d*sin(e+f*x))+1//8*d*a^-3*f^-1*(c+im*d)^-5*(c+d*tan(e+f*x))^-1*(c+-1*im*d)^-2*(c^4+55*d^4+-16*c^2*d^2+6*im*d*c^3+94*im*c*d^3)+1//8*d*a^-3*f^-1*(c+im*d)^-4*(c+d*tan(e+f*x))^-2*(c+-1*im*d)^-1*(c^3+-17*c*d^2+28*im*d^3+6*im*d*c^2))
@test integrate((a+im*a*tan(e+f*x))^3*(c+d*tan(e+f*x))^(1/2), x) == :(8*im*a^3*f^-1*(c+d*tan(e+f*x))^(1/2)+-1//5*d^-1*f^-1*(c+d*tan(e+f*x))^3//2*(2*a^3+2*im*a^3*tan(e+f*x))+-8*im*a^3*f^-1*(c+-1*im*d)^(1/2)*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+4//15*a^3*d^-2*f^-1*(c+d*tan(e+f*x))^3//2*(-6d+im*c))
@test integrate((a+im*a*tan(e+f*x))^2*(c+d*tan(e+f*x))^(1/2), x) == :(4*im*a^2*f^-1*(c+d*tan(e+f*x))^(1/2)+-2//3*a^2*d^-1*f^-1*(c+d*tan(e+f*x))^3//2+-4*im*a^2*f^-1*(c+-1*im*d)^(1/2)*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((c+d*tan(e+f*x))^(1/2)*(a+im*a*tan(e+f*x)), x) == :(2*im*a*f^-1*(c+d*tan(e+f*x))^(1/2)+-2*im*a*f^-1*(c+-1*im*d)^(1/2)*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+im*a*tan(e+f*x))^-1*(c+d*tan(e+f*x))^(1/2), x) == :((1/2)*im*f^-1*(a+im*a*tan(e+f*x))^-1*(c+d*tan(e+f*x))^(1/2)+-1//2*im*a^-1*f^-1*(c+-1*im*d)^(1/2)*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+(1/2)*im*c*a^-1*f^-1*(c+im*d)^-1//2*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2)))
@test integrate((a+im*a*tan(e+f*x))^-2*(c+d*tan(e+f*x))^(1/2), x) == :(1//4*im*f^-1*(a+im*a*tan(e+f*x))^-2*(c+d*tan(e+f*x))^(1/2)+-1//4*im*a^-2*f^-1*(c+-1*im*d)^(1/2)*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1//8*a^-2*f^-1*(c+im*d)^-3//2*(-1*im*(d^2+2*c^2)+2*c*d)*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+1//8*a^-2*f^-1*(1+im*tan(e+f*x))^-1*(c+im*d)^-1*(c+d*tan(e+f*x))^(1/2)*(-1d+2*im*c))
@test integrate((a+im*a*tan(e+f*x))^-3*(c+d*tan(e+f*x))^(1/2), x) == :(1//6*im*f^-1*(a+im*a*tan(e+f*x))^-3*(c+d*tan(e+f*x))^(1/2)+-1//8*im*a^-3*f^-1*(c+-1*im*d)^(1/2)*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+1//16*a^-3*f^-1*(c+im*d)^-5//2*(-2*d^3+-4*d*c^2+2*im*c^3+-1*im*c*d^2)*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+1//16*c*f^-1*(c+im*d)^-2*(c+d*tan(e+f*x))^(1/2)*(a^3+im*a^3*tan(e+f*x))^-1*(-3d+2*im*c)+1//24*a^-1*f^-1*(a+im*a*tan(e+f*x))^-2*(c+im*d)^-1*(c+d*tan(e+f*x))^(1/2)*(-2d+3*im*c))
@test integrate((a+im*a*tan(e+f*x))^3*(c+d*tan(e+f*x))^3//2, x) == :(8*a^3*f^-1*(c+d*tan(e+f*x))^(1/2)*(d+im*c)+-1//7*d^-1*f^-1*(c+d*tan(e+f*x))^5//2*(2*a^3+2*im*a^3*tan(e+f*x))+8//3*im*a^3*f^-1*(c+d*tan(e+f*x))^3//2+-8*im*a^3*f^-1*(c+-1*im*d)^3//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+4//35*a^3*d^-2*f^-1*(c+d*tan(e+f*x))^5//2*(-8d+im*c))
@test integrate((a+im*a*tan(e+f*x))^2*(c+d*tan(e+f*x))^3//2, x) == :(4*a^2*f^-1*(c+d*tan(e+f*x))^(1/2)*(d+im*c)+-2//5*a^2*d^-1*f^-1*(c+d*tan(e+f*x))^5//2+4//3*im*a^2*f^-1*(c+d*tan(e+f*x))^3//2+-4*im*a^2*f^-1*(c+-1*im*d)^3//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((c+d*tan(e+f*x))^3//2*(a+im*a*tan(e+f*x)), x) == :(2*a*f^-1*(c+d*tan(e+f*x))^(1/2)*(d+im*c)+2//3*im*a*f^-1*(c+d*tan(e+f*x))^3//2+-2*im*a*f^-1*(c+-1*im*d)^3//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+im*a*tan(e+f*x))^-1*(c+d*tan(e+f*x))^3//2, x) == :((1/2)*f^-1*(a+im*a*tan(e+f*x))^-1*(c+d*tan(e+f*x))^(1/2)*(-1d+im*c)+(1/2)*a^-1*f^-1*(c+im*d)^(1/2)*(2d+im*c)*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1//2*im*a^-1*f^-1*(c+-1*im*d)^3//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+im*a*tan(e+f*x))^-2*(c+d*tan(e+f*x))^3//2, x) == :(1//4*f^-1*(a+im*a*tan(e+f*x))^-2*(c+d*tan(e+f*x))^(1/2)*(-1d+im*c)+-1//4*im*a^-2*f^-1*(c+-1*im*d)^3//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+1//8*a^-2*f^-1*(1+im*tan(e+f*x))^-1*(c+d*tan(e+f*x))^(1/2)*(3d+2*im*c)+1//8*a^-2*f^-1*(c+im*d)^-1//2*(im*(d^2+2*c^2)+2*c*d)*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2)))
@test integrate((a+im*a*tan(e+f*x))^-3*(c+d*tan(e+f*x))^3//2, x) == :(1//6*f^-1*(a+im*a*tan(e+f*x))^-3*(c+d*tan(e+f*x))^(1/2)*(-1d+im*c)+-1*f^-1*(c+d*tan(e+f*x))^(1/2)*(a^3+im*a^3*tan(e+f*x))^-1*(-16d+16*im*c)^-1*(2*c^2+2*d^2+-1*im*c*d)+-1//8*im*a^-3*f^-1*(c+-1*im*d)^3//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+1//24*a^-1*f^-1*(a+im*a*tan(e+f*x))^-2*(c+d*tan(e+f*x))^(1/2)*(4d+3*im*c)+1//16*im*c*a^-3*f^-1*(c+im*d)^-3//2*(2*c^2+3*d^2)*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2)))
@test integrate((a+im*a*tan(e+f*x))^3*(c+d*tan(e+f*x))^5//2, x) == :(-1//9*d^-1*f^-1*(c+d*tan(e+f*x))^7//2*(2*a^3+2*im*a^3*tan(e+f*x))+8//3*a^3*f^-1*(c+d*tan(e+f*x))^3//2*(d+im*c)+8//5*im*a^3*f^-1*(c+d*tan(e+f*x))^5//2+-8*im*a^3*f^-1*(c+-1*im*d)^5//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+8*im*a^3*f^-1*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^2+4//63*a^3*d^-2*f^-1*(c+d*tan(e+f*x))^7//2*(-10d+im*c))
@test integrate((a+im*a*tan(e+f*x))^2*(c+d*tan(e+f*x))^5//2, x) == :(-2//7*a^2*d^-1*f^-1*(c+d*tan(e+f*x))^7//2+4//3*a^2*f^-1*(c+d*tan(e+f*x))^3//2*(d+im*c)+4//5*im*a^2*f^-1*(c+d*tan(e+f*x))^5//2+-4*im*a^2*f^-1*(c+-1*im*d)^5//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+4*im*a^2*f^-1*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^2)
@test integrate((c+d*tan(e+f*x))^5//2*(a+im*a*tan(e+f*x)), x) == :(2//3*a*f^-1*(c+d*tan(e+f*x))^3//2*(d+im*c)+2//5*im*a*f^-1*(c+d*tan(e+f*x))^5//2+-2*im*a*f^-1*(c+-1*im*d)^5//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+2*im*a*f^-1*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^2)
@test integrate((a+im*a*tan(e+f*x))^-1*(c+d*tan(e+f*x))^5//2, x) == :((1/2)*f^-1*(a+im*a*tan(e+f*x))^-1*(c+d*tan(e+f*x))^3//2*(-1d+im*c)+(1/2)*a^-1*f^-1*(c+im*d)^3//2*(4d+im*c)*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1//2*im*a^-1*f^-1*(c+-1*im*d)^5//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1//2*d*a^-1*f^-1*(c+d*tan(e+f*x))^(1/2)*(c+5*im*d))
@test integrate((a+im*a*tan(e+f*x))^-2*(c+d*tan(e+f*x))^5//2, x) == :(1//4*f^-1*(a+im*a*tan(e+f*x))^-2*(c+d*tan(e+f*x))^3//2*(-1d+im*c)+-1//4*im*a^-2*f^-1*(c+-1*im*d)^5//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+1//8*a^-2*f^-1*(c+im*d)^(1/2)*(-7*im*d^2+2*im*c^2+6*c*d)*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+1//8*a^-2*f^-1*(1+im*tan(e+f*x))^-1*(c+d*tan(e+f*x))^(1/2)*(c+im*d)*(5d+2*im*c))
@test integrate((a+im*a*tan(e+f*x))^-3*(c+d*tan(e+f*x))^5//2, x) == :(1//6*f^-1*(a+im*a*tan(e+f*x))^-3*(c+d*tan(e+f*x))^3//2*(-1d+im*c)+1//16*f^-1*(c+d*tan(e+f*x))^(1/2)*(a^3+im*a^3*tan(e+f*x))^-1*(-4*im*d^2+2*im*c^2+5*c*d)+-1//8*im*a^-3*f^-1*(c+-1*im*d)^5//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+1//16*a^-3*f^-1*(c+im*d)^-1//2*(2*d^3+2*im*c^3+4*d*c^2+-1*im*c*d^2)*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+1//8*a^-1*f^-1*(a+im*a*tan(e+f*x))^-2*(c+d*tan(e+f*x))^(1/2)*(c+im*d)*(2d+im*c))
@test integrate((a+im*a*tan(e+f*x))^3*(c+d*tan(e+f*x))^-1//2, x) == :(-1//3*d^-1*f^-1*(c+d*tan(e+f*x))^(1/2)*(2*a^3+2*im*a^3*tan(e+f*x))+-8*im*a^3*f^-1*(c+-1*im*d)^-1//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+4//3*a^3*d^-2*f^-1*(c+d*tan(e+f*x))^(1/2)*(-4d+im*c))
@test integrate((a+im*a*tan(e+f*x))^2*(c+d*tan(e+f*x))^-1//2, x) == :(-2*a^2*d^-1*f^-1*(c+d*tan(e+f*x))^(1/2)+-4*im*a^2*f^-1*(c+-1*im*d)^-1//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((c+d*tan(e+f*x))^-1//2*(a+im*a*tan(e+f*x)), x) == :(-2*im*a*f^-1*(c+-1*im*d)^-1//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+im*a*tan(e+f*x))^-1*(c+d*tan(e+f*x))^-1//2, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-1*(c+d*tan(e+f*x))^(1/2)*(-2d+2*im*c)^-1+(1/2)*a^-1*f^-1*(c+im*d)^-3//2*(-2d+im*c)*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1//2*im*a^-1*f^-1*(c+-1*im*d)^-1//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+im*a*tan(e+f*x))^-2*(c+d*tan(e+f*x))^-1//2, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-2*(c+d*tan(e+f*x))^(1/2)*(-4d+4*im*c)^-1+-1//4*im*a^-2*f^-1*(c+-1*im*d)^-1//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+1//8*a^-2*f^-1*(c+im*d)^-5//2*(-7*im*d^2+-6*c*d+2*im*c^2)*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+1//8*a^-2*f^-1*(1+im*tan(e+f*x))^-1*(c+im*d)^-2*(c+d*tan(e+f*x))^(1/2)*(-5d+2*im*c))
@test integrate((a+im*a*tan(e+f*x))^-3*(c+d*tan(e+f*x))^-1//2, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-3*(c+d*tan(e+f*x))^(1/2)*(-6d+6*im*c)^-1+-1//8*im*a^-3*f^-1*(c+-1*im*d)^-1//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+1//16*a^-3*f^-1*(c+im*d)^-7//2*(12*d^3+-8*d*c^2+2*im*c^3+-13*im*c*d^2)*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+1//16*f^-1*(c+d*tan(e+f*x))^(1/2)*(a^3+im*a^3*tan(e+f*x))^-1*(-1d+im*c)^-3*(-10*d^2+2*c^2+7*im*c*d)+1//24*a^-1*f^-1*(a+im*a*tan(e+f*x))^-2*(c+im*d)^-2*(c+d*tan(e+f*x))^(1/2)*(-8d+3*im*c))
@test integrate((a+im*a*tan(e+f*x))^3*(c+d*tan(e+f*x))^-3//2, x) == :(-8*im*a^3*f^-1*(c+-1*im*d)^-3//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+d^-1*f^-1*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^-1*(a^3+im*a^3*tan(e+f*x))*(2c+2*im*d)+4*c*a^3*d^-2*f^-1*(c+d*tan(e+f*x))^(1/2)*(d+im*c)^-1)
@test integrate((a+im*a*tan(e+f*x))^2*(c+d*tan(e+f*x))^-3//2, x) == :(-4*im*a^2*f^-1*(c+-1*im*d)^-3//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+2*a^2*d^-1*f^-1*(c+d*tan(e+f*x))^-1//2*(d+im*c)^-1*(-1d+im*c))
@test integrate((c+d*tan(e+f*x))^-3//2*(a+im*a*tan(e+f*x)), x) == :(-2*a*f^-1*(c+d*tan(e+f*x))^-1//2*(d+im*c)^-1+-2*im*a*f^-1*(c+-1*im*d)^-3//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+im*a*tan(e+f*x))^-1*(c+d*tan(e+f*x))^-3//2, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-1*(c+d*tan(e+f*x))^-1//2*(-2d+2*im*c)^-1+(1/2)*a^-1*f^-1*(c+im*d)^-5//2*(-4d+im*c)*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1//2*im*a^-1*f^-1*(c+-1*im*d)^-3//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+(1/2)*d*a^-1*f^-1*(c+im*d)^-2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^-1*(c+-5*im*d))
@test integrate((a+im*a*tan(e+f*x))^-2*(c+d*tan(e+f*x))^-3//2, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-2*(c+d*tan(e+f*x))^-1//2*(-4d+4*im*c)^-1+-1//4*im*a^-2*f^-1*(c+-1*im*d)^-3//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+1//8*a^-2*f^-1*(c+im*d)^-7//2*(-23*im*d^2+-10*c*d+2*im*c^2)*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+1//8*a^-2*f^-1*(1+im*tan(e+f*x))^-1*(c+im*d)^-2*(c+d*tan(e+f*x))^-1//2*(-7d+2*im*c)+1//8*d*a^-2*f^-1*(c+im*d)^-3*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^-1*(2*c^2+25*d^2+7*im*c*d))
@test integrate((a+im*a*tan(e+f*x))^-3*(c+d*tan(e+f*x))^-3//2, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-3*(c+d*tan(e+f*x))^-1//2*(-6d+6*im*c)^-1+-1//8*im*a^-3*f^-1*(c+-1*im*d)^-3//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+1//16*a^-3*f^-1*(c+im*d)^-9//2*(58*d^3+-12*d*c^2+2*im*c^3+-33*im*c*d^2)*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+1//48*f^-1*(c+d*tan(e+f*x))^-1//2*(a^3+im*a^3*tan(e+f*x))^-1*(-1d+im*c)^-3*(-56*d^2+6*c^2+27*im*c*d)+1//24*a^-1*f^-1*(a+im*a*tan(e+f*x))^-2*(c+im*d)^-2*(c+d*tan(e+f*x))^-1//2*(-10d+3*im*c)+1//16*d*a^-3*f^-1*(c+im*d)^-4*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^-1*(2*c^3+-17*c*d^2+60*im*d^3+9*im*d*c^2))
@test integrate((a+im*a*tan(e+f*x))^3*(c+d*tan(e+f*x))^-5//2, x) == :(-8*im*a^3*f^-1*(c+-1*im*d)^-5//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+d^-1*f^-1*(c+d*tan(e+f*x))^-3//2*(3c+-3*im*d)^-1*(a^3+im*a^3*tan(e+f*x))*(2c+2*im*d)+4//3*a^3*d^-2*f^-1*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^-2*(c+-4*im*d)*(-1d+im*c))
@test integrate((a+im*a*tan(e+f*x))^2*(c+d*tan(e+f*x))^-5//2, x) == :(-4*im*a^2*f^-1*(c+-1*im*d)^-5//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+4*im*a^2*f^-1*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^-2+2//3*a^2*d^-1*f^-1*(c+d*tan(e+f*x))^-3//2*(d+im*c)^-1*(-1d+im*c))
@test integrate((c+d*tan(e+f*x))^-5//2*(a+im*a*tan(e+f*x)), x) == :(-2*a*f^-1*(c+d*tan(e+f*x))^-3//2*(3d+3*im*c)^-1+-2*im*a*f^-1*(c+-1*im*d)^-5//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+2*im*a*f^-1*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^-2)
@test integrate((a+im*a*tan(e+f*x))^-1*(c+d*tan(e+f*x))^-5//2, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-1*(c+d*tan(e+f*x))^-3//2*(-2d+2*im*c)^-1+(1/2)*a^-1*f^-1*(c+im*d)^-7//2*(-6d+im*c)*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1//2*im*a^-1*f^-1*(c+-1*im*d)^-5//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+(1/2)*d*a^-1*f^-1*(c+im*d)^-3*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^-2*(c^2+-5*d^2+-14*im*c*d)+1//6*d*a^-1*f^-1*(c+d*tan(e+f*x))^-3//2*(c^2+d^2)^-1*(-1d+im*c)^-1*(7d+3*im*c))
@test integrate((a+im*a*tan(e+f*x))^-2*(c+d*tan(e+f*x))^-5//2, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-2*(c+d*tan(e+f*x))^-3//2*(-4d+4*im*c)^-1+-1//4*im*a^-2*f^-1*(c+-1*im*d)^-5//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+1//8*a^-2*f^-1*(c+im*d)^-9//2*(-47*im*d^2+-14*c*d+2*im*c^2)*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+1//8*a^-2*f^-1*(1+im*tan(e+f*x))^-1*(c+im*d)^-2*(c+d*tan(e+f*x))^-3//2*(-9d+2*im*c)+1//8*d*a^-2*f^-1*(c+im*d)^-4*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^-2*(2*c^3+-45*im*d^3+88*c*d^2+9*im*d*c^2)+1//24*d*a^-2*f^-1*(c+im*d)^-3*(c+d*tan(e+f*x))^-3//2*(c+-1*im*d)^-1*(6*c^2+49*d^2+27*im*c*d))
@test integrate((a+im*a*tan(e+f*x))^-3*(c+d*tan(e+f*x))^-5//2, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-3*(c+d*tan(e+f*x))^-3//2*(-6d+6*im*c)^-1+-1//8*im*a^-3*f^-1*(c+-1*im*d)^-5//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+1//16*a^-3*f^-1*(c+im*d)^-11//2*(152*d^3+-16*d*c^2+2*im*c^3+-61*im*c*d^2)*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+1//16*f^-1*(c+d*tan(e+f*x))^-3//2*(a^3+im*a^3*tan(e+f*x))^-1*(-1d+im*c)^-3*(-30*d^2+2*c^2+11*im*c*d)+1//8*a^-1*f^-1*(a+im*a*tan(e+f*x))^-2*(c+im*d)^-2*(c+d*tan(e+f*x))^-3//2*(-4d+im*c)+1//16*d*a^-3*f^-1*(c+im*d)^-5*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^-2*(2*c^4+150*d^4+-26*c^2*d^2+11*im*d*c^3+253*im*c*d^3)+1//48*d*a^-3*f^-1*(c+im*d)^-4*(c+d*tan(e+f*x))^-3//2*(c+-1*im*d)^-1*(6*c^3+-83*c*d^2+154*im*d^3+33*im*d*c^2))
@test integrate((a+im*a*tan(e+f*x))^5//2*(c+d*tan(e+f*x))^(1/2), x) == :(-1//2*a^2*d^-1*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^3//2+-4*im*2^(1/2)*a^5//2*f^-1*(c+-1*im*d)^(1/2)*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1//4*(-1)^1//4*a^5//2*d^-3//2*f^-1*(c^2+23*d^2+10*im*c*d)*arctanh((-1)^3//4*a^-1//2*d^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2)+1//4*a^2*d^-1*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^(1/2)*(c+9*im*d))
@test integrate((a+im*a*tan(e+f*x))^3//2*(c+d*tan(e+f*x))^(1/2), x) == :(-1*a^2*d^-1*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^3//2+a^2*d^-1*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+im*d)+-1*(-1)^1//4*a^3//2*d^-1//2*f^-1*(3d+im*c)*arctanh((-1)^3//4*a^-1//2*d^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2)+-2*im*2^(1/2)*a^3//2*f^-1*(c+-1*im*d)^(1/2)*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^(1/2), x) == :(-2*(-1)^1//4*a^(1/2)*d^(1/2)*f^-1*arctanh((-1)^3//4*a^-1//2*d^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*2^(1/2)*a^(1/2)*f^-1*(c+-1*im*d)^(1/2)*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2), x) == :(im*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)+-1//2*im*2^(1/2)*a^-1//2*f^-1*(c+-1*im*d)^(1/2)*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+im*a*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^(1/2), x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^3//2*(-3d+3*im*c)^-1+(1/2)*im*a^-1*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)+-1//4*im*2^(1/2)*a^-3//2*f^-1*(c+-1*im*d)^(1/2)*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+im*a*tan(e+f*x))^-5//2*(c+d*tan(e+f*x))^(1/2), x) == :(1//5*im*f^-1*(a+im*a*tan(e+f*x))^-5//2*(c+d*tan(e+f*x))^(1/2)+-1//8*im*2^(1/2)*a^-5//2*f^-1*(c+-1*im*d)^(1/2)*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1//60*a^-2*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+im*d)^-2*(c+d*tan(e+f*x))^(1/2)*(-1*im*(3*d^2+15*c^2)+20*c*d)+1//30*a^-1*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+im*d)^-1*(c+d*tan(e+f*x))^(1/2)*(-3d+5*im*c))
@test integrate((a+im*a*tan(e+f*x))^5//2*(c+d*tan(e+f*x))^3//2, x) == :(-1//3*a^2*d^-1*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^5//2+-4*im*2^(1/2)*a^5//2*f^-1*(c+-1*im*d)^3//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+1//8*a^2*d^-1*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^(1/2)*(c^2+19*d^2+14*im*c*d)+1//12*a^2*d^-1*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^3//2*(c+13*im*d)+-1//8*(-1)^1//4*a^5//2*d^-3//2*f^-1*(c+-3*im*d)*(c^2+15*d^2+18*im*c*d)*arctanh((-1)^3//4*a^-1//2*d^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2))
@test integrate((a+im*a*tan(e+f*x))^3//2*(c+d*tan(e+f*x))^3//2, x) == :(-1//2*a^2*d^-1*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^5//2+1//4*a*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^(1/2)*(5d+3*im*c)+(1/2)*a^2*d^-1*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^3//2*(c+im*d)+-2*im*2^(1/2)*a^3//2*f^-1*(c+-1*im*d)^3//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1//4*(-1)^1//4*a^3//2*d^-1//2*f^-1*(-11*im*d^2+3*im*c^2+18*c*d)*arctanh((-1)^3//4*a^-1//2*d^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2))
@test integrate((a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^3//2, x) == :(d*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^(1/2)+-1*im*2^(1/2)*a^(1/2)*f^-1*(c+-1*im*d)^3//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1*(-1)^1//4*a^(1/2)*d^(1/2)*f^-1*(3c+-1*im*d)*arctanh((-1)^3//4*a^-1//2*d^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2))
@test integrate((a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^3//2, x) == :(f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(-1d+im*c)+2*(-1)^3//4*a^-1//2*d^3//2*f^-1*arctanh((-1)^3//4*a^-1//2*d^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1//2*im*2^(1/2)*a^-1//2*f^-1*(c+-1*im*d)^3//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+im*a*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^3//2, x) == :(1//3*im*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^3//2+(1/2)*a^-1*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(d+im*c)+-1//4*im*2^(1/2)*a^-3//2*f^-1*(c+-1*im*d)^3//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+im*a*tan(e+f*x))^-5//2*(c+d*tan(e+f*x))^3//2, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-5//2*(c+d*tan(e+f*x))^5//2*(-5d+5*im*c)^-1+1//4*a^-2*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(d+im*c)+1//6*im*a^-1*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^3//2+-1//8*im*2^(1/2)*a^-5//2*f^-1*(c+-1*im*d)^3//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+im*a*tan(e+f*x))^5//2*(c+d*tan(e+f*x))^5//2, x) == :(-1//4*a^2*d^-1*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^7//2+-4*im*2^(1/2)*a^5//2*f^-1*(c+-1*im*d)^5//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1//64*(-1)^1//4*a^5//2*d^-3//2*f^-1*(-363*d^4+5*c^4+690*c^2*d^2+-900*im*c*d^3+100*im*d*c^3)*arctanh((-1)^3//4*a^-1//2*d^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2)+1//24*a^2*d^-1*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^5//2*(c+17*im*d)+1//64*a^2*d^-1*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^(1/2)*(5*c^3+-149*im*d^3+273*c*d^2+95*im*d*c^2)+1//96*a^2*d^-1*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^3//2*(5*c^2+107*d^2+90*im*c*d))
@test integrate((a+im*a*tan(e+f*x))^3//2*(c+d*tan(e+f*x))^5//2, x) == :(-1//3*a^2*d^-1*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^7//2+1//12*a*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^3//2*(7d+5*im*c)+-2*im*2^(1/2)*a^3//2*f^-1*(c+-1*im*d)^5//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1//8*(-1)^1//4*a^3//2*d^-1//2*f^-1*(-23*d^3+5*im*c^3+45*d*c^2+-55*im*c*d^2)*arctanh((-1)^3//4*a^-1//2*d^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2)+1//3*a^2*d^-1*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^5//2*(c+im*d)+1//8*a*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^(1/2)*(c+-3*im*d)*(3d+5*im*c))
@test integrate((a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^5//2, x) == :((1/2)*d*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^3//2+1//4*d*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^(1/2)*(7c+-1*im*d)+-1*im*2^(1/2)*a^(1/2)*f^-1*(c+-1*im*d)^5//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1//4*(-1)^1//4*a^(1/2)*d^(1/2)*f^-1*(-7*d^2+15*c^2+-10*im*c*d)*arctanh((-1)^3//4*a^-1//2*d^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2))
@test integrate((a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^5//2, x) == :(f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^3//2*(-1d+im*c)+(-1)^1//4*a^-1//2*d^3//2*f^-1*(-1d+5*im*c)*arctanh((-1)^3//4*a^-1//2*d^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*d*a^-1*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^(1/2)*(c+2*im*d)+-1//2*im*2^(1/2)*a^-1//2*f^-1*(c+-1*im*d)^5//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+im*a*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^5//2, x) == :(1//3*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^3//2*(-1d+im*c)+2*(-1)^1//4*a^-3//2*d^5//2*f^-1*arctanh((-1)^3//4*a^-1//2*d^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2)+(1/2)*a^-1*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+im*d)*(3d+im*c)+-1//4*im*2^(1/2)*a^-3//2*f^-1*(c+-1*im*d)^5//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+im*a*tan(e+f*x))^-5//2*(c+d*tan(e+f*x))^5//2, x) == :(1//5*im*f^-1*(a+im*a*tan(e+f*x))^-5//2*(c+d*tan(e+f*x))^5//2+1//6*a^-1*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^3//2*(d+im*c)+-1//8*im*2^(1/2)*a^-5//2*f^-1*(c+-1*im*d)^5//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+1//4*im*a^-2*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^2)
@test integrate((a+im*a*tan(e+f*x))^5//2*(c+d*tan(e+f*x))^-1//2, x) == :(-1*a^2*d^-1*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^(1/2)+-1*(-1)^1//4*a^5//2*d^-3//2*f^-1*(c+5*im*d)*arctanh((-1)^3//4*a^-1//2*d^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2)+-4*im*2^(1/2)*a^5//2*f^-1*(c+-1*im*d)^-1//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+im*a*tan(e+f*x))^3//2*(c+d*tan(e+f*x))^-1//2, x) == :(-2*(-1)^3//4*a^3//2*d^-1//2*f^-1*arctanh((-1)^3//4*a^-1//2*d^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2)+-2*im*2^(1/2)*a^3//2*f^-1*(c+-1*im*d)^-1//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2, x) == :(-1*im*2^(1/2)*a^(1/2)*f^-1*(c+-1*im*d)^-1//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^-1//2, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(d+im*c)^-1+2*d*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c^2+d^2)^-1+-1//2*im*2^(1/2)*a^-1//2*f^-1*(c+-1*im*d)^-1//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+im*a*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^-1//2, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^(1/2)*(-3d+3*im*c)^-1+-1//4*im*2^(1/2)*a^-3//2*f^-1*(c+-1*im*d)^-1//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+1//6*a^-1*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+im*d)^-2*(c+d*tan(e+f*x))^(1/2)*(-7d+3*im*c))
@test integrate((a+im*a*tan(e+f*x))^-5//2*(c+d*tan(e+f*x))^-1//2, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-5//2*(c+d*tan(e+f*x))^(1/2)*(-5d+5*im*c)^-1+-1//8*im*2^(1/2)*a^-5//2*f^-1*(c+-1*im*d)^-1//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+1//30*a^-1*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+im*d)^-2*(c+d*tan(e+f*x))^(1/2)*(-13d+5*im*c)+1//60*a^-2*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(-1d+im*c)^-3*(-67*d^2+15*c^2+50*im*c*d))
@test integrate((a+im*a*tan(e+f*x))^5//2*(c+d*tan(e+f*x))^-3//2, x) == :(2*(-1)^1//4*a^5//2*d^-3//2*f^-1*arctanh((-1)^3//4*a^-1//2*d^(1/2)*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2)+-4*im*2^(1/2)*a^5//2*f^-1*(c+-1*im*d)^-3//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+2*a^2*d^-1*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^-1*(c+im*d))
@test integrate((a+im*a*tan(e+f*x))^3//2*(c+d*tan(e+f*x))^-3//2, x) == :(-2*a*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2*(d+im*c)^-1+-2*im*2^(1/2)*a^3//2*f^-1*(c+-1*im*d)^-3//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-3//2, x) == :(-2*d*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2*(c^2+d^2)^-1+-1*im*2^(1/2)*a^(1/2)*f^-1*(c+-1*im*d)^-3//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^-3//2, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^-1//2*(-1d+im*c)^-1+-1//2*im*2^(1/2)*a^-1//2*f^-1*(c+-1*im*d)^-3//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+d*a^-1*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+im*d)^-2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^-1*(c+-3*im*d))
@test integrate((a+im*a*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^-3//2, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^-1//2*(-3d+3*im*c)^-1+-1//4*im*2^(1/2)*a^-3//2*f^-1*(c+-1*im*d)^-3//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+1//6*a^-1*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+im*d)^-2*(c+d*tan(e+f*x))^-1//2*(-11d+3*im*c)+1//6*d*a^-2*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+im*d)^-3*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^-1*(c+5*im*d)*(3c+-5*im*d))
@test integrate((a+im*a*tan(e+f*x))^-5//2*(c+d*tan(e+f*x))^-3//2, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-5//2*(c+d*tan(e+f*x))^-1//2*(-5d+5*im*c)^-1+-1//8*im*2^(1/2)*a^-5//2*f^-1*(c+-1*im*d)^-3//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+1//30*a^-1*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+im*d)^-2*(c+d*tan(e+f*x))^-1//2*(-17d+5*im*c)+1//60*a^-2*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^-1//2*(-1d+im*c)^-3*(-151*d^2+15*c^2+70*im*c*d)+1//60*d*a^-3*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+im*d)^-4*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^-1*(15*c^3+-117*c*d^2+317*im*d^3+65*im*d*c^2))
@test integrate((a+im*a*tan(e+f*x))^5//2*(c+d*tan(e+f*x))^-5//2, x) == :(-2*a*f^-1*(a+im*a*tan(e+f*x))^3//2*(c+d*tan(e+f*x))^-3//2*(3d+3*im*c)^-1+-4*im*2^(1/2)*a^5//2*f^-1*(c+-1*im*d)^-5//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+4*im*a^2*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^-2)
@test integrate((a+im*a*tan(e+f*x))^3//2*(c+d*tan(e+f*x))^-5//2, x) == :(-2*d*f^-1*(a+im*a*tan(e+f*x))^3//2*(c+d*tan(e+f*x))^-3//2*(3*c^2+3*d^2)^-1+-2*im*2^(1/2)*a^3//2*f^-1*(c+-1*im*d)^-5//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+2*im*a*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^-2)
@test integrate((a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-5//2, x) == :(-2*d*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-3//2*(3*c^2+3*d^2)^-1+-1*im*2^(1/2)*a^(1/2)*f^-1*(c+-1*im*d)^-5//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1//3*d*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2*(c^2+d^2)^-2*(10c+2*im*d))
@test integrate((a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^-5//2, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^-3//2*(-1d+im*c)^-1+-1//2*im*2^(1/2)*a^-1//2*f^-1*(c+-1*im*d)^-5//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+1//3*d*a^-1*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-3//2*(c^2+d^2)^-1*(-1d+im*c)^-1*(5d+3*im*c)+1//3*d*a^-1*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+im*d)^-3*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^-2*(c+-7*im*d)*(3c+-1*im*d))
@test integrate((a+im*a*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^-5//2, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^-3//2*(-3d+3*im*c)^-1+(1/2)*a^-1*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+im*d)^-2*(c+d*tan(e+f*x))^-3//2*(-5d+im*c)+-1//4*im*2^(1/2)*a^-3//2*f^-1*(c+-1*im*d)^-5//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+1//6*d*a^-2*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+im*d)^-3*(c+d*tan(e+f*x))^-3//2*(c+-1*im*d)^-1*(3*c^2+21*d^2+14*im*c*d)+1//6*d*a^-2*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+im*d)^-4*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^-2*(c+-3*im*d)*(3*c^2+13*d^2+22*im*c*d))
@test integrate((a+im*a*tan(e+f*x))^-5//2*(c+d*tan(e+f*x))^-5//2, x) == :(-1*f^-1*(a+im*a*tan(e+f*x))^-5//2*(c+d*tan(e+f*x))^-3//2*(-5d+5*im*c)^-1+-1//8*im*2^(1/2)*a^-5//2*f^-1*(c+-1*im*d)^-5//2*arctanh(2^(1/2)*a^(1/2)*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+1//20*a^-2*f^-1*(a+im*a*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^-3//2*(-1d+im*c)^-3*(-89*d^2+5*c^2+30*im*c*d)+1//30*a^-1*f^-1*(a+im*a*tan(e+f*x))^-3//2*(c+im*d)^-2*(c+d*tan(e+f*x))^-3//2*(-21d+5*im*c)+1//60*d*a^-3*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+im*d)^-5*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^-2*(15*c^4+707*d^4+-182*c^2*d^2+80*im*d*c^3+1224*im*c*d^3)+1//60*d*a^-3*f^-1*(a+im*a*tan(e+f*x))^(1/2)*(c+im*d)^-4*(c+d*tan(e+f*x))^-3//2*(c+-1*im*d)^-1*(15*c^3+-221*c*d^2+361*im*d^3+85*im*d*c^2))
@test integrate((a+b*tan(e+f*x))^3*(c+d*tan(e+f*x)), x) == :(x*(c*a^3+d*b^3+-3*a*c*b^2+-3*b*d*a^2)+(1/2)*f^-1*(a+b*tan(e+f*x))^2*(a*d+b*c)+-1*f^-1*(d*a^3+-1*c*b^3+-3*a*d*b^2+3*b*c*a^2)*log(cos(e+f*x))+1//3*d*f^-1*(a+b*tan(e+f*x))^3+b*f^-1*(d*a^2+-1*d*b^2+2*a*b*c)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x))^2*(c+d*tan(e+f*x)), x) == :(x*(c*a^2+-1*c*b^2+-2*a*b*d)+(1/2)*d*f^-1*(a+b*tan(e+f*x))^2+-1*f^-1*(d*a^2+-1*d*b^2+2*a*b*c)*log(cos(e+f*x))+b*f^-1*(a*d+b*c)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x))*(c+d*tan(e+f*x)), x) == :(x*(a*c+-1*b*d)+-1*f^-1*(a*d+b*c)*log(cos(e+f*x))+b*d*f^-1*tan(e+f*x))
@test integrate((a+b*tan(e+f*x))^-1*(c+d*tan(e+f*x)), x) == :(x*(a^2+b^2)^-1*(a*c+b*d)+f^-1*(a^2+b^2)^-1*(b*c+-1*a*d)*log(a*cos(e+f*x)+b*sin(e+f*x)))
@test integrate((a+b*tan(e+f*x))^-2*(c+d*tan(e+f*x)), x) == :(x*(a^2+b^2)^-2*(c*a^2+-1*c*b^2+2*a*b*d)+f^-1*(a^2+b^2)^-2*(d*b^2+-1*d*a^2+2*a*b*c)*log(a*cos(e+f*x)+b*sin(e+f*x))+-1*f^-1*(a+b*tan(e+f*x))^-1*(a^2+b^2)^-1*(b*c+-1*a*d))
@test integrate((a+b*tan(e+f*x))^-3*(c+d*tan(e+f*x)), x) == :(x*(a^2+b^2)^-3*(c*a^3+-1*d*b^3+-3*a*c*b^2+3*b*d*a^2)+f^-1*(a^2+b^2)^-3*(-1*c*b^3+-1*d*a^3+3*a*d*b^2+3*b*c*a^2)*log(a*cos(e+f*x)+b*sin(e+f*x))+-1*f^-1*(a+b*tan(e+f*x))^-1*(a^2+b^2)^-2*(d*b^2+-1*d*a^2+2*a*b*c)+-1*f^-1*(a+b*tan(e+f*x))^-2*(2*a^2+2*b^2)^-1*(b*c+-1*a*d))
@test integrate((a+b*tan(e+f*x))^3*(c+d*tan(e+f*x))^2, x) == :(-1*x*(-1*a^3*(c^2+-1*d^2)+-2*c*d*b^3+3*a*b^2*(c^2+-1*d^2)+6*b*c*d*a^2)+(1/2)*f^-1*(a+b*tan(e+f*x))^2*(b*(c^2+-1*d^2)+2*a*c*d)+-1*f^-1*(-1*b^3*(c^2+-1*d^2)+2*c*d*a^3+3*b*a^2*(c^2+-1*d^2)+-6*a*c*d*b^2)*log(cos(e+f*x))+1//4*b^-1*d^2*f^-1*(a+b*tan(e+f*x))^4+2//3*c*d*f^-1*(a+b*tan(e+f*x))^3+2*b*f^-1*(a*c+-1*b*d)*(a*d+b*c)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x))^2*(c+d*tan(e+f*x))^2, x) == :(x*(a*c+a*d+b*c+-1*b*d)*(a*c+-1*a*d+-1*b*c+-1*b*d)+b*f^-1*(b*(c^2+-1*d^2)+2*a*c*d)*tan(e+f*x)+c*d*f^-1*(a+b*tan(e+f*x))^2+-1*f^-1*(a*c+-1*b*d)*(2*a*d+2*b*c)*log(cos(e+f*x))+1//3*b^-1*d^2*f^-1*(a+b*tan(e+f*x))^3)
@test integrate((c+d*tan(e+f*x))^2*(a+b*tan(e+f*x)), x) == :(-1*x*(-1*a*(c^2+-1*d^2)+2*b*c*d)+(1/2)*b*f^-1*(c+d*tan(e+f*x))^2+-1*f^-1*(b*(c^2+-1*d^2)+2*a*c*d)*log(cos(e+f*x))+d*f^-1*(a*d+b*c)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x))^-1*(c+d*tan(e+f*x))^2, x) == :(d*x*b^-2*(-1*a*d+2*b*c)+-1*b^-1*d^2*f^-1*log(cos(e+f*x))+a*x*b^-2*(a^2+b^2)^-1*(b*c+-1*a*d)^2+b^-1*f^-1*(a^2+b^2)^-1*(b*c+-1*a*d)^2*log(a*cos(e+f*x)+b*sin(e+f*x)))
@test integrate((a+b*tan(e+f*x))^-2*(c+d*tan(e+f*x))^2, x) == :(-1*x*(a^2+b^2)^-2*(a*(c+-1d)+b*(c+d))*(b*(c+-1d)+-1*a*(c+d))+f^-1*(a^2+b^2)^-2*(a*c+b*d)*(-2*a*d+2*b*c)*log(a*cos(e+f*x)+b*sin(e+f*x))+-1*b^-1*f^-1*(a+b*tan(e+f*x))^-1*(a^2+b^2)^-1*(b*c+-1*a*d)^2)
@test integrate((a+b*tan(e+f*x))^-3*(c+d*tan(e+f*x))^2, x) == :(x*(a^2+b^2)^-3*(a^3*(c^2+-1*d^2)+-3*a*b^2*(c^2+-1*d^2)+-2*c*d*b^3+6*b*c*d*a^2)+-1*f^-1*(a^2+b^2)^-3*(b^3*(c^2+-1*d^2)+-3*b*a^2*(c^2+-1*d^2)+2*c*d*a^3+-6*a*c*d*b^2)*log(a*cos(e+f*x)+b*sin(e+f*x))+-1*f^-1*(a+b*tan(e+f*x))^-1*(a^2+b^2)^-2*(a*c+b*d)*(-2*a*d+2*b*c)+-1//2*b^-1*f^-1*(a+b*tan(e+f*x))^-2*(a^2+b^2)^-1*(b*c+-1*a*d)^2)
@test integrate((a+b*tan(e+f*x))^3*(c+d*tan(e+f*x))^3, x) == :((1/2)*f^-1*(c+d*tan(e+f*x))^2*(d*a^3+-1*c*b^3+-3*a*d*b^2+3*b*c*a^2)+-1*x*(a*c+-1*b*d)*(b^2*(-1*d^2+3*c^2)+-1*a^2*(c^2+-3*d^2)+8*a*b*c*d)+d*f^-1*(-1*b^3*(c^2+-1*d^2)+2*c*d*a^3+3*b*a^2*(c^2+-1*d^2)+-6*a*c*d*b^2)*tan(e+f*x)+f^-1*(a*d+b*c)*(b^2*(c^2+-3*d^2)+-1*a^2*(-1*d^2+3*c^2)+8*a*b*c*d)*log(cos(e+f*x))+1//3*b*f^-1*(c+d*tan(e+f*x))^3*(-1*b^2+3*a^2)+-1//20*b^2*d^-2*f^-1*(c+d*tan(e+f*x))^4*(b*c+-11*a*d)+1//5*b^2*d^-1*f^-1*(c+d*tan(e+f*x))^4*(a+b*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x))^2*(c+d*tan(e+f*x))^3, x) == :(-1*x*(-1*a^2*(c^3+-3*c*d^2)+c*b^2*(c^2+-3*d^2)+2*a*b*d*(-1*d^2+3*c^2))+(1/2)*f^-1*(c+d*tan(e+f*x))^2*(d*a^2+-1*d*b^2+2*a*b*c)+-1*f^-1*(a^2*(-1*d^3+3*d*c^2)+-1*d*b^2*(-1*d^2+3*c^2)+2*a*b*c*(c^2+-3*d^2))*log(cos(e+f*x))+1//4*b^2*d^-1*f^-1*(c+d*tan(e+f*x))^4+2//3*a*b*f^-1*(c+d*tan(e+f*x))^3+2*d*f^-1*(a*c+-1*b*d)*(a*d+b*c)*tan(e+f*x))
@test integrate((c+d*tan(e+f*x))^3*(a+b*tan(e+f*x)), x) == :(-1*x*(-1*a*(c^3+-3*c*d^2)+b*d*(-1*d^2+3*c^2))+(1/2)*f^-1*(c+d*tan(e+f*x))^2*(a*d+b*c)+-1*f^-1*(b*c^3+-1*a*d^3+-3*b*c*d^2+3*a*d*c^2)*log(cos(e+f*x))+1//3*b*f^-1*(c+d*tan(e+f*x))^3+d*f^-1*(b*(c^2+-1*d^2)+2*a*c*d)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x))^-1*(c+d*tan(e+f*x))^3, x) == :(x*(a^2+b^2)^-1*(a*c^3+-1*b*d^3+-3*a*c*d^2+3*b*d*c^2)+b^-1*d^2*f^-1*(c+d*tan(e+f*x))+f^-1*(a^2+b^2)^-1*(a*d^3+b*c^3+-3*a*d*c^2+-3*b*c*d^2)*log(cos(e+f*x))+b^-2*f^-1*(a^2+b^2)^-1*(b*c+-1*a*d)^3*log(a+b*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x))^-2*(c+d*tan(e+f*x))^3, x) == :(-1*x*(a^2+b^2)^-2*(-1*a^2*(c^3+-3*c*d^2)+c*b^2*(c^2+-3*d^2)+-2*a*b*d*(-1*d^2+3*c^2))+f^-1*(a^2+b^2)^-2*(-1*a^2*(-1*d^3+3*d*c^2)+d*b^2*(-1*d^2+3*c^2)+2*a*b*c*(c^2+-3*d^2))*log(cos(e+f*x))+b^-2*f^-1*(a^2+b^2)^-2*(b*c+-1*a*d)^2*(d*a^2+3*d*b^2+2*a*b*c)*log(a+b*tan(e+f*x))+-1*b^-1*f^-1*(a+b*tan(e+f*x))^-1*(a^2+b^2)^-1*(b*c+-1*a*d)^2*(c+d*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x))^-3*(c+d*tan(e+f*x))^3, x) == :(x*(a^2+b^2)^-3*(a*c+b*d)*(a^2*(c^2+-3*d^2)+-1*b^2*(-1*d^2+3*c^2)+8*a*b*c*d)+f^-1*(a^2+b^2)^-3*(b*c+-1*a*d)*(a^2*(-1*d^2+3*c^2)+-1*b^2*(c^2+-3*d^2)+8*a*b*c*d)*log(a*cos(e+f*x)+b*sin(e+f*x))+-1//2*b^-1*f^-1*(a+b*tan(e+f*x))^-2*(a^2+b^2)^-1*(b*c+-1*a*d)^2*(c+d*tan(e+f*x))+-1//2*b^-2*f^-1*(a+b*tan(e+f*x))^-1*(a^2+b^2)^-2*(b*c+-1*a*d)^2*(d*a^2+5*d*b^2+4*a*b*c))
@test integrate((a+b*tan(e+f*x))^4*(c+d*tan(e+f*x))^-1, x) == :(x*(c^2+d^2)^-1*(c*a^4+c*b^4+-6*c*a^2*b^2+-4*a*d*b^3+4*b*d*a^3)+(1/2)*b^2*d^-1*f^-1*(a+b*tan(e+f*x))^2+-1*f^-1*(c^2+d^2)^-1*(-1*d*a^4+-1*d*b^4+-4*a*c*b^3+4*b*c*a^3+6*d*a^2*b^2)*log(cos(e+f*x))+d^-3*f^-1*(c^2+d^2)^-1*(b*c+-1*a*d)^4*log(c+d*tan(e+f*x))+-1*b^3*d^-2*f^-1*(b*c+-3*a*d)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x))^3*(c+d*tan(e+f*x))^-1, x) == :(x*(c^2+d^2)^-1*(c*a^3+-1*d*b^3+-3*a*c*b^2+3*b*d*a^2)+b^2*d^-1*f^-1*(a+b*tan(e+f*x))+-1*f^-1*(c^2+d^2)^-1*(-1*c*b^3+-1*d*a^3+3*a*d*b^2+3*b*c*a^2)*log(cos(e+f*x))+-1*d^-2*f^-1*(c^2+d^2)^-1*(b*c+-1*a*d)^3*log(c+d*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x))^2*(c+d*tan(e+f*x))^-1, x) == :(-1*b*x*d^-2*(b*c+-2*a*d)+-1*b^2*d^-1*f^-1*log(cos(e+f*x))+c*x*d^-2*(c^2+d^2)^-1*(b*c+-1*a*d)^2+d^-1*f^-1*(c^2+d^2)^-1*(b*c+-1*a*d)^2*log(c*cos(e+f*x)+d*sin(e+f*x)))
@test integrate((c+d*tan(e+f*x))^-1*(a+b*tan(e+f*x)), x) == :(x*(c^2+d^2)^-1*(a*c+b*d)+-1*f^-1*(c^2+d^2)^-1*(b*c+-1*a*d)*log(c*cos(e+f*x)+d*sin(e+f*x)))
@test integrate((a+b*tan(e+f*x))^-1*(c+d*tan(e+f*x))^-1, x) == :(x*(a^2+b^2)^-1*(c^2+d^2)^-1*(a*c+-1*b*d)+b^2*f^-1*(a^2+b^2)^-1*(b*c+-1*a*d)^-1*log(a*cos(e+f*x)+b*sin(e+f*x))+-1*d^2*f^-1*(c^2+d^2)^-1*(b*c+-1*a*d)^-1*log(c*cos(e+f*x)+d*sin(e+f*x)))
@test integrate((a+b*tan(e+f*x))^-2*(c+d*tan(e+f*x))^-1, x) == :(x*(a^2+b^2)^-2*(c^2+d^2)^-1*(c*a^2+-1*c*b^2+-2*a*b*d)+d^3*f^-1*(c^2+d^2)^-1*(b*c+-1*a*d)^-2*log(c*cos(e+f*x)+d*sin(e+f*x))+-1*b^2*f^-1*(a+b*tan(e+f*x))^-1*(a^2+b^2)^-1*(b*c+-1*a*d)^-1+b^2*f^-1*(a^2+b^2)^-2*(b*c+-1*a*d)^-2*(-1*d*b^2+-3*d*a^2+2*a*b*c)*log(a*cos(e+f*x)+b*sin(e+f*x)))
@test integrate((a+b*tan(e+f*x))^-3*(c+d*tan(e+f*x))^-1, x) == :(x*(a^2+b^2)^-3*(c^2+d^2)^-1*(c*a^3+d*b^3+-3*a*c*b^2+-3*b*d*a^2)+-1*b^2*f^-1*(a+b*tan(e+f*x))^-2*(2*a^2+2*b^2)^-1*(b*c+-1*a*d)^-1+-1*d^4*f^-1*(c^2+d^2)^-1*(b*c+-1*a*d)^-3*log(c*cos(e+f*x)+d*sin(e+f*x))+-1*b^2*f^-1*(a+b*tan(e+f*x))^-1*(a^2+b^2)^-2*(b*c+-1*a*d)^-2*(-1*d*b^2+-3*d*a^2+2*a*b*c)+-1*b^2*f^-1*(a^2+b^2)^-3*(b*c+-1*a*d)^-3*(b^4*(c^2+-1*d^2)+-6*a^4*d^2+-3*a^2*b^2*(c^2+d^2)+8*b*c*d*a^3)*log(a*cos(e+f*x)+b*sin(e+f*x)))
@test integrate((a+b*tan(e+f*x))^4*(c+d*tan(e+f*x))^-2, x) == :(x*(c^2+d^2)^-2*(a^4*(c^2+-1*d^2)+b^4*(c^2+-1*d^2)+-6*a^2*b^2*(c^2+-1*d^2)+-8*a*c*d*b^3+8*b*c*d*a^3)+-1*f^-1*(c^2+d^2)^-2*(d*b^2+-1*d*a^2+2*a*b*c)*(-2*c*b^2+2*c*a^2+4*a*b*d)*log(cos(e+f*x))+-1*b^2*d^-2*f^-1*(c^2+d^2)^-1*(-1*b^2*(d^2+2*c^2)+a*d*(-1*a*d+2*b*c))*tan(e+f*x)+-1*d^-1*f^-1*(a+b*tan(e+f*x))^2*(c+d*tan(e+f*x))^-1*(c^2+d^2)^-1*(b*c+-1*a*d)^2+-2*d^-3*f^-1*(c^2+d^2)^-2*(b*c+-1*a*d)^3*(b*(c^2+2*d^2)+a*c*d)*log(c+d*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x))^3*(c+d*tan(e+f*x))^-2, x) == :(x*(c^2+d^2)^-2*(a^3*(c^2+-1*d^2)+-3*a*b^2*(c^2+-1*d^2)+-2*c*d*b^3+6*b*c*d*a^2)+f^-1*(c^2+d^2)^-2*(b^3*(c^2+-1*d^2)+-3*b*a^2*(c^2+-1*d^2)+2*c*d*a^3+-6*a*c*d*b^2)*log(cos(e+f*x))+d^-2*f^-1*(c^2+d^2)^-2*(b*c+-1*a*d)^2*(b*(c^2+3*d^2)+2*a*c*d)*log(c+d*tan(e+f*x))+-1*d^-1*f^-1*(c+d*tan(e+f*x))^-1*(c^2+d^2)^-1*(b*c+-1*a*d)^2*(a+b*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x))^2*(c+d*tan(e+f*x))^-2, x) == :(-1*x*(c^2+d^2)^-2*(a*(c+-1d)+b*(c+d))*(b*(c+-1d)+-1*a*(c+d))+-1*d^-1*f^-1*(c+d*tan(e+f*x))^-1*(c^2+d^2)^-1*(b*c+-1*a*d)^2+-1*f^-1*(c^2+d^2)^-2*(a*c+b*d)*(-2*a*d+2*b*c)*log(c*cos(e+f*x)+d*sin(e+f*x)))
@test integrate((c+d*tan(e+f*x))^-2*(a+b*tan(e+f*x)), x) == :(x*(c^2+d^2)^-2*(a*(c^2+-1*d^2)+2*b*c*d)+f^-1*(c+d*tan(e+f*x))^-1*(c^2+d^2)^-1*(b*c+-1*a*d)+f^-1*(c^2+d^2)^-2*(-1*b*(c^2+-1*d^2)+2*a*c*d)*log(c*cos(e+f*x)+d*sin(e+f*x)))
@test integrate((a+b*tan(e+f*x))^-1*(c+d*tan(e+f*x))^-2, x) == :(-1*x*(a^2+b^2)^-1*(c^2+d^2)^-2*(-1*a*(c^2+-1*d^2)+2*b*c*d)+b^3*f^-1*(a^2+b^2)^-1*(b*c+-1*a*d)^-2*log(a*cos(e+f*x)+b*sin(e+f*x))+d^2*f^-1*(c+d*tan(e+f*x))^-1*(c^2+d^2)^-1*(b*c+-1*a*d)^-1+d^2*f^-1*(c^2+d^2)^-2*(b*c+-1*a*d)^-2*(-1*b*(d^2+3*c^2)+2*a*c*d)*log(c*cos(e+f*x)+d*sin(e+f*x)))
@test integrate((a+b*tan(e+f*x))^-2*(c+d*tan(e+f*x))^-2, x) == :(x*(a^2+b^2)^-2*(c^2+d^2)^-2*(a*(c+d)+b*(c+-1d))*(a*(c+-1d)+-1*b*(c+d))+-1*b^2*f^-1*(a+b*tan(e+f*x))^-1*(c+d*tan(e+f*x))^-1*(a^2+b^2)^-1*(b*c+-1*a*d)^-1+-2*d^3*f^-1*(c^2+d^2)^-2*(b*c+-1*a*d)^-3*(-1*b*(d^2+2*c^2)+a*c*d)*log(c*cos(e+f*x)+d*sin(e+f*x))+2*b^3*f^-1*(a^2+b^2)^-2*(b*c+-1*a*d)^-3*(-1*d*b^2+-2*d*a^2+a*b*c)*log(a*cos(e+f*x)+b*sin(e+f*x))+-1*d*f^-1*(c+d*tan(e+f*x))^-1*(a^2+b^2)^-1*(c^2+d^2)^-1*(b*c+-1*a*d)^-2*(a^2*d^2+b^2*(c^2+2*d^2)))
@test integrate((a+b*tan(e+f*x))^-3*(c+d*tan(e+f*x))^-2, x) == :(-1*x*(a^2+b^2)^-3*(c^2+d^2)^-2*(-1*a^3*(c^2+-1*d^2)+-2*c*d*b^3+3*a*b^2*(c^2+-1*d^2)+6*b*c*d*a^2)+-1*b^2*f^-1*(a+b*tan(e+f*x))^-2*(c+d*tan(e+f*x))^-1*(2*a^2+2*b^2)^-1*(b*c+-1*a*d)^-1+-1*b^3*f^-1*(a^2+b^2)^-3*(b*c+-1*a*d)^-4*(b^4*(c^2+-3*d^2)+-10*a^4*d^2+-3*a^2*b^2*(c^2+3*d^2)+2*a*c*d*b^3+10*b*c*d*a^3)*log(a*cos(e+f*x)+b*sin(e+f*x))+-1*d^4*f^-1*(c^2+d^2)^-2*(b*c+-1*a*d)^-4*(3*b*d^2+5*b*c^2+-2*a*c*d)*log(c*cos(e+f*x)+d*sin(e+f*x))+d*f^-1*(c+d*tan(e+f*x))^-1*(a^2+b^2)^-2*(c^2+d^2)^-1*(b*c+-1*a*d)^-3*(a^4*d^3+d*b^4*(2*c^2+3*d^2)+-2*a*c*b^3*(c^2+d^2)+2*d*a^2*b^2*(2*c^2+3*d^2))+-1//2*b^2*f^-1*(a+b*tan(e+f*x))^-1*(c+d*tan(e+f*x))^-1*(a^2+b^2)^-2*(b*c+-1*a*d)^-2*(-7*d*a^2+-3*d*b^2+4*a*b*c))
@test integrate((a+b*tan(e+f*x))^4*(c+d*tan(e+f*x))^-3, x) == :(-1*x*(c^2+d^2)^-3*(-1*a^4*(c^3+-3*c*d^2)+-1*c*b^4*(c^2+-3*d^2)+-4*b*d*a^3*(-1*d^2+3*c^2)+4*a*d*b^3*(-1*d^2+3*c^2)+6*c*a^2*b^2*(c^2+-3*d^2))+-1*f^-1*(c^2+d^2)^-3*(-1*a^4*(-1*d^3+3*d*c^2)+-1*d*b^4*(-1*d^2+3*c^2)+-4*a*c*b^3*(c^2+-3*d^2)+4*b*c*a^3*(c^2+-3*d^2)+6*d*a^2*b^2*(-1*d^2+3*c^2))*log(cos(e+f*x))+d^-3*f^-1*(c+d*tan(e+f*x))^-1*(c^2+d^2)^-2*(b*c+-1*a*d)^3*(b*(c^2+3*d^2)+2*a*c*d)+d^-3*f^-1*(c^2+d^2)^-3*(b*c+-1*a*d)^2*(b^2*(c^4+6*d^4+3*c^2*d^2)+a^2*d^2*(-1*d^2+3*c^2)+2*a*b*c*d*(c^2+5*d^2))*log(c+d*tan(e+f*x))+-1//2*d^-1*f^-1*(a+b*tan(e+f*x))^2*(c+d*tan(e+f*x))^-2*(c^2+d^2)^-1*(b*c+-1*a*d)^2)
@test integrate((a+b*tan(e+f*x))^3*(c+d*tan(e+f*x))^-3, x) == :(x*(c^2+d^2)^-3*(a*c+b*d)*(a^2*(c^2+-3*d^2)+-1*b^2*(-1*d^2+3*c^2)+8*a*b*c*d)+-1*f^-1*(c^2+d^2)^-3*(b*c+-1*a*d)*(a^2*(-1*d^2+3*c^2)+-1*b^2*(c^2+-3*d^2)+8*a*b*c*d)*log(c*cos(e+f*x)+d*sin(e+f*x))+-1//2*d^-1*f^-1*(c+d*tan(e+f*x))^-2*(c^2+d^2)^-1*(b*c+-1*a*d)^2*(a+b*tan(e+f*x))+-1//2*d^-2*f^-1*(c+d*tan(e+f*x))^-1*(c^2+d^2)^-2*(b*c+-1*a*d)^2*(b*(c^2+5*d^2)+4*a*c*d))
@test integrate((a+b*tan(e+f*x))^2*(c+d*tan(e+f*x))^-3, x) == :(-1*x*(c^2+d^2)^-3*(-1*a^2*(c^3+-3*c*d^2)+c*b^2*(c^2+-3*d^2)+-2*a*b*d*(-1*d^2+3*c^2))+-1*f^-1*(c^2+d^2)^-3*(-1*a^2*(-1*d^3+3*d*c^2)+d*b^2*(-1*d^2+3*c^2)+2*a*b*c*(c^2+-3*d^2))*log(c*cos(e+f*x)+d*sin(e+f*x))+f^-1*(c+d*tan(e+f*x))^-1*(c^2+d^2)^-2*(a*c+b*d)*(-2*a*d+2*b*c)+-1//2*d^-1*f^-1*(c+d*tan(e+f*x))^-2*(c^2+d^2)^-1*(b*c+-1*a*d)^2)
@test integrate((c+d*tan(e+f*x))^-3*(a+b*tan(e+f*x)), x) == :(x*(c^2+d^2)^-3*(a*c^3+-1*b*d^3+-3*a*c*d^2+3*b*d*c^2)+f^-1*(c+d*tan(e+f*x))^-2*(2*c^2+2*d^2)^-1*(b*c+-1*a*d)+f^-1*(c^2+d^2)^-3*(-1*b*(c^3+-3*c*d^2)+a*d*(-1*d^2+3*c^2))*log(c*cos(e+f*x)+d*sin(e+f*x))+-1*f^-1*(c+d*tan(e+f*x))^-1*(c^2+d^2)^-2*(-1*b*(c^2+-1*d^2)+2*a*c*d))
@test integrate((a+b*tan(e+f*x))^-1*(c+d*tan(e+f*x))^-3, x) == :(-1*x*(a^2+b^2)^-1*(c^2+d^2)^-3*(-1*a*(c^3+-3*c*d^2)+b*d*(-1*d^2+3*c^2))+b^4*f^-1*(a^2+b^2)^-1*(b*c+-1*a*d)^-3*log(a*cos(e+f*x)+b*sin(e+f*x))+d^2*f^-1*(c+d*tan(e+f*x))^-2*(c^2+d^2)^-1*(-2*a*d+2*b*c)^-1+d^2*f^-1*(c^2+d^2)^-3*(b*c+-1*a*d)^-3*(-1*b^2*(d^4+6*c^4+3*c^2*d^2)+-1*a^2*d^2*(-1*d^2+3*c^2)+8*a*b*d*c^3)*log(c*cos(e+f*x)+d*sin(e+f*x))+-1*d^2*f^-1*(c+d*tan(e+f*x))^-1*(c^2+d^2)^-2*(b*c+-1*a*d)^-2*(-1*b*(d^2+3*c^2)+2*a*c*d))
@test integrate((a+b*tan(e+f*x))^-2*(c+d*tan(e+f*x))^-3, x) == :(-1*x*(a^2+b^2)^-2*(c^2+d^2)^-3*(-1*a^2*(c^3+-3*c*d^2)+a*b*(-2*d^3+6*d*c^2)+c*b^2*(c^2+-3*d^2))+b^4*f^-1*(a^2+b^2)^-2*(b*c+-1*a*d)^-4*(-5*d*a^2+-3*d*b^2+2*a*b*c)*log(a*cos(e+f*x)+b*sin(e+f*x))+d^3*f^-1*(c^2+d^2)^-3*(b*c+-1*a*d)^-4*(b^2*(3*d^4+10*c^4+9*c^2*d^2)+a^2*d^2*(-1*d^2+3*c^2)+-2*a*b*c*d*(d^2+5*c^2))*log(c*cos(e+f*x)+d*sin(e+f*x))+-1*b^2*f^-1*(a+b*tan(e+f*x))^-1*(c+d*tan(e+f*x))^-2*(a^2+b^2)^-1*(b*c+-1*a*d)^-1+d*f^-1*(c+d*tan(e+f*x))^-1*(a^2+b^2)^-1*(c^2+d^2)^-2*(b*c+-1*a*d)^-3*(-1*b^3*(c^4+3*d^4+6*c^2*d^2)+2*c*a^3*d^3+-2*b*a^2*d^2*(d^2+2*c^2)+2*a*c*b^2*d^3)+-1*d*f^-1*(c+d*tan(e+f*x))^-2*(c^2+d^2)^-1*(2*a^2+2*b^2)^-1*(b*c+-1*a*d)^-2*(a^2*d^2+b^2*(2*c^2+3*d^2)))
@test integrate((a+b*tan(e+f*x))^3*(c+d*tan(e+f*x))^(1/2), x) == :(f^-1*(b+im*a)^3*(c+-1*im*d)^(1/2)*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1*f^-1*(c+im*d)^(1/2)*(-1b+im*a)^3*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+2*b*f^-1*(c+d*tan(e+f*x))^(1/2)*(-1*b^2+3*a^2)+-4//15*b^2*d^-2*f^-1*(c+d*tan(e+f*x))^3//2*(b*c+-6*a*d)+2//5*b^2*d^-1*f^-1*(c+d*tan(e+f*x))^3//2*(a+b*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x))^2*(c+d*tan(e+f*x))^(1/2), x) == :(4*a*b*f^-1*(c+d*tan(e+f*x))^(1/2)+2//3*b^2*d^-1*f^-1*(c+d*tan(e+f*x))^3//2+im*f^-1*(a+im*b)^2*(c+im*d)^(1/2)*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1*im*f^-1*(a+-1*im*b)^2*(c+-1*im*d)^(1/2)*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((c+d*tan(e+f*x))^(1/2)*(a+b*tan(e+f*x)), x) == :(2*b*f^-1*(c+d*tan(e+f*x))^(1/2)+f^-1*(c+im*d)^(1/2)*(-1b+im*a)*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1*f^-1*(c+-1*im*d)^(1/2)*(b+im*a)*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+b*tan(e+f*x))^-1*(c+d*tan(e+f*x))^(1/2), x) == :(f^-1*(b+im*a)^-1*(c+-1*im*d)^(1/2)*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1*f^-1*(c+im*d)^(1/2)*(-1b+im*a)^-1*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-2*b^(1/2)*f^-1*(a^2+b^2)^-1*(b*c+-1*a*d)^(1/2)*arctanh(b^(1/2)*(c+d*tan(e+f*x))^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*tan(e+f*x))^-2*(c+d*tan(e+f*x))^(1/2), x) == :(im*f^-1*(a+im*b)^-2*(c+im*d)^(1/2)*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1*im*f^-1*(a+-1*im*b)^-2*(c+-1*im*d)^(1/2)*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1*b*f^-1*(a+b*tan(e+f*x))^-1*(c+d*tan(e+f*x))^(1/2)*(a^2+b^2)^-1+-1*b^(1/2)*f^-1*(a^2+b^2)^-2*(b*c+-1*a*d)^-1//2*(d*b^2+-3*d*a^2+4*a*b*c)*arctanh(b^(1/2)*(c+d*tan(e+f*x))^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*tan(e+f*x))^-3*(c+d*tan(e+f*x))^(1/2), x) == :(f^-1*(c+im*d)^(1/2)*(-1b+im*a)^-3*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1*f^-1*(b+im*a)^-3*(c+-1*im*d)^(1/2)*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1*b*f^-1*(a+b*tan(e+f*x))^-2*(c+d*tan(e+f*x))^(1/2)*(2*a^2+2*b^2)^-1+1//4*b^(1/2)*f^-1*(a^2+b^2)^-3*(b*c+-1*a*d)^-3//2*(b^4*(d^2+8*c^2)+-15*a^4*d^2+-6*a^2*b^2*(-3*d^2+4*c^2)+-24*a*c*d*b^3+40*b*c*d*a^3)*arctanh(b^(1/2)*(c+d*tan(e+f*x))^(1/2)*(b*c+-1*a*d)^-1//2)+-1//4*b*f^-1*(a+b*tan(e+f*x))^-1*(c+d*tan(e+f*x))^(1/2)*(a^2+b^2)^-2*(b*c+-1*a*d)^-1*(d*b^2+-7*d*a^2+8*a*b*c))
@test integrate((a+b*tan(e+f*x))^3*(c+d*tan(e+f*x))^3//2, x) == :(f^-1*(c+d*tan(e+f*x))^(1/2)*(-2*c*b^3+2*d*a^3+-6*a*d*b^2+6*b*c*a^2)+f^-1*(b+im*a)^3*(c+-1*im*d)^3//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1*f^-1*(c+im*d)^3//2*(-1b+im*a)^3*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+2//3*b*f^-1*(c+d*tan(e+f*x))^3//2*(-1*b^2+3*a^2)+-4//35*b^2*d^-2*f^-1*(c+d*tan(e+f*x))^5//2*(b*c+-8*a*d)+2//7*b^2*d^-1*f^-1*(c+d*tan(e+f*x))^5//2*(a+b*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x))^2*(c+d*tan(e+f*x))^3//2, x) == :(f^-1*(c+d*tan(e+f*x))^(1/2)*(-2*d*b^2+2*d*a^2+4*a*b*c)+2//5*b^2*d^-1*f^-1*(c+d*tan(e+f*x))^5//2+4//3*a*b*f^-1*(c+d*tan(e+f*x))^3//2+im*f^-1*(a+im*b)^2*(c+im*d)^3//2*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1*im*f^-1*(a+-1*im*b)^2*(c+-1*im*d)^3//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((c+d*tan(e+f*x))^3//2*(a+b*tan(e+f*x)), x) == :(f^-1*(c+d*tan(e+f*x))^(1/2)*(2*a*d+2*b*c)+2//3*b*f^-1*(c+d*tan(e+f*x))^3//2+f^-1*(c+im*d)^3//2*(-1b+im*a)*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1*f^-1*(c+-1*im*d)^3//2*(b+im*a)*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+b*tan(e+f*x))^-1*(c+d*tan(e+f*x))^3//2, x) == :(f^-1*(b+im*a)^-1*(c+-1*im*d)^3//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1*f^-1*(c+im*d)^3//2*(-1b+im*a)^-1*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-2*b^-1//2*f^-1*(a^2+b^2)^-1*(b*c+-1*a*d)^3//2*arctanh(b^(1/2)*(c+d*tan(e+f*x))^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*tan(e+f*x))^-2*(c+d*tan(e+f*x))^3//2, x) == :(im*f^-1*(a+im*b)^-2*(c+im*d)^3//2*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1*im*f^-1*(a+-1*im*b)^-2*(c+-1*im*d)^3//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1*f^-1*(a+b*tan(e+f*x))^-1*(c+d*tan(e+f*x))^(1/2)*(a^2+b^2)^-1*(b*c+-1*a*d)+-1*b^-1//2*f^-1*(a^2+b^2)^-2*(b*c+-1*a*d)^(1/2)*(-1*d*a^2+3*d*b^2+4*a*b*c)*arctanh(b^(1/2)*(c+d*tan(e+f*x))^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*tan(e+f*x))^-3*(c+d*tan(e+f*x))^3//2, x) == :(f^-1*(c+im*d)^3//2*(-1b+im*a)^-3*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1*f^-1*(b+im*a)^-3*(c+-1*im*d)^3//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1*f^-1*(a+b*tan(e+f*x))^-2*(c+d*tan(e+f*x))^(1/2)*(2*a^2+2*b^2)^-1*(b*c+-1*a*d)+-1//4*f^-1*(a+b*tan(e+f*x))^-1*(c+d*tan(e+f*x))^(1/2)*(a^2+b^2)^-2*(-3*d*a^2+5*d*b^2+8*a*b*c)+1//4*b^-1//2*f^-1*(a^2+b^2)^-3*(b*c+-1*a*d)^-1//2*(b^4*(-3*d^2+8*c^2)+-3*a^4*d^2+-2*a^2*b^2*(-13*d^2+12*c^2)+-40*a*c*d*b^3+24*b*c*d*a^3)*arctanh(b^(1/2)*(c+d*tan(e+f*x))^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*tan(e+f*x))^3*(c+d*tan(e+f*x))^5//2, x) == :(f^-1*(c+d*tan(e+f*x))^(1/2)*(-2*b^3*(c^2+-1*d^2)+4*c*d*a^3+6*b*a^2*(c^2+-1*d^2)+-12*a*c*d*b^2)+1//3*f^-1*(c+d*tan(e+f*x))^3//2*(-2*c*b^3+2*d*a^3+-6*a*d*b^2+6*b*c*a^2)+f^-1*(b+im*a)^3*(c+-1*im*d)^5//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1*f^-1*(c+im*d)^5//2*(-1b+im*a)^3*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+2//5*b*f^-1*(c+d*tan(e+f*x))^5//2*(-1*b^2+3*a^2)+-4//63*b^2*d^-2*f^-1*(c+d*tan(e+f*x))^7//2*(b*c+-10*a*d)+2//9*b^2*d^-1*f^-1*(c+d*tan(e+f*x))^7//2*(a+b*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x))^2*(c+d*tan(e+f*x))^5//2, x) == :(1//3*f^-1*(c+d*tan(e+f*x))^3//2*(-2*d*b^2+2*d*a^2+4*a*b*c)+f^-1*(c+d*tan(e+f*x))^(1/2)*(a*c+-1*b*d)*(4*a*d+4*b*c)+2//7*b^2*d^-1*f^-1*(c+d*tan(e+f*x))^7//2+4//5*a*b*f^-1*(c+d*tan(e+f*x))^5//2+im*f^-1*(a+im*b)^2*(c+im*d)^5//2*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1*im*f^-1*(a+-1*im*b)^2*(c+-1*im*d)^5//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((c+d*tan(e+f*x))^5//2*(a+b*tan(e+f*x)), x) == :(f^-1*(c+d*tan(e+f*x))^(1/2)*(2*b*(c^2+-1*d^2)+4*a*c*d)+1//3*f^-1*(c+d*tan(e+f*x))^3//2*(2*a*d+2*b*c)+2//5*b*f^-1*(c+d*tan(e+f*x))^5//2+f^-1*(c+im*d)^5//2*(-1b+im*a)*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1*f^-1*(c+-1*im*d)^5//2*(b+im*a)*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+b*tan(e+f*x))^-1*(c+d*tan(e+f*x))^5//2, x) == :(f^-1*(b+im*a)^-1*(c+-1*im*d)^5//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1*f^-1*(c+im*d)^5//2*(-1b+im*a)^-1*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+2*b^-1*d^2*f^-1*(c+d*tan(e+f*x))^(1/2)+-2*b^-3//2*f^-1*(a^2+b^2)^-1*(b*c+-1*a*d)^5//2*arctanh(b^(1/2)*(c+d*tan(e+f*x))^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*tan(e+f*x))^-2*(c+d*tan(e+f*x))^5//2, x) == :(im*f^-1*(a+im*b)^-2*(c+im*d)^5//2*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1*im*f^-1*(a+-1*im*b)^-2*(c+-1*im*d)^5//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1*b^-1*f^-1*(a+b*tan(e+f*x))^-1*(c+d*tan(e+f*x))^(1/2)*(a^2+b^2)^-1*(b*c+-1*a*d)^2+-1*b^-3//2*f^-1*(a^2+b^2)^-2*(b*c+-1*a*d)^3//2*(d*a^2+5*d*b^2+4*a*b*c)*arctanh(b^(1/2)*(c+d*tan(e+f*x))^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*tan(e+f*x))^-3*(c+d*tan(e+f*x))^5//2, x) == :(f^-1*(c+im*d)^5//2*(-1b+im*a)^-3*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1*f^-1*(b+im*a)^-3*(c+-1*im*d)^5//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1//2*b^-1*f^-1*(a+b*tan(e+f*x))^-2*(c+d*tan(e+f*x))^(1/2)*(a^2+b^2)^-1*(b*c+-1*a*d)^2+1//4*b^-3//2*f^-1*(a^2+b^2)^-3*(b*c+-1*a*d)^(1/2)*(a^4*d^2+b^4*(-15*d^2+8*c^2)+-6*a^2*b^2*(-3*d^2+4*c^2)+-56*a*c*d*b^3+8*b*c*d*a^3)*arctanh(b^(1/2)*(c+d*tan(e+f*x))^(1/2)*(b*c+-1*a*d)^-1//2)+-1//4*b^-1*f^-1*(a+b*tan(e+f*x))^-1*(c+d*tan(e+f*x))^(1/2)*(a^2+b^2)^-2*(b*c+-1*a*d)*(d*a^2+9*d*b^2+8*a*b*c))
@test integrate((a+b*tan(e+f*x))^4*(c+d*tan(e+f*x))^-1//2, x) == :(im*f^-1*(a+im*b)^4*(c+im*d)^-1//2*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1*im*f^-1*(a+-1*im*b)^4*(c+-1*im*d)^-1//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-2//15*b^2*d^-3*f^-1*(c+d*tan(e+f*x))^(1/2)*(-1*b^2*(-15*d^2+8*c^2)+-87*a^2*d^2+40*a*b*c*d)+2//5*b^2*d^-1*f^-1*(a+b*tan(e+f*x))^2*(c+d*tan(e+f*x))^(1/2)+-4//15*b^3*d^-2*f^-1*(c+d*tan(e+f*x))^(1/2)*(-7*a*d+2*b*c)*tan(e+f*x))
@test integrate((a+b*tan(e+f*x))^3*(c+d*tan(e+f*x))^-1//2, x) == :(f^-1*(b+im*a)^3*(c+-1*im*d)^-1//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1*f^-1*(c+im*d)^-1//2*(-1b+im*a)^3*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-4//3*b^2*d^-2*f^-1*(c+d*tan(e+f*x))^(1/2)*(b*c+-4*a*d)+2//3*b^2*d^-1*f^-1*(c+d*tan(e+f*x))^(1/2)*(a+b*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x))^2*(c+d*tan(e+f*x))^-1//2, x) == :(2*b^2*d^-1*f^-1*(c+d*tan(e+f*x))^(1/2)+im*f^-1*(a+im*b)^2*(c+im*d)^-1//2*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1*im*f^-1*(a+-1*im*b)^2*(c+-1*im*d)^-1//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((c+d*tan(e+f*x))^-1//2*(a+b*tan(e+f*x)), x) == :(f^-1*(c+im*d)^-1//2*(-1b+im*a)*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1*f^-1*(c+-1*im*d)^-1//2*(b+im*a)*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+b*tan(e+f*x))^-1*(c+d*tan(e+f*x))^-1//2, x) == :(f^-1*(b+im*a)^-1*(c+-1*im*d)^-1//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1*f^-1*(c+im*d)^-1//2*(-1b+im*a)^-1*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-2*b^3//2*f^-1*(a^2+b^2)^-1*(b*c+-1*a*d)^-1//2*arctanh(b^(1/2)*(c+d*tan(e+f*x))^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*tan(e+f*x))^-2*(c+d*tan(e+f*x))^-1//2, x) == :(im*f^-1*(a+im*b)^-2*(c+im*d)^-1//2*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1*im*f^-1*(a+-1*im*b)^-2*(c+-1*im*d)^-1//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1*b^2*f^-1*(a+b*tan(e+f*x))^-1*(c+d*tan(e+f*x))^(1/2)*(a^2+b^2)^-1*(b*c+-1*a*d)^-1+-1*b^3//2*f^-1*(a^2+b^2)^-2*(b*c+-1*a*d)^-3//2*(-1*d*b^2+-5*d*a^2+4*a*b*c)*arctanh(b^(1/2)*(c+d*tan(e+f*x))^(1/2)*(b*c+-1*a*d)^-1//2))
@test integrate((a+b*tan(e+f*x))^4*(c+d*tan(e+f*x))^-3//2, x) == :(im*f^-1*(a+im*b)^4*(c+im*d)^-3//2*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1*im*f^-1*(a+-1*im*b)^4*(c+-1*im*d)^-3//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-2*d^-1*f^-1*(a+b*tan(e+f*x))^2*(c+d*tan(e+f*x))^-1//2*(c^2+d^2)^-1*(b*c+-1*a*d)^2+-2//3*b*d^-3*f^-1*(c+d*tan(e+f*x))^(1/2)*(c^2+d^2)^-1*(b^3*(8*c^3+5*c*d^2)+-6*a^3*d^3+-12*a*d*b^2*(d^2+2*c^2)+15*b*c*a^2*d^2)+-2//3*b^2*d^-2*f^-1*(c+d*tan(e+f*x))^(1/2)*(c^2+d^2)^-1*(-1*b^2*(d^2+4*c^2)+3*a*d*(-1*a*d+2*b*c))*tan(e+f*x))
@test integrate((a+b*tan(e+f*x))^3*(c+d*tan(e+f*x))^-3//2, x) == :(f^-1*(b+im*a)^3*(c+-1*im*d)^-3//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1*f^-1*(c+im*d)^-3//2*(-1b+im*a)^3*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-2*b*d^-2*f^-1*(c+d*tan(e+f*x))^(1/2)*(c^2+d^2)^-1*(-1*b^2*(d^2+2*c^2)+a*d*(-1*a*d+2*b*c))+-2*d^-1*f^-1*(c+d*tan(e+f*x))^-1//2*(c^2+d^2)^-1*(b*c+-1*a*d)^2*(a+b*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x))^2*(c+d*tan(e+f*x))^-3//2, x) == :(im*f^-1*(a+im*b)^2*(c+im*d)^-3//2*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1*im*f^-1*(a+-1*im*b)^2*(c+-1*im*d)^-3//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-2*d^-1*f^-1*(c+d*tan(e+f*x))^-1//2*(c^2+d^2)^-1*(b*c+-1*a*d)^2)
@test integrate((c+d*tan(e+f*x))^-3//2*(a+b*tan(e+f*x)), x) == :(f^-1*(c+im*d)^-3//2*(-1b+im*a)*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+f^-1*(c+d*tan(e+f*x))^-1//2*(c^2+d^2)^-1*(-2*a*d+2*b*c)+-1*f^-1*(c+-1*im*d)^-3//2*(b+im*a)*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+b*tan(e+f*x))^-1*(c+d*tan(e+f*x))^-3//2, x) == :(f^-1*(b+im*a)^-1*(c+-1*im*d)^-3//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1*f^-1*(c+im*d)^-3//2*(-1b+im*a)^-1*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-2*b^5//2*f^-1*(a^2+b^2)^-1*(b*c+-1*a*d)^-3//2*arctanh(b^(1/2)*(c+d*tan(e+f*x))^(1/2)*(b*c+-1*a*d)^-1//2)+2*d^2*f^-1*(c+d*tan(e+f*x))^-1//2*(c^2+d^2)^-1*(b*c+-1*a*d)^-1)
@test integrate((a+b*tan(e+f*x))^-2*(c+d*tan(e+f*x))^-3//2, x) == :(im*f^-1*(a+im*b)^-2*(c+im*d)^-3//2*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1*im*f^-1*(a+-1*im*b)^-2*(c+-1*im*d)^-3//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1*b^2*f^-1*(a+b*tan(e+f*x))^-1*(c+d*tan(e+f*x))^-1//2*(a^2+b^2)^-1*(b*c+-1*a*d)^-1+-1*b^5//2*f^-1*(a^2+b^2)^-2*(b*c+-1*a*d)^-5//2*(-7*d*a^2+-3*d*b^2+4*a*b*c)*arctanh(b^(1/2)*(c+d*tan(e+f*x))^(1/2)*(b*c+-1*a*d)^-1//2)+-1*d*f^-1*(c+d*tan(e+f*x))^-1//2*(a^2+b^2)^-1*(c^2+d^2)^-1*(b*c+-1*a*d)^-2*(b^2*(c^2+3*d^2)+2*a^2*d^2))
@test integrate((a+b*tan(e+f*x))^4*(c+d*tan(e+f*x))^-5//2, x) == :(im*f^-1*(a+im*b)^4*(c+im*d)^-5//2*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1*im*f^-1*(a+-1*im*b)^4*(c+-1*im*d)^-5//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-2//3*b^2*d^-3*f^-1*(c+d*tan(e+f*x))^(1/2)*(c^2+d^2)^-1*(-1*b^2*(3*d^2+4*c^2)+a*d*(-1*a*d+2*b*c))+-2//3*d^-1*f^-1*(a+b*tan(e+f*x))^2*(c+d*tan(e+f*x))^-3//2*(c^2+d^2)^-1*(b*c+-1*a*d)^2+4//3*d^-3*f^-1*(c+d*tan(e+f*x))^-1//2*(c^2+d^2)^-2*(b*c+-1*a*d)^3*(2*b*c^2+5*b*d^2+3*a*c*d))
@test integrate((a+b*tan(e+f*x))^3*(c+d*tan(e+f*x))^-5//2, x) == :(f^-1*(b+im*a)^3*(c+-1*im*d)^-5//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1*f^-1*(c+im*d)^-5//2*(-1b+im*a)^3*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-4//3*d^-2*f^-1*(c+d*tan(e+f*x))^-1//2*(c^2+d^2)^-2*(b*c+-1*a*d)^2*(b*(c^2+4*d^2)+3*a*c*d)+-2//3*d^-1*f^-1*(c+d*tan(e+f*x))^-3//2*(c^2+d^2)^-1*(b*c+-1*a*d)^2*(a+b*tan(e+f*x)))
@test integrate((a+b*tan(e+f*x))^2*(c+d*tan(e+f*x))^-5//2, x) == :(im*f^-1*(a+im*b)^2*(c+im*d)^-5//2*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+f^-1*(c+d*tan(e+f*x))^-1//2*(c^2+d^2)^-2*(a*c+b*d)*(-4*a*d+4*b*c)+-1*im*f^-1*(a+-1*im*b)^2*(c+-1*im*d)^-5//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-2//3*d^-1*f^-1*(c+d*tan(e+f*x))^-3//2*(c^2+d^2)^-1*(b*c+-1*a*d)^2)
@test integrate((c+d*tan(e+f*x))^-5//2*(a+b*tan(e+f*x)), x) == :(f^-1*(c+im*d)^-5//2*(-1b+im*a)*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+f^-1*(c+d*tan(e+f*x))^-3//2*(3*c^2+3*d^2)^-1*(-2*a*d+2*b*c)+-1*f^-1*(c+d*tan(e+f*x))^-1//2*(c^2+d^2)^-2*(-2*b*(c^2+-1*d^2)+4*a*c*d)+-1*f^-1*(c+-1*im*d)^-5//2*(b+im*a)*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2))
@test integrate((a+b*tan(e+f*x))^-1*(c+d*tan(e+f*x))^-5//2, x) == :(f^-1*(b+im*a)^-1*(c+-1*im*d)^-5//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1*f^-1*(c+im*d)^-5//2*(-1b+im*a)^-1*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-2*b^7//2*f^-1*(a^2+b^2)^-1*(b*c+-1*a*d)^-5//2*arctanh(b^(1/2)*(c+d*tan(e+f*x))^(1/2)*(b*c+-1*a*d)^-1//2)+2*d^2*f^-1*(c+d*tan(e+f*x))^-3//2*(c^2+d^2)^-1*(-3*a*d+3*b*c)^-1+-2*d^2*f^-1*(c+d*tan(e+f*x))^-1//2*(c^2+d^2)^-2*(b*c+-1*a*d)^-2*(-1*b*(d^2+3*c^2)+2*a*c*d))
@test integrate((a+b*tan(e+f*x))^-2*(c+d*tan(e+f*x))^-5//2, x) == :(im*f^-1*(a+im*b)^-2*(c+im*d)^-5//2*arctanh((c+im*d)^-1//2*(c+d*tan(e+f*x))^(1/2))+-1*im*f^-1*(a+-1*im*b)^-2*(c+-1*im*d)^-5//2*arctanh((c+d*tan(e+f*x))^(1/2)*(c+-1*im*d)^-1//2)+-1*b^2*f^-1*(a+b*tan(e+f*x))^-1*(c+d*tan(e+f*x))^-3//2*(a^2+b^2)^-1*(b*c+-1*a*d)^-1+-1*b^7//2*f^-1*(a^2+b^2)^-2*(b*c+-1*a*d)^-7//2*(-9*d*a^2+-5*d*b^2+4*a*b*c)*arctanh(b^(1/2)*(c+d*tan(e+f*x))^(1/2)*(b*c+-1*a*d)^-1//2)+d*f^-1*(c+d*tan(e+f*x))^-1//2*(a^2+b^2)^-1*(c^2+d^2)^-2*(b*c+-1*a*d)^-3*(-1*b^3*(c^4+5*d^4+10*c^2*d^2)+4*c*a^3*d^3+-4*b*a^2*d^2*(d^2+2*c^2)+4*a*c*b^2*d^3)+-1*d*f^-1*(c+d*tan(e+f*x))^-3//2*(c^2+d^2)^-1*(3*a^2+3*b^2)^-1*(b*c+-1*a*d)^-2*(b^2*(3*c^2+5*d^2)+2*a^2*d^2))
@test integrate((a+b*tan(e+f*x))^5//2*(c+d*tan(e+f*x))^(1/2), x) == :(im*f^-1*(a+im*b)^5//2*(c+im*d)^(1/2)*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+(1/2)*b^2*d^-1*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^3//2+-1*im*f^-1*(a+-1*im*b)^5//2*(c+-1*im*d)^(1/2)*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+1//4*b^(1/2)*d^-3//2*f^-1*(-1*b^2*(c^2+8*d^2)+15*a^2*d^2+10*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1//4*b*d^-1*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^(1/2)*(b*c+-9*a*d))
@test integrate((a+b*tan(e+f*x))^3//2*(c+d*tan(e+f*x))^(1/2), x) == :(b*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^(1/2)+im*f^-1*(a+im*b)^3//2*(c+im*d)^(1/2)*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+b^(1/2)*d^-1//2*f^-1*(b*c+3*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^3//2*(c+-1*im*d)^(1/2)*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2)))
@test integrate((a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^(1/2), x) == :(2*b^(1/2)*d^(1/2)*f^-1*arctanh(b^-1//2*d^(1/2)*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2)+im*f^-1*(a+im*b)^(1/2)*(c+im*d)^(1/2)*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^(1/2)*(c+-1*im*d)^(1/2)*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2)))
@test integrate((a+b*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2), x) == :(im*f^-1*(a+im*b)^-1//2*(c+im*d)^(1/2)*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^-1//2*(c+-1*im*d)^(1/2)*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2)))
@test integrate((a+b*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^(1/2), x) == :(im*f^-1*(a+im*b)^-3//2*(c+im*d)^(1/2)*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^-3//2*(c+-1*im*d)^(1/2)*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+-2*b*f^-1*(a+b*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(a^2+b^2)^-1)
@test integrate((a+b*tan(e+f*x))^-5//2*(c+d*tan(e+f*x))^(1/2), x) == :(im*f^-1*(a+im*b)^-5//2*(c+im*d)^(1/2)*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^-5//2*(c+-1*im*d)^(1/2)*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+-2*b*f^-1*(a+b*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^(1/2)*(3*a^2+3*b^2)^-1+-2//3*b*f^-1*(a+b*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(a^2+b^2)^-2*(b*c+-1*a*d)^-1*(d*b^2+-5*d*a^2+6*a*b*c))
@test integrate((a+b*tan(e+f*x))^3//2*(c+d*tan(e+f*x))^3//2, x) == :((1/2)*b*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^3//2+1//4*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^(1/2)*(3*b*c+5*a*d)+im*f^-1*(a+im*b)^3//2*(c+im*d)^3//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^3//2*(c+-1*im*d)^3//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+1//4*b^-1//2*d^-1//2*f^-1*(b^2*(-8*d^2+3*c^2)+3*a^2*d^2+18*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2))
@test integrate((a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^3//2, x) == :(d*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^(1/2)+im*f^-1*(a+im*b)^(1/2)*(c+im*d)^3//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+b^-1//2*d^(1/2)*f^-1*(a*d+3*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^(1/2)*(c+-1*im*d)^3//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2)))
@test integrate((a+b*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^3//2, x) == :(2*b^-1//2*d^3//2*f^-1*arctanh(b^-1//2*d^(1/2)*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2)+im*f^-1*(a+im*b)^-1//2*(c+im*d)^3//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^-1//2*(c+-1*im*d)^3//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2)))
@test integrate((a+b*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^3//2, x) == :(im*f^-1*(a+im*b)^-3//2*(c+im*d)^3//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^-3//2*(c+-1*im*d)^3//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+-1*f^-1*(a+b*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(a^2+b^2)^-1*(-2*a*d+2*b*c))
@test integrate((a+b*tan(e+f*x))^-5//2*(c+d*tan(e+f*x))^3//2, x) == :(im*f^-1*(a+im*b)^-5//2*(c+im*d)^3//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^-5//2*(c+-1*im*d)^3//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+-1*f^-1*(a+b*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^(1/2)*(3*a^2+3*b^2)^-1*(-2*a*d+2*b*c)+-1//3*f^-1*(a+b*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(a^2+b^2)^-2*(-4*d*a^2+8*d*b^2+12*a*b*c))
@test integrate((a+b*tan(e+f*x))^-7//2*(c+d*tan(e+f*x))^3//2, x) == :(im*f^-1*(a+im*b)^-7//2*(c+im*d)^3//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^-7//2*(c+-1*im*d)^3//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+-1*f^-1*(a+b*tan(e+f*x))^-5//2*(c+d*tan(e+f*x))^(1/2)*(5*a^2+5*b^2)^-1*(-2*a*d+2*b*c)+-1//15*f^-1*(a+b*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^(1/2)*(a^2+b^2)^-2*(-8*d*a^2+12*d*b^2+20*a*b*c)+1//15*f^-1*(a+b*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(a^2+b^2)^-3*(b*c+-1*a*d)^-1*(-16*a^4*d^2+6*b^4*(-1*d^2+5*c^2)+-2*a^2*b^2*(-49*d^2+45*c^2)+-140*a*c*d*b^3+100*b*c*d*a^3))
@test integrate((a+b*tan(e+f*x))^3//2*(c+d*tan(e+f*x))^5//2, x) == :(im*f^-1*(a+im*b)^3//2*(c+im*d)^5//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^3//2*(c+-1*im*d)^5//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+1//3*b^-1*d^2*f^-1*(a+b*tan(e+f*x))^5//2*(c+d*tan(e+f*x))^(1/2)+1//8*b^-1*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^(1/2)*(b^2*(-8*d^2+11*c^2)+-1*a^2*d^2+14*a*b*c*d)+1//8*b^-3//2*d^-1//2*f^-1*(-1*a^3*d^3+5*b^3*(c^3+-8*c*d^2)+3*a*d*b^2*(-8*d^2+15*c^2)+15*b*c*a^2*d^2)*arctanh(b^-1//2*d^(1/2)*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2)+1//12*d*b^-1*f^-1*(a+b*tan(e+f*x))^3//2*(c+d*tan(e+f*x))^(1/2)*(-1*a*d+13*b*c))
@test integrate((a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^5//2, x) == :(im*f^-1*(a+im*b)^(1/2)*(c+im*d)^5//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+(1/2)*b^-1*d^2*f^-1*(a+b*tan(e+f*x))^3//2*(c+d*tan(e+f*x))^(1/2)+-1*im*f^-1*(a+-1*im*b)^(1/2)*(c+-1*im*d)^5//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+1//4*b^-3//2*d^(1/2)*f^-1*(b^2*(-8*d^2+15*c^2)+-1*a^2*d^2+10*a*b*c*d)*arctanh(b^-1//2*d^(1/2)*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2)+1//4*d*b^-1*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^(1/2)*(-1*a*d+9*b*c))
@test integrate((a+b*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^5//2, x) == :(im*f^-1*(a+im*b)^-1//2*(c+im*d)^5//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+b^-1*d^2*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^(1/2)+b^-3//2*d^3//2*f^-1*(-1*a*d+5*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^-1//2*(c+-1*im*d)^5//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2)))
@test integrate((a+b*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^5//2, x) == :(2*b^-3//2*d^5//2*f^-1*arctanh(b^-1//2*d^(1/2)*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2)+im*f^-1*(a+im*b)^-3//2*(c+im*d)^5//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^-3//2*(c+-1*im*d)^5//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+-2*b^-1*f^-1*(a+b*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(a^2+b^2)^-1*(b*c+-1*a*d)^2)
@test integrate((a+b*tan(e+f*x))^-5//2*(c+d*tan(e+f*x))^5//2, x) == :(im*f^-1*(a+im*b)^-5//2*(c+im*d)^5//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^-5//2*(c+-1*im*d)^5//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+-2//3*b^-1*f^-1*(a+b*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^(1/2)*(a^2+b^2)^-1*(b*c+-1*a*d)^2+-1//3*b^-1*f^-1*(a+b*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(a^2+b^2)^-2*(-2*a*d+2*b*c)*(d*a^2+7*d*b^2+6*a*b*c))
@test integrate((a+b*tan(e+f*x))^-7//2*(c+d*tan(e+f*x))^5//2, x) == :(im*f^-1*(a+im*b)^-7//2*(c+im*d)^5//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^-7//2*(c+-1*im*d)^5//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+-2//5*b^-1*f^-1*(a+b*tan(e+f*x))^-5//2*(c+d*tan(e+f*x))^(1/2)*(a^2+b^2)^-1*(b*c+-1*a*d)^2+1//15*b^-1*f^-1*(a+b*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(a^2+b^2)^-3*(2*b^4*(-23*d^2+15*c^2)+4*a^4*d^2+-6*a^2*b^2*(-13*d^2+15*c^2)+-200*a*c*d*b^3+40*b*c*d*a^3)+-1//15*b^-1*f^-1*(a+b*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^(1/2)*(a^2+b^2)^-2*(-2*a*d+2*b*c)*(d*a^2+11*d*b^2+10*a*b*c))
@test integrate((a+b*tan(e+f*x))^5//2*(c+d*tan(e+f*x))^-1//2, x) == :(im*f^-1*(a+im*b)^5//2*(c+im*d)^-1//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+b^2*d^-1*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^(1/2)+-1*im*f^-1*(a+-1*im*b)^5//2*(c+-1*im*d)^-1//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+-1*b^3//2*d^-3//2*f^-1*(b*c+-5*a*d)*arctanh(b^-1//2*d^(1/2)*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2))
@test integrate((a+b*tan(e+f*x))^3//2*(c+d*tan(e+f*x))^-1//2, x) == :(2*b^3//2*d^-1//2*f^-1*arctanh(b^-1//2*d^(1/2)*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2)+im*f^-1*(a+im*b)^3//2*(c+im*d)^-1//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^3//2*(c+-1*im*d)^-1//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2)))
@test integrate((a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2, x) == :(im*f^-1*(a+im*b)^(1/2)*(c+im*d)^-1//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^(1/2)*(c+-1*im*d)^-1//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2)))
@test integrate((a+b*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^-1//2, x) == :(im*f^-1*(a+im*b)^-1//2*(c+im*d)^-1//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^-1//2*(c+-1*im*d)^-1//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2)))
@test integrate((a+b*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^-1//2, x) == :(im*f^-1*(a+im*b)^-3//2*(c+im*d)^-1//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^-3//2*(c+-1*im*d)^-1//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+-2*b^2*f^-1*(a+b*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(a^2+b^2)^-1*(b*c+-1*a*d)^-1)
@test integrate((a+b*tan(e+f*x))^-5//2*(c+d*tan(e+f*x))^-1//2, x) == :(im*f^-1*(a+im*b)^-5//2*(c+im*d)^-1//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^-5//2*(c+-1*im*d)^-1//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+-2*b^2*f^-1*(a+b*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^(1/2)*(3*a^2+3*b^2)^-1*(b*c+-1*a*d)^-1+-4//3*b^2*f^-1*(a+b*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^(1/2)*(a^2+b^2)^-2*(b*c+-1*a*d)^-2*(-1*d*b^2+-4*d*a^2+3*a*b*c))
@test integrate((a+b*tan(e+f*x))^7//2*(c+d*tan(e+f*x))^-3//2, x) == :(im*f^-1*(a+im*b)^7//2*(c+im*d)^-3//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^7//2*(c+-1*im*d)^-3//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+-1*b^5//2*d^-5//2*f^-1*(-7*a*d+3*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2)+-2*d^-1*f^-1*(a+b*tan(e+f*x))^3//2*(c+d*tan(e+f*x))^-1//2*(c^2+d^2)^-1*(b*c+-1*a*d)^2+-1*b*d^-2*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^(1/2)*(c^2+d^2)^-1*(-1*b^2*(d^2+3*c^2)+2*a*d*(-1*a*d+2*b*c)))
@test integrate((a+b*tan(e+f*x))^5//2*(c+d*tan(e+f*x))^-3//2, x) == :(2*b^5//2*d^-3//2*f^-1*arctanh(b^-1//2*d^(1/2)*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2)+im*f^-1*(a+im*b)^5//2*(c+im*d)^-3//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^5//2*(c+-1*im*d)^-3//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+-2*d^-1*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2*(c^2+d^2)^-1*(b*c+-1*a*d)^2)
@test integrate((a+b*tan(e+f*x))^3//2*(c+d*tan(e+f*x))^-3//2, x) == :(im*f^-1*(a+im*b)^3//2*(c+im*d)^-3//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2*(c^2+d^2)^-1*(-2*a*d+2*b*c)+-1*im*f^-1*(a+-1*im*b)^3//2*(c+-1*im*d)^-3//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2)))
@test integrate((a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-3//2, x) == :(im*f^-1*(a+im*b)^(1/2)*(c+im*d)^-3//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^(1/2)*(c+-1*im*d)^-3//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+-2*d*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2*(c^2+d^2)^-1)
@test integrate((a+b*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^-3//2, x) == :(im*f^-1*(a+im*b)^-1//2*(c+im*d)^-3//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^-1//2*(c+-1*im*d)^-3//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+2*d^2*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2*(c^2+d^2)^-1*(b*c+-1*a*d)^-1)
@test integrate((a+b*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^-3//2, x) == :(im*f^-1*(a+im*b)^-3//2*(c+im*d)^-3//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^-3//2*(c+-1*im*d)^-3//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+-2*b^2*f^-1*(a+b*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^-1//2*(a^2+b^2)^-1*(b*c+-1*a*d)^-1+-2*d*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2*(a^2+b^2)^-1*(c^2+d^2)^-1*(b*c+-1*a*d)^-2*(a^2*d^2+b^2*(c^2+2*d^2)))
@test integrate((a+b*tan(e+f*x))^-5//2*(c+d*tan(e+f*x))^-3//2, x) == :(im*f^-1*(a+im*b)^-5//2*(c+im*d)^-3//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^-5//2*(c+-1*im*d)^-3//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+-2*b^2*f^-1*(a+b*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^-1//2*(3*a^2+3*b^2)^-1*(b*c+-1*a*d)^-1+-4//3*b^2*f^-1*(a+b*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^-1//2*(a^2+b^2)^-2*(b*c+-1*a*d)^-2*(-5*d*a^2+-2*d*b^2+3*a*b*c)+2//3*d*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2*(a^2+b^2)^-2*(c^2+d^2)^-1*(b*c+-1*a*d)^-3*(3*a^4*d^3+d*b^4*(5*c^2+8*d^2)+d*a^2*b^2*(11*c^2+17*d^2)+-6*a*c*b^3*(c^2+d^2)))
@test integrate((a+b*tan(e+f*x))^9//2*(c+d*tan(e+f*x))^-5//2, x) == :(im*f^-1*(a+im*b)^9//2*(c+im*d)^-5//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^9//2*(c+-1*im*d)^-5//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+-1*b^7//2*d^-7//2*f^-1*(-9*a*d+5*b*c)*arctanh(b^-1//2*d^(1/2)*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2)+-2//3*d^-1*f^-1*(a+b*tan(e+f*x))^5//2*(c+d*tan(e+f*x))^-3//2*(c^2+d^2)^-1*(b*c+-1*a*d)^2+b*d^-3*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^(1/2)*(c^2+d^2)^-2*(b^3*(d^4+5*c^4+10*c^2*d^2)+4*c*a^3*d^3+-4*b*a^2*d^2*(c^2+-2*d^2)+-4*a*c*d*b^2*(c^2+4*d^2))+-2//3*d^-2*f^-1*(a+b*tan(e+f*x))^3//2*(c+d*tan(e+f*x))^-1//2*(c^2+d^2)^-2*(b*c+-1*a*d)^2*(5*b*c^2+11*b*d^2+6*a*c*d))
@test integrate((a+b*tan(e+f*x))^7//2*(c+d*tan(e+f*x))^-5//2, x) == :(2*b^7//2*d^-5//2*f^-1*arctanh(b^-1//2*d^(1/2)*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2)+im*f^-1*(a+im*b)^7//2*(c+im*d)^-5//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^7//2*(c+-1*im*d)^-5//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+-2//3*d^-1*f^-1*(a+b*tan(e+f*x))^3//2*(c+d*tan(e+f*x))^-3//2*(c^2+d^2)^-1*(b*c+-1*a*d)^2+-2*d^-2*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2*(c^2+d^2)^-2*(b*c+-1*a*d)^2*(b*(c^2+3*d^2)+2*a*c*d))
@test integrate((a+b*tan(e+f*x))^5//2*(c+d*tan(e+f*x))^-5//2, x) == :(im*f^-1*(a+im*b)^5//2*(c+im*d)^-5//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^5//2*(c+-1*im*d)^-5//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+-2//3*d^-1*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-3//2*(c^2+d^2)^-1*(b*c+-1*a*d)^2+1//3*d^-1*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2*(c^2+d^2)^-2*(b*(c^2+7*d^2)+6*a*c*d)*(-2*a*d+2*b*c))
@test integrate((a+b*tan(e+f*x))^3//2*(c+d*tan(e+f*x))^-5//2, x) == :(im*f^-1*(a+im*b)^3//2*(c+im*d)^-5//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-3//2*(3*c^2+3*d^2)^-1*(-2*a*d+2*b*c)+-1*im*f^-1*(a+-1*im*b)^3//2*(c+-1*im*d)^-5//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+1//3*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2*(c^2+d^2)^-2*(-8*b*d^2+4*b*c^2+-12*a*c*d))
@test integrate((a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-5//2, x) == :(im*f^-1*(a+im*b)^(1/2)*(c+im*d)^-5//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^(1/2)*(c+-1*im*d)^-5//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+-2*d*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-3//2*(3*c^2+3*d^2)^-1+2*d*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2*(c^2+d^2)^-2*(-3*a*d+3*b*c)^-1*(-1*b*(-1*d^2+5*c^2)+6*a*c*d))
@test integrate((a+b*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^-5//2, x) == :(im*f^-1*(a+im*b)^-1//2*(c+im*d)^-5//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^-1//2*(c+-1*im*d)^-5//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+2*d^2*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-3//2*(c^2+d^2)^-1*(-3*a*d+3*b*c)^-1+-4//3*d^2*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2*(c^2+d^2)^-2*(b*c+-1*a*d)^-2*(-1*b*(d^2+4*c^2)+3*a*c*d))
@test integrate((a+b*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^-5//2, x) == :(im*f^-1*(a+im*b)^-3//2*(c+im*d)^-5//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^-3//2*(c+-1*im*d)^-5//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+-2*b^2*f^-1*(a+b*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^-3//2*(a^2+b^2)^-1*(b*c+-1*a*d)^-1+f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2*(c^2+d^2)^-2*(3*a^2+3*b^2)^-1*(b*c+-1*a*d)^-3*(-2*b^3*(8*d^5+3*d*c^4+17*c^2*d^3)+12*c*a^3*d^4+-2*b*a^2*d^3*(5*d^2+11*c^2)+12*a*c*b^2*d^4)+-2*d*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-3//2*(c^2+d^2)^-1*(3*a^2+3*b^2)^-1*(b*c+-1*a*d)^-2*(a^2*d^2+b^2*(3*c^2+4*d^2)))
@test integrate((a+b*tan(e+f*x))^-5//2*(c+d*tan(e+f*x))^-5//2, x) == :(im*f^-1*(a+im*b)^-5//2*(c+im*d)^-5//2*arctanh((a+im*b)^-1//2*(a+b*tan(e+f*x))^(1/2)*(c+im*d)^(1/2)*(c+d*tan(e+f*x))^-1//2)+-1*im*f^-1*(a+-1*im*b)^-5//2*(c+-1*im*d)^-5//2*arctanh((a+b*tan(e+f*x))^(1/2)*(a+-1*im*b)^-1//2*(c+d*tan(e+f*x))^-1//2*(c+-1*im*d)^(1/2))+-2*b^2*f^-1*(a+b*tan(e+f*x))^-3//2*(c+d*tan(e+f*x))^-3//2*(3*a^2+3*b^2)^-1*(b*c+-1*a*d)^-1+-4*b^2*f^-1*(a+b*tan(e+f*x))^-1//2*(c+d*tan(e+f*x))^-3//2*(a^2+b^2)^-2*(b*c+-1*a*d)^-2*(-1*d*b^2+-2*d*a^2+a*b*c)+-4//3*d*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-1//2*(a^2+b^2)^-2*(c^2+d^2)^-2*(b*c+-1*a*d)^-4*(-1*d*b^5*(4*c^4+8*d^4+15*c^2*d^2)+3*c*a^5*d^4+-1*b*a^4*d^3*(4*d^2+7*c^2)+-1*d*a^2*b^3*(7*c^4+15*d^4+28*c^2*d^2)+3*a*c*b^4*(c^4+2*d^4+2*c^2*d^2)+6*c*a^3*b^2*d^4)+2//3*d*f^-1*(a+b*tan(e+f*x))^(1/2)*(c+d*tan(e+f*x))^-3//2*(a^2+b^2)^-2*(c^2+d^2)^-1*(b*c+-1*a*d)^-3*(a^4*d^3+d*b^4*(7*c^2+8*d^2)+d*a^2*b^2*(13*c^2+15*d^2)+-6*a*c*b^3*(c^2+d^2)))

max_stars_repo_path: test/4 Trig functions/4.3 Tangent/4.3.2.1 (a+b tan)^m (c+d tan)^n.jl