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

@test integrate(tan(c+d*x)^9*(a+a*sec(c+d*x)), x) == :(a*d^-1*sec(c+d*x)+-1*a*d^-1*log(cos(c+d*x))+-2*a*d^-1*sec(c+d*x)^2+-4//3*a*d^-1*sec(c+d*x)^3+-4//7*a*d^-1*sec(c+d*x)^7+-2//3*a*d^-1*sec(c+d*x)^6+1//8*a*d^-1*sec(c+d*x)^8+1//9*a*d^-1*sec(c+d*x)^9+3//2*a*d^-1*sec(c+d*x)^4+6//5*a*d^-1*sec(c+d*x)^5)
@test integrate(tan(c+d*x)^7*(a+a*sec(c+d*x)), x) == :(a*d^-1*sec(c+d*x)^3+a*d^-1*log(cos(c+d*x))+-1*a*d^-1*sec(c+d*x)+-3//4*a*d^-1*sec(c+d*x)^4+-3//5*a*d^-1*sec(c+d*x)^5+1//6*a*d^-1*sec(c+d*x)^6+1//7*a*d^-1*sec(c+d*x)^7+3//2*a*d^-1*sec(c+d*x)^2)
@test integrate(tan(c+d*x)^5*(a+a*sec(c+d*x)), x) == :(a*d^-1*sec(c+d*x)+-1*a*d^-1*sec(c+d*x)^2+-1*a*d^-1*log(cos(c+d*x))+-2//3*a*d^-1*sec(c+d*x)^3+1//4*a*d^-1*sec(c+d*x)^4+1//5*a*d^-1*sec(c+d*x)^5)
@test integrate(tan(c+d*x)^3*(a+a*sec(c+d*x)), x) == :(a*d^-1*log(cos(c+d*x))+(1/2)*a*d^-1*sec(c+d*x)^2+-1*a*d^-1*sec(c+d*x)+1//3*a*d^-1*sec(c+d*x)^3)
@test integrate((a+a*sec(c+d*x))*tan(c+d*x), x) == :(a*d^-1*sec(c+d*x)+-1*a*d^-1*log(cos(c+d*x)))
@test integrate((a+a*sec(c+d*x))*cot(c+d*x), x) == :(a*d^-1*log(1+-1*cos(c+d*x)))
@test integrate(cot(c+d*x)^3*(a+a*sec(c+d*x)), x) == :(-3//4*a*d^-1*log(1+-1*cos(c+d*x))+-1//2*a*d^-1*(1+-1*cos(c+d*x))^-1+-1//4*a*d^-1*log(1+cos(c+d*x)))
@test integrate(cot(c+d*x)^5*(a+a*sec(c+d*x)), x) == :(-1//8*a*d^-1*(1+-1*cos(c+d*x))^-2+1//8*a*d^-1*(1+cos(c+d*x))^-1+3//4*a*d^-1*(1+-1*cos(c+d*x))^-1+5//16*a*d^-1*log(1+cos(c+d*x))+11//16*a*d^-1*log(1+-1*cos(c+d*x)))
@test integrate(cot(c+d*x)^7*(a+a*sec(c+d*x)), x) == :(-21//32*a*d^-1*log(1+-1*cos(c+d*x))+-15//16*a*d^-1*(1+-1*cos(c+d*x))^-1+-11//32*a*d^-1*log(1+cos(c+d*x))+-1//4*a*d^-1*(1+cos(c+d*x))^-1+-1//24*a*d^-1*(1+-1*cos(c+d*x))^-3+1//32*a*d^-1*(1+cos(c+d*x))^-2+9//32*a*d^-1*(1+-1*cos(c+d*x))^-2)
@test integrate(tan(c+d*x)^8*(a+a*sec(c+d*x)), x) == :(a*x+-1//128*d^-1*(128a+35*a*sec(c+d*x))*tan(c+d*x)+-1//240*d^-1*tan(c+d*x)^5*(48a+35*a*sec(c+d*x))+1//56*d^-1*tan(c+d*x)^7*(8a+7*a*sec(c+d*x))+1//192*d^-1*tan(c+d*x)^3*(64a+35*a*sec(c+d*x))+35//128*a*d^-1*arctanh(sin(c+d*x)))
@test integrate(tan(c+d*x)^6*(a+a*sec(c+d*x)), x) == :(-1*a*x+-5//16*a*d^-1*arctanh(sin(c+d*x))+-1//24*d^-1*tan(c+d*x)^3*(8a+5*a*sec(c+d*x))+1//16*d^-1*(16a+5*a*sec(c+d*x))*tan(c+d*x)+1//30*d^-1*tan(c+d*x)^5*(6a+5*a*sec(c+d*x)))
@test integrate(tan(c+d*x)^4*(a+a*sec(c+d*x)), x) == :(a*x+-1//8*d^-1*(8a+3*a*sec(c+d*x))*tan(c+d*x)+1//12*d^-1*tan(c+d*x)^3*(4a+3*a*sec(c+d*x))+3//8*a*d^-1*arctanh(sin(c+d*x)))
@test integrate(tan(c+d*x)^2*(a+a*sec(c+d*x)), x) == :(-1*a*x+(1/2)*d^-1*(2a+a*sec(c+d*x))*tan(c+d*x)+-1//2*a*d^-1*arctanh(sin(c+d*x)))
@test integrate(cot(c+d*x)^2*(a+a*sec(c+d*x)), x) == :(-1*a*x+-1*d^-1*(a+a*sec(c+d*x))*cot(c+d*x))
@test integrate(cot(c+d*x)^4*(a+a*sec(c+d*x)), x) == :(a*x+-1//3*d^-1*cot(c+d*x)^3*(a+a*sec(c+d*x))+1//3*d^-1*(3a+2*a*sec(c+d*x))*cot(c+d*x))
@test integrate(cot(c+d*x)^6*(a+a*sec(c+d*x)), x) == :(-1*a*x+-1//5*d^-1*cot(c+d*x)^5*(a+a*sec(c+d*x))+-1//15*d^-1*(15a+8*a*sec(c+d*x))*cot(c+d*x)+1//15*d^-1*cot(c+d*x)^3*(5a+4*a*sec(c+d*x)))
@test integrate(cot(c+d*x)^8*(a+a*sec(c+d*x)), x) == :(a*x+-1//7*d^-1*cot(c+d*x)^7*(a+a*sec(c+d*x))+-1//105*d^-1*cot(c+d*x)^3*(35a+24*a*sec(c+d*x))+1//35*d^-1*cot(c+d*x)^5*(7a+6*a*sec(c+d*x))+1//35*d^-1*(35a+16*a*sec(c+d*x))*cot(c+d*x))
@test integrate(cot(c+d*x)^10*(a+a*sec(c+d*x)), x) == :(-1*a*x+-1//9*d^-1*cot(c+d*x)^9*(a+a*sec(c+d*x))+-1//105*d^-1*cot(c+d*x)^5*(21a+16*a*sec(c+d*x))+-1//315*d^-1*(315a+128*a*sec(c+d*x))*cot(c+d*x)+1//63*d^-1*cot(c+d*x)^7*(9a+8*a*sec(c+d*x))+1//315*d^-1*cot(c+d*x)^3*(105a+64*a*sec(c+d*x)))
@test integrate((a+a*sec(c+d*x))^2*tan(c+d*x)^9, x) == :((1/2)*a^2*d^-1*sec(c+d*x)^4+-1*a^2*d^-1*log(cos(c+d*x))+2*a^2*d^-1*sec(c+d*x)+-8//3*a^2*d^-1*sec(c+d*x)^3+-8//7*a^2*d^-1*sec(c+d*x)^7+-3//2*a^2*d^-1*sec(c+d*x)^2+-3//8*a^2*d^-1*sec(c+d*x)^8+1//3*a^2*d^-1*sec(c+d*x)^6+1//10*a^2*d^-1*sec(c+d*x)^10+2//9*a^2*d^-1*sec(c+d*x)^9+12//5*a^2*d^-1*sec(c+d*x)^5)
@test integrate((a+a*sec(c+d*x))^2*tan(c+d*x)^7, x) == :(a^2*d^-1*sec(c+d*x)^2+a^2*d^-1*log(cos(c+d*x))+-2*a^2*d^-1*sec(c+d*x)+2*a^2*d^-1*sec(c+d*x)^3+-6//5*a^2*d^-1*sec(c+d*x)^5+-1//3*a^2*d^-1*sec(c+d*x)^6+1//8*a^2*d^-1*sec(c+d*x)^8+2//7*a^2*d^-1*sec(c+d*x)^7)
@test integrate((a+a*sec(c+d*x))^2*tan(c+d*x)^5, x) == :(-1*a^2*d^-1*log(cos(c+d*x))+2*a^2*d^-1*sec(c+d*x)+-4//3*a^2*d^-1*sec(c+d*x)^3+-1//2*a^2*d^-1*sec(c+d*x)^2+-1//4*a^2*d^-1*sec(c+d*x)^4+1//6*a^2*d^-1*sec(c+d*x)^6+2//5*a^2*d^-1*sec(c+d*x)^5)
@test integrate((a+a*sec(c+d*x))^2*tan(c+d*x)^3, x) == :(a^2*d^-1*log(cos(c+d*x))+-2*a^2*d^-1*sec(c+d*x)+1//4*a^2*d^-1*sec(c+d*x)^4+2//3*a^2*d^-1*sec(c+d*x)^3)
@test integrate((a+a*sec(c+d*x))^2*tan(c+d*x), x) == :((1/2)*a^2*d^-1*sec(c+d*x)^2+-1*a^2*d^-1*log(cos(c+d*x))+2*a^2*d^-1*sec(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cot(c+d*x), x) == :(-1*a^2*d^-1*log(cos(c+d*x))+2*a^2*d^-1*log(1+-1*cos(c+d*x)))
@test integrate((a+a*sec(c+d*x))^2*cot(c+d*x)^3, x) == :(-1*a^2*d^-1*(1+-1*cos(c+d*x))^-1+-1*a^2*d^-1*log(1+-1*cos(c+d*x)))
@test integrate((a+a*sec(c+d*x))^2*cot(c+d*x)^5, x) == :(-1//4*a^2*d^-1*(1+-1*cos(c+d*x))^-2+1//8*a^2*d^-1*log(1+cos(c+d*x))+5//4*a^2*d^-1*(1+-1*cos(c+d*x))^-1+7//8*a^2*d^-1*log(1+-1*cos(c+d*x)))
@test integrate((a+a*sec(c+d*x))^2*cot(c+d*x)^7, x) == :((1/2)*a^2*d^-1*(1+-1*cos(c+d*x))^-2+-23//16*a^2*d^-1*(1+-1*cos(c+d*x))^-1+-13//16*a^2*d^-1*log(1+-1*cos(c+d*x))+-3//16*a^2*d^-1*log(1+cos(c+d*x))+-1//12*a^2*d^-1*(1+-1*cos(c+d*x))^-3+-1//16*a^2*d^-1*(1+cos(c+d*x))^-1)
@test integrate((a+a*sec(c+d*x))^2*cot(c+d*x)^9, x) == :(-3//4*a^2*d^-1*(1+-1*cos(c+d*x))^-2+-1//32*a^2*d^-1*(1+-1*cos(c+d*x))^-4+-1//64*a^2*d^-1*(1+cos(c+d*x))^-2+9//64*a^2*d^-1*(1+cos(c+d*x))^-1+11//48*a^2*d^-1*(1+-1*cos(c+d*x))^-3+29//128*a^2*d^-1*log(1+cos(c+d*x))+51//32*a^2*d^-1*(1+-1*cos(c+d*x))^-1+99//128*a^2*d^-1*log(1+-1*cos(c+d*x)))
@test integrate((a+a*sec(c+d*x))^2*tan(c+d*x)^6, x) == :(-1*x*a^2+a^2*d^-1*tan(c+d*x)+-5//8*a^2*d^-1*arctanh(sin(c+d*x))+-1//3*a^2*d^-1*tan(c+d*x)^3+1//5*a^2*d^-1*tan(c+d*x)^5+1//7*a^2*d^-1*tan(c+d*x)^7+-5//12*a^2*d^-1*tan(c+d*x)^3*sec(c+d*x)+1//3*a^2*d^-1*tan(c+d*x)^5*sec(c+d*x)+5//8*a^2*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*tan(c+d*x)^4, x) == :(x*a^2+-1*a^2*d^-1*tan(c+d*x)+1//3*a^2*d^-1*tan(c+d*x)^3+1//5*a^2*d^-1*tan(c+d*x)^5+3//4*a^2*d^-1*arctanh(sin(c+d*x))+(1/2)*a^2*d^-1*tan(c+d*x)^3*sec(c+d*x)+-3//4*a^2*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*tan(c+d*x)^2, x) == :(-1*x*a^2+a^2*d^-1*tan(c+d*x)+-1*a^2*d^-1*arctanh(sin(c+d*x))+1//3*a^2*d^-1*tan(c+d*x)^3+a^2*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cot(c+d*x)^2, x) == :(-1*x*a^2+-2*a^2*d^-1*cot(c+d*x)+-2*a^2*d^-1*csc(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cot(c+d*x)^4, x) == :(x*a^2+a^2*d^-1*cot(c+d*x)+2*a^2*d^-1*csc(c+d*x)+-2//3*a^2*d^-1*cot(c+d*x)^3+-2//3*a^2*d^-1*csc(c+d*x)^3)
@test integrate((a+a*sec(c+d*x))^2*cot(c+d*x)^6, x) == :(-1*x*a^2+-1*a^2*d^-1*cot(c+d*x)+-2*a^2*d^-1*csc(c+d*x)+-2//5*a^2*d^-1*cot(c+d*x)^5+-2//5*a^2*d^-1*csc(c+d*x)^5+1//3*a^2*d^-1*cot(c+d*x)^3+4//3*a^2*d^-1*csc(c+d*x)^3)
@test integrate((a+a*sec(c+d*x))^2*cot(c+d*x)^8, x) == :(x*a^2+a^2*d^-1*cot(c+d*x)+-2*a^2*d^-1*csc(c+d*x)^3+2*a^2*d^-1*csc(c+d*x)+-2//7*a^2*d^-1*cot(c+d*x)^7+-2//7*a^2*d^-1*csc(c+d*x)^7+-1//3*a^2*d^-1*cot(c+d*x)^3+1//5*a^2*d^-1*cot(c+d*x)^5+6//5*a^2*d^-1*csc(c+d*x)^5)
@test integrate((a+a*sec(c+d*x))^2*cot(c+d*x)^10, x) == :(-1*x*a^2+-1*a^2*d^-1*cot(c+d*x)+-2*a^2*d^-1*csc(c+d*x)+-12//5*a^2*d^-1*csc(c+d*x)^5+-2//9*a^2*d^-1*cot(c+d*x)^9+-2//9*a^2*d^-1*csc(c+d*x)^9+-1//5*a^2*d^-1*cot(c+d*x)^5+1//3*a^2*d^-1*cot(c+d*x)^3+1//7*a^2*d^-1*cot(c+d*x)^7+8//3*a^2*d^-1*csc(c+d*x)^3+8//7*a^2*d^-1*csc(c+d*x)^7)
@test integrate((a+a*sec(c+d*x))^3*tan(c+d*x)^9, x) == :(-1*a^3*d^-1*log(cos(c+d*x))+3*a^3*d^-1*sec(c+d*x)+-11//3*a^3*d^-1*sec(c+d*x)^3+-11//8*a^3*d^-1*sec(c+d*x)^8+-6//7*a^3*d^-1*sec(c+d*x)^7+-3//2*a^3*d^-1*sec(c+d*x)^4+-1//2*a^3*d^-1*sec(c+d*x)^2+-1//9*a^3*d^-1*sec(c+d*x)^9+1//11*a^3*d^-1*sec(c+d*x)^11+3//10*a^3*d^-1*sec(c+d*x)^10+7//3*a^3*d^-1*sec(c+d*x)^6+14//5*a^3*d^-1*sec(c+d*x)^5)
@test integrate((a+a*sec(c+d*x))^3*tan(c+d*x)^7, x) == :(a^3*d^-1*log(cos(c+d*x))+-3*a^3*d^-1*sec(c+d*x)+-6//5*a^3*d^-1*sec(c+d*x)^5+-4//3*a^3*d^-1*sec(c+d*x)^6+1//9*a^3*d^-1*sec(c+d*x)^9+3//2*a^3*d^-1*sec(c+d*x)^4+3//8*a^3*d^-1*sec(c+d*x)^8+8//3*a^3*d^-1*sec(c+d*x)^3)
@test integrate((a+a*sec(c+d*x))^3*tan(c+d*x)^5, x) == :((1/2)*a^3*d^-1*sec(c+d*x)^2+(1/2)*a^3*d^-1*sec(c+d*x)^6+-1*a^3*d^-1*log(cos(c+d*x))+3*a^3*d^-1*sec(c+d*x)+-5//3*a^3*d^-1*sec(c+d*x)^3+-5//4*a^3*d^-1*sec(c+d*x)^4+1//5*a^3*d^-1*sec(c+d*x)^5+1//7*a^3*d^-1*sec(c+d*x)^7)
@test integrate((a+a*sec(c+d*x))^3*tan(c+d*x)^3, x) == :(a^3*d^-1*log(cos(c+d*x))+-1*a^3*d^-1*sec(c+d*x)^2+-3*a^3*d^-1*sec(c+d*x)+1//5*a^3*d^-1*sec(c+d*x)^5+2//3*a^3*d^-1*sec(c+d*x)^3+3//4*a^3*d^-1*sec(c+d*x)^4)
@test integrate((a+a*sec(c+d*x))^3*tan(c+d*x), x) == :(-1*a^3*d^-1*log(cos(c+d*x))+3*a^3*d^-1*sec(c+d*x)+1//3*a^3*d^-1*sec(c+d*x)^3+3//2*a^3*d^-1*sec(c+d*x)^2)
@test integrate((a+a*sec(c+d*x))^3*cot(c+d*x), x) == :(a^3*d^-1*sec(c+d*x)+-3*a^3*d^-1*log(cos(c+d*x))+4*a^3*d^-1*log(1+-1*cos(c+d*x)))
@test integrate((a+a*sec(c+d*x))^3*cot(c+d*x)^3, x) == :(-1*a^3*d^-1*log(1+-1*cos(c+d*x))+-2*a^3*d^-1*(1+-1*cos(c+d*x))^-1)
@test integrate((a+a*sec(c+d*x))^3*cot(c+d*x)^5, x) == :(a^3*d^-1*log(1+-1*cos(c+d*x))+2*a^3*d^-1*(1+-1*cos(c+d*x))^-1+-1//2*a^3*d^-1*(1+-1*cos(c+d*x))^-2)
@test integrate((a+a*sec(c+d*x))^3*cot(c+d*x)^7, x) == :(-17//8*a^3*d^-1*(1+-1*cos(c+d*x))^-1+-15//16*a^3*d^-1*log(1+-1*cos(c+d*x))+-1//6*a^3*d^-1*(1+-1*cos(c+d*x))^-3+-1//16*a^3*d^-1*log(1+cos(c+d*x))+7//8*a^3*d^-1*(1+-1*cos(c+d*x))^-2)
@test integrate((a+a*sec(c+d*x))^3*cot(c+d*x)^9, x) == :(-39//32*a^3*d^-1*(1+-1*cos(c+d*x))^-2+-1//16*a^3*d^-1*(1+-1*cos(c+d*x))^-4+1//32*a^3*d^-1*(1+cos(c+d*x))^-1+5//12*a^3*d^-1*(1+-1*cos(c+d*x))^-3+7//64*a^3*d^-1*log(1+cos(c+d*x))+9//4*a^3*d^-1*(1+-1*cos(c+d*x))^-1+57//64*a^3*d^-1*log(1+-1*cos(c+d*x)))
@test integrate((a+a*sec(c+d*x))^3*tan(c+d*x)^6, x) == :(-1*x*a^3+a^3*d^-1*tan(c+d*x)+-125//128*a^3*d^-1*arctanh(sin(c+d*x))+-1//3*a^3*d^-1*tan(c+d*x)^3+1//5*a^3*d^-1*tan(c+d*x)^5+3//7*a^3*d^-1*tan(c+d*x)^7+(1/2)*a^3*d^-1*tan(c+d*x)^5*sec(c+d*x)+-5//8*a^3*d^-1*tan(c+d*x)^3*sec(c+d*x)+-5//48*a^3*d^-1*sec(c+d*x)^3*tan(c+d*x)^3+1//8*a^3*d^-1*sec(c+d*x)^3*tan(c+d*x)^5+5//64*a^3*d^-1*sec(c+d*x)^3*tan(c+d*x)+115//128*a^3*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*tan(c+d*x)^4, x) == :(x*a^3+-1*a^3*d^-1*tan(c+d*x)+1//3*a^3*d^-1*tan(c+d*x)^3+3//5*a^3*d^-1*tan(c+d*x)^5+19//16*a^3*d^-1*arctanh(sin(c+d*x))+-17//16*a^3*d^-1*sec(c+d*x)*tan(c+d*x)+-1//8*a^3*d^-1*sec(c+d*x)^3*tan(c+d*x)+1//6*a^3*d^-1*sec(c+d*x)^3*tan(c+d*x)^3+3//4*a^3*d^-1*tan(c+d*x)^3*sec(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*tan(c+d*x)^2, x) == :(-1*x*a^3+a^3*d^-1*tan(c+d*x)^3+a^3*d^-1*tan(c+d*x)+-13//8*a^3*d^-1*arctanh(sin(c+d*x))+1//4*a^3*d^-1*sec(c+d*x)^3*tan(c+d*x)+11//8*a^3*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cot(c+d*x)^2, x) == :(-1*x*a^3+a^3*d^-1*arctanh(sin(c+d*x))+-4*a^3*d^-1*cot(c+d*x)+-4*a^3*d^-1*csc(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cot(c+d*x)^4, x) == :(x*a^3+a^3*d^-1*cot(c+d*x)+3*a^3*d^-1*csc(c+d*x)+-4//3*a^3*d^-1*cot(c+d*x)^3+-4//3*a^3*d^-1*csc(c+d*x)^3)
@test integrate((a+a*sec(c+d*x))^3*cot(c+d*x)^6, x) == :(-1*x*a^3+-1*a^3*d^-1*cot(c+d*x)+-3*a^3*d^-1*csc(c+d*x)+-4//5*a^3*d^-1*cot(c+d*x)^5+-4//5*a^3*d^-1*csc(c+d*x)^5+1//3*a^3*d^-1*cot(c+d*x)^3+7//3*a^3*d^-1*csc(c+d*x)^3)
@test integrate((a+a*sec(c+d*x))^3*cot(c+d*x)^8, x) == :(x*a^3+a^3*d^-1*cot(c+d*x)+3*a^3*d^-1*csc(c+d*x)+-10//3*a^3*d^-1*csc(c+d*x)^3+-4//7*a^3*d^-1*cot(c+d*x)^7+-4//7*a^3*d^-1*csc(c+d*x)^7+-1//3*a^3*d^-1*cot(c+d*x)^3+1//5*a^3*d^-1*cot(c+d*x)^5+11//5*a^3*d^-1*csc(c+d*x)^5)
@test integrate((a+a*sec(c+d*x))^3*cot(c+d*x)^10, x) == :(-1*x*a^3+-1*a^3*d^-1*cot(c+d*x)+-3*a^3*d^-1*csc(c+d*x)+-21//5*a^3*d^-1*csc(c+d*x)^5+-4//9*a^3*d^-1*cot(c+d*x)^9+-4//9*a^3*d^-1*csc(c+d*x)^9+-1//5*a^3*d^-1*cot(c+d*x)^5+1//3*a^3*d^-1*cot(c+d*x)^3+1//7*a^3*d^-1*cot(c+d*x)^7+13//3*a^3*d^-1*csc(c+d*x)^3+15//7*a^3*d^-1*csc(c+d*x)^7)
@test integrate((a+a*sec(c+d*x))^3*cot(c+d*x)^12, x) == :(x*a^3+a^3*d^-1*cot(c+d*x)+3*a^3*d^-1*csc(c+d*x)+-36//7*a^3*d^-1*csc(c+d*x)^7+-16//3*a^3*d^-1*csc(c+d*x)^3+-4//11*a^3*d^-1*cot(c+d*x)^11+-4//11*a^3*d^-1*csc(c+d*x)^11+-1//3*a^3*d^-1*cot(c+d*x)^3+-1//7*a^3*d^-1*cot(c+d*x)^7+1//5*a^3*d^-1*cot(c+d*x)^5+1//9*a^3*d^-1*cot(c+d*x)^9+19//9*a^3*d^-1*csc(c+d*x)^9+34//5*a^3*d^-1*csc(c+d*x)^5)
@test integrate((a+a*sec(c+d*x))^-1*tan(c+d*x)^9, x) == :(a^-1*d^-1*sec(c+d*x)^3+-1*a^-1*d^-1*log(cos(c+d*x))+-1*a^-1*d^-1*sec(c+d*x)+-3//2*a^-1*d^-1*sec(c+d*x)^2+-3//5*a^-1*d^-1*sec(c+d*x)^5+-1//6*a^-1*d^-1*sec(c+d*x)^6+1//7*a^-1*d^-1*sec(c+d*x)^7+3//4*a^-1*d^-1*sec(c+d*x)^4)
@test integrate((a+a*sec(c+d*x))^-1*tan(c+d*x)^7, x) == :(a^-1*d^-1*sec(c+d*x)^2+a^-1*d^-1*log(cos(c+d*x))+a^-1*d^-1*sec(c+d*x)+-2//3*a^-1*d^-1*sec(c+d*x)^3+-1//4*a^-1*d^-1*sec(c+d*x)^4+1//5*a^-1*d^-1*sec(c+d*x)^5)
@test integrate((a+a*sec(c+d*x))^-1*tan(c+d*x)^5, x) == :(-1*a^-1*d^-1*log(cos(c+d*x))+-1*a^-1*d^-1*sec(c+d*x)+-1//2*a^-1*d^-1*sec(c+d*x)^2+1//3*a^-1*d^-1*sec(c+d*x)^3)
@test integrate((a+a*sec(c+d*x))^-1*tan(c+d*x)^3, x) == :(a^-1*d^-1*log(cos(c+d*x))+a^-1*d^-1*sec(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*tan(c+d*x), x) == :(-1*a^-1*d^-1*log(1+cos(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1*cot(c+d*x), x) == :((1/2)*a^-1*d^-1*(1+cos(c+d*x))^-1+1//4*a^-1*d^-1*log(1+-1*cos(c+d*x))+3//4*a^-1*d^-1*log(1+cos(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1*cot(c+d*x)^3, x) == :(-11//16*a^-1*d^-1*log(1+cos(c+d*x))+-5//16*a^-1*d^-1*log(1+-1*cos(c+d*x))+-3//4*a^-1*d^-1*(1+cos(c+d*x))^-1+-1//8*a^-1*d^-1*(1+-1*cos(c+d*x))^-1+1//8*a^-1*d^-1*(1+cos(c+d*x))^-2)
@test integrate((a+a*sec(c+d*x))^-1*cot(c+d*x)^5, x) == :(-9//32*a^-1*d^-1*(1+cos(c+d*x))^-2+-1//32*a^-1*d^-1*(1+-1*cos(c+d*x))^-2+1//4*a^-1*d^-1*(1+-1*cos(c+d*x))^-1+1//24*a^-1*d^-1*(1+cos(c+d*x))^-3+11//32*a^-1*d^-1*log(1+-1*cos(c+d*x))+15//16*a^-1*d^-1*(1+cos(c+d*x))^-1+21//32*a^-1*d^-1*log(1+cos(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1*tan(c+d*x)^8, x) == :(x*a^-1+-5//16*a^-1*d^-1*arctanh(sin(c+d*x))+-1//16*a^-1*d^-1*(16+-5*sec(c+d*x))*tan(c+d*x)+-1//30*a^-1*d^-1*tan(c+d*x)^5*(6+-5*sec(c+d*x))+1//24*a^-1*d^-1*tan(c+d*x)^3*(8+-5*sec(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1*tan(c+d*x)^6, x) == :(-1*x*a^-1+3//8*a^-1*d^-1*arctanh(sin(c+d*x))+-1//12*a^-1*d^-1*tan(c+d*x)^3*(4+-3*sec(c+d*x))+1//8*a^-1*d^-1*(8+-3*sec(c+d*x))*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*tan(c+d*x)^4, x) == :(x*a^-1+-1//2*a^-1*d^-1*arctanh(sin(c+d*x))+-1//2*a^-1*d^-1*(2+-1*sec(c+d*x))*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*tan(c+d*x)^2, x) == :(-1*x*a^-1+a^-1*d^-1*arctanh(sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1*cot(c+d*x)^2, x) == :(-1*x*a^-1+-1//3*a^-1*d^-1*(3+-2*sec(c+d*x))*cot(c+d*x)+1//3*a^-1*d^-1*cot(c+d*x)^3*(1+-1*sec(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1*cot(c+d*x)^4, x) == :(x*a^-1+-1//15*a^-1*d^-1*cot(c+d*x)^3*(5+-4*sec(c+d*x))+1//5*a^-1*d^-1*cot(c+d*x)^5*(1+-1*sec(c+d*x))+1//15*a^-1*d^-1*(15+-8*sec(c+d*x))*cot(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cot(c+d*x)^6, x) == :(-1*x*a^-1+-1//35*a^-1*d^-1*cot(c+d*x)^5*(7+-6*sec(c+d*x))+-1//35*a^-1*d^-1*(35+-16*sec(c+d*x))*cot(c+d*x)+1//7*a^-1*d^-1*cot(c+d*x)^7*(1+-1*sec(c+d*x))+1//105*a^-1*d^-1*cot(c+d*x)^3*(35+-24*sec(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-2*tan(c+d*x)^9, x) == :(-1*a^-2*d^-1*log(cos(c+d*x))+-2*a^-2*d^-1*sec(c+d*x)+-2//5*a^-2*d^-1*sec(c+d*x)^5+-1//2*a^-2*d^-1*sec(c+d*x)^2+-1//4*a^-2*d^-1*sec(c+d*x)^4+1//6*a^-2*d^-1*sec(c+d*x)^6+4//3*a^-2*d^-1*sec(c+d*x)^3)
@test integrate((a+a*sec(c+d*x))^-2*tan(c+d*x)^7, x) == :(a^-2*d^-1*log(cos(c+d*x))+2*a^-2*d^-1*sec(c+d*x)+-2//3*a^-2*d^-1*sec(c+d*x)^3+1//4*a^-2*d^-1*sec(c+d*x)^4)
@test integrate((a+a*sec(c+d*x))^-2*tan(c+d*x)^5, x) == :((1/2)*a^-2*d^-1*sec(c+d*x)^2+-1*a^-2*d^-1*log(cos(c+d*x))+-2*a^-2*d^-1*sec(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*tan(c+d*x)^3, x) == :(-1*a^-2*d^-1*log(cos(c+d*x))+2*a^-2*d^-1*log(1+cos(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-2*tan(c+d*x), x) == :(-1*a^-2*d^-1*(1+cos(c+d*x))^-1+-1*a^-2*d^-1*log(1+cos(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-2*cot(c+d*x), x) == :(-1//4*a^-2*d^-1*(1+cos(c+d*x))^-2+1//8*a^-2*d^-1*log(1+-1*cos(c+d*x))+5//4*a^-2*d^-1*(1+cos(c+d*x))^-1+7//8*a^-2*d^-1*log(1+cos(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-2*cot(c+d*x)^3, x) == :((1/2)*a^-2*d^-1*(1+cos(c+d*x))^-2+-23//16*a^-2*d^-1*(1+cos(c+d*x))^-1+-13//16*a^-2*d^-1*log(1+cos(c+d*x))+-3//16*a^-2*d^-1*log(1+-1*cos(c+d*x))+-1//12*a^-2*d^-1*(1+cos(c+d*x))^-3+-1//16*a^-2*d^-1*(1+-1*cos(c+d*x))^-1)
@test integrate((a+a*sec(c+d*x))^-2*cot(c+d*x)^5, x) == :(-3//4*a^-2*d^-1*(1+cos(c+d*x))^-2+-1//32*a^-2*d^-1*(1+cos(c+d*x))^-4+-1//64*a^-2*d^-1*(1+-1*cos(c+d*x))^-2+9//64*a^-2*d^-1*(1+-1*cos(c+d*x))^-1+11//48*a^-2*d^-1*(1+cos(c+d*x))^-3+29//128*a^-2*d^-1*log(1+-1*cos(c+d*x))+51//32*a^-2*d^-1*(1+cos(c+d*x))^-1+99//128*a^-2*d^-1*log(1+cos(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-2*tan(c+d*x)^8, x) == :(x*a^-2+-1*a^-2*d^-1*tan(c+d*x)+-3//4*a^-2*d^-1*arctanh(sin(c+d*x))+1//3*a^-2*d^-1*tan(c+d*x)^3+1//5*a^-2*d^-1*tan(c+d*x)^5+-1//2*a^-2*d^-1*tan(c+d*x)^3*sec(c+d*x)+3//4*a^-2*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*tan(c+d*x)^6, x) == :(-1*x*a^-2+a^-2*d^-1*arctanh(sin(c+d*x))+a^-2*d^-1*tan(c+d*x)+1//3*a^-2*d^-1*tan(c+d*x)^3+-1*a^-2*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*tan(c+d*x)^4, x) == :(x*a^-2+a^-2*d^-1*tan(c+d*x)+-2*a^-2*d^-1*arctanh(sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-2*cot(c+d*x)^2, x) == :(-1*x*a^-2+-1*a^-2*d^-1*cot(c+d*x)+2*a^-2*d^-1*csc(c+d*x)+-4//3*a^-2*d^-1*csc(c+d*x)^3+-2//5*a^-2*d^-1*cot(c+d*x)^5+1//3*a^-2*d^-1*cot(c+d*x)^3+2//5*a^-2*d^-1*csc(c+d*x)^5)
@test integrate((a+a*sec(c+d*x))^-2*cot(c+d*x)^4, x) == :(x*a^-2+a^-2*d^-1*cot(c+d*x)+-2*a^-2*d^-1*csc(c+d*x)+2*a^-2*d^-1*csc(c+d*x)^3+-6//5*a^-2*d^-1*csc(c+d*x)^5+-2//7*a^-2*d^-1*cot(c+d*x)^7+-1//3*a^-2*d^-1*cot(c+d*x)^3+1//5*a^-2*d^-1*cot(c+d*x)^5+2//7*a^-2*d^-1*csc(c+d*x)^7)
@test integrate((a+a*sec(c+d*x))^-2*cot(c+d*x)^6, x) == :(-1*x*a^-2+-1*a^-2*d^-1*cot(c+d*x)+2*a^-2*d^-1*csc(c+d*x)+-8//3*a^-2*d^-1*csc(c+d*x)^3+-8//7*a^-2*d^-1*csc(c+d*x)^7+-2//9*a^-2*d^-1*cot(c+d*x)^9+-1//5*a^-2*d^-1*cot(c+d*x)^5+1//3*a^-2*d^-1*cot(c+d*x)^3+1//7*a^-2*d^-1*cot(c+d*x)^7+2//9*a^-2*d^-1*csc(c+d*x)^9+12//5*a^-2*d^-1*csc(c+d*x)^5)
@test integrate((a+a*sec(c+d*x))^-3*tan(c+d*x)^11, x) == :(a^-3*d^-1*log(cos(c+d*x))+3*a^-3*d^-1*sec(c+d*x)+-5//3*a^-3*d^-1*sec(c+d*x)^3+-1//2*a^-3*d^-1*sec(c+d*x)^2+-1//2*a^-3*d^-1*sec(c+d*x)^6+1//5*a^-3*d^-1*sec(c+d*x)^5+1//7*a^-3*d^-1*sec(c+d*x)^7+5//4*a^-3*d^-1*sec(c+d*x)^4)
@test integrate((a+a*sec(c+d*x))^-3*tan(c+d*x)^9, x) == :(a^-3*d^-1*sec(c+d*x)^2+-1*a^-3*d^-1*log(cos(c+d*x))+-3*a^-3*d^-1*sec(c+d*x)+-3//4*a^-3*d^-1*sec(c+d*x)^4+1//5*a^-3*d^-1*sec(c+d*x)^5+2//3*a^-3*d^-1*sec(c+d*x)^3)
@test integrate((a+a*sec(c+d*x))^-3*tan(c+d*x)^7, x) == :(a^-3*d^-1*log(cos(c+d*x))+3*a^-3*d^-1*sec(c+d*x)+-3//2*a^-3*d^-1*sec(c+d*x)^2+1//3*a^-3*d^-1*sec(c+d*x)^3)
@test integrate((a+a*sec(c+d*x))^-3*tan(c+d*x)^5, x) == :(a^-3*d^-1*sec(c+d*x)+-4*a^-3*d^-1*log(1+cos(c+d*x))+3*a^-3*d^-1*log(cos(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3*tan(c+d*x)^3, x) == :(a^-3*d^-1*log(1+cos(c+d*x))+2*a^-3*d^-1*(1+cos(c+d*x))^-1)
@test integrate((a+a*sec(c+d*x))^-3*tan(c+d*x), x) == :((1/2)*a^-3*d^-1*(1+cos(c+d*x))^-2+-1*a^-3*d^-1*log(1+cos(c+d*x))+-2*a^-3*d^-1*(1+cos(c+d*x))^-1)
@test integrate((a+a*sec(c+d*x))^-3*cot(c+d*x), x) == :(-7//8*a^-3*d^-1*(1+cos(c+d*x))^-2+1//6*a^-3*d^-1*(1+cos(c+d*x))^-3+1//16*a^-3*d^-1*log(1+-1*cos(c+d*x))+15//16*a^-3*d^-1*log(1+cos(c+d*x))+17//8*a^-3*d^-1*(1+cos(c+d*x))^-1)
@test integrate((a+a*sec(c+d*x))^-3*cot(c+d*x)^3, x) == :(-57//64*a^-3*d^-1*log(1+cos(c+d*x))+-9//4*a^-3*d^-1*(1+cos(c+d*x))^-1+-7//64*a^-3*d^-1*log(1+-1*cos(c+d*x))+-5//12*a^-3*d^-1*(1+cos(c+d*x))^-3+-1//32*a^-3*d^-1*(1+-1*cos(c+d*x))^-1+1//16*a^-3*d^-1*(1+cos(c+d*x))^-4+39//32*a^-3*d^-1*(1+cos(c+d*x))^-2)
@test integrate((a+a*sec(c+d*x))^-3*cot(c+d*x)^5, x) == :(-99//64*a^-3*d^-1*(1+cos(c+d*x))^-2+-13//64*a^-3*d^-1*(1+cos(c+d*x))^-4+-1//128*a^-3*d^-1*(1+-1*cos(c+d*x))^-2+1//40*a^-3*d^-1*(1+cos(c+d*x))^-5+5//64*a^-3*d^-1*(1+-1*cos(c+d*x))^-1+35//48*a^-3*d^-1*(1+cos(c+d*x))^-3+37//256*a^-3*d^-1*log(1+-1*cos(c+d*x))+219//256*a^-3*d^-1*log(1+cos(c+d*x))+303//128*a^-3*d^-1*(1+cos(c+d*x))^-1)
@test integrate((a+a*sec(c+d*x))^-3*tan(c+d*x)^12, x) == :(x*a^-3+-1*a^-3*d^-1*tan(c+d*x)+-125//128*a^-3*d^-1*arctanh(sin(c+d*x))+-3//7*a^-3*d^-1*tan(c+d*x)^7+-1//5*a^-3*d^-1*tan(c+d*x)^5+1//3*a^-3*d^-1*tan(c+d*x)^3+(1/2)*a^-3*d^-1*tan(c+d*x)^5*sec(c+d*x)+-5//8*a^-3*d^-1*tan(c+d*x)^3*sec(c+d*x)+-5//48*a^-3*d^-1*sec(c+d*x)^3*tan(c+d*x)^3+1//8*a^-3*d^-1*sec(c+d*x)^3*tan(c+d*x)^5+5//64*a^-3*d^-1*sec(c+d*x)^3*tan(c+d*x)+115//128*a^-3*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*tan(c+d*x)^10, x) == :(-1*x*a^-3+a^-3*d^-1*tan(c+d*x)+-3//5*a^-3*d^-1*tan(c+d*x)^5+-1//3*a^-3*d^-1*tan(c+d*x)^3+19//16*a^-3*d^-1*arctanh(sin(c+d*x))+-17//16*a^-3*d^-1*sec(c+d*x)*tan(c+d*x)+-1//8*a^-3*d^-1*sec(c+d*x)^3*tan(c+d*x)+1//6*a^-3*d^-1*sec(c+d*x)^3*tan(c+d*x)^3+3//4*a^-3*d^-1*tan(c+d*x)^3*sec(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*tan(c+d*x)^8, x) == :(x*a^-3+-1*a^-3*d^-1*tan(c+d*x)^3+-1*a^-3*d^-1*tan(c+d*x)+-13//8*a^-3*d^-1*arctanh(sin(c+d*x))+1//4*a^-3*d^-1*sec(c+d*x)^3*tan(c+d*x)+11//8*a^-3*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*tan(c+d*x)^6, x) == :(-1*x*a^-3+-5//2*a^-3*d^-1*tan(c+d*x)+7//2*a^-3*d^-1*arctanh(sin(c+d*x))+-1//2*a^-3*d^-1*(1+-1*sec(c+d*x))*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cot(c+d*x)^2, x) == :(-1*x*a^-3+-1*a^-3*d^-1*cot(c+d*x)+3*a^-3*d^-1*csc(c+d*x)+-10//3*a^-3*d^-1*csc(c+d*x)^3+-4//7*a^-3*d^-1*csc(c+d*x)^7+-1//5*a^-3*d^-1*cot(c+d*x)^5+1//3*a^-3*d^-1*cot(c+d*x)^3+4//7*a^-3*d^-1*cot(c+d*x)^7+11//5*a^-3*d^-1*csc(c+d*x)^5)
@test integrate((a+a*sec(c+d*x))^-3*cot(c+d*x)^4, x) == :(x*a^-3+a^-3*d^-1*cot(c+d*x)+-3*a^-3*d^-1*csc(c+d*x)+-21//5*a^-3*d^-1*csc(c+d*x)^5+-4//9*a^-3*d^-1*csc(c+d*x)^9+-1//3*a^-3*d^-1*cot(c+d*x)^3+-1//7*a^-3*d^-1*cot(c+d*x)^7+1//5*a^-3*d^-1*cot(c+d*x)^5+4//9*a^-3*d^-1*cot(c+d*x)^9+13//3*a^-3*d^-1*csc(c+d*x)^3+15//7*a^-3*d^-1*csc(c+d*x)^7)
@test integrate((a+a*sec(c+d*x))^-3*cot(c+d*x)^6, x) == :(-1*x*a^-3+-1*a^-3*d^-1*cot(c+d*x)+3*a^-3*d^-1*csc(c+d*x)+-36//7*a^-3*d^-1*csc(c+d*x)^7+-16//3*a^-3*d^-1*csc(c+d*x)^3+-4//11*a^-3*d^-1*csc(c+d*x)^11+-1//5*a^-3*d^-1*cot(c+d*x)^5+-1//9*a^-3*d^-1*cot(c+d*x)^9+1//3*a^-3*d^-1*cot(c+d*x)^3+1//7*a^-3*d^-1*cot(c+d*x)^7+4//11*a^-3*d^-1*cot(c+d*x)^11+19//9*a^-3*d^-1*csc(c+d*x)^9+34//5*a^-3*d^-1*csc(c+d*x)^5)
@test integrate((e*tan(c+d*x))^5//2*(a+a*sec(c+d*x)), x) == :(2//15*e*d^-1*(e*tan(c+d*x))^3//2*(5a+3*a*sec(c+d*x))+(1/2)*a*2^(1/2)*d^-1*e^5//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-6//5*a*e*d^-1*(e*tan(c+d*x))^3//2*cos(c+d*x)+-1//2*a*2^(1/2)*d^-1*e^5//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*a*2^(1/2)*d^-1*e^5//2*log(e^(1/2)+e^(1/2)*tan(c+d*x)+-1*2^(1/2)*(e*tan(c+d*x))^(1/2))+1//4*a*2^(1/2)*d^-1*e^5//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+6//5*a*d^-1*e^2*(e*tan(c+d*x))^(1/2)*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*cos(c+d*x))
@test integrate((e*tan(c+d*x))^3//2*(a+a*sec(c+d*x)), x) == :(2//3*e*d^-1*(e*tan(c+d*x))^(1/2)*(3a+a*sec(c+d*x))+(1/2)*a*2^(1/2)*d^-1*e^3//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//2*a*2^(1/2)*d^-1*e^3//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*a*2^(1/2)*d^-1*e^3//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+1//4*a*2^(1/2)*d^-1*e^3//2*log(e^(1/2)+e^(1/2)*tan(c+d*x)+-1*2^(1/2)*(e*tan(c+d*x))^(1/2))+-1//3*a*d^-1*e^2*(e*tan(c+d*x))^-1//2*sin(2c+2*d*x)^(1/2)*Elliptic.F(c+-1//4*pi+d*x,2)*sec(c+d*x))
@test integrate((e*tan(c+d*x))^(1/2)*(a+a*sec(c+d*x)), x) == :((1/2)*a*2^(1/2)*d^-1*e^(1/2)*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+2*a*d^-1*e^-1*(e*tan(c+d*x))^3//2*cos(c+d*x)+-1//2*a*2^(1/2)*d^-1*e^(1/2)*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*a*2^(1/2)*d^-1*e^(1/2)*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+1//4*a*2^(1/2)*d^-1*e^(1/2)*log(e^(1/2)+e^(1/2)*tan(c+d*x)+-1*2^(1/2)*(e*tan(c+d*x))^(1/2))+-2*a*d^-1*(e*tan(c+d*x))^(1/2)*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*cos(c+d*x))
@test integrate((e*tan(c+d*x))^-1//2*(a+a*sec(c+d*x)), x) == :((1/2)*a*2^(1/2)*d^-1*e^-1//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//2*a*2^(1/2)*d^-1*e^-1//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*a*2^(1/2)*d^-1*e^-1//2*log(e^(1/2)+e^(1/2)*tan(c+d*x)+-1*2^(1/2)*(e*tan(c+d*x))^(1/2))+1//4*a*2^(1/2)*d^-1*e^-1//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+a*d^-1*(e*tan(c+d*x))^-1//2*sin(2c+2*d*x)^(1/2)*Elliptic.F(c+-1//4*pi+d*x,2)*sec(c+d*x))
@test integrate((e*tan(c+d*x))^-3//2*(a+a*sec(c+d*x)), x) == :(-1*d^-1*e^-1*(e*tan(c+d*x))^-1//2*(2a+2*a*sec(c+d*x))+(1/2)*a*2^(1/2)*d^-1*e^-3//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+2*a*d^-1*e^-3*(e*tan(c+d*x))^3//2*cos(c+d*x)+-1//2*a*2^(1/2)*d^-1*e^-3//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*a*2^(1/2)*d^-1*e^-3//2*log(e^(1/2)+e^(1/2)*tan(c+d*x)+-1*2^(1/2)*(e*tan(c+d*x))^(1/2))+1//4*a*2^(1/2)*d^-1*e^-3//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+-2*a*d^-1*e^-2*(e*tan(c+d*x))^(1/2)*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*cos(c+d*x))
@test integrate((e*tan(c+d*x))^-5//2*(a+a*sec(c+d*x)), x) == :(-1//3*d^-1*e^-1*(e*tan(c+d*x))^-3//2*(2a+2*a*sec(c+d*x))+(1/2)*a*2^(1/2)*d^-1*e^-5//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//2*a*2^(1/2)*d^-1*e^-5//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*a*2^(1/2)*d^-1*e^-5//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+1//4*a*2^(1/2)*d^-1*e^-5//2*log(e^(1/2)+e^(1/2)*tan(c+d*x)+-1*2^(1/2)*(e*tan(c+d*x))^(1/2))+-1//3*a*d^-1*e^-2*(e*tan(c+d*x))^-1//2*sin(2c+2*d*x)^(1/2)*Elliptic.F(c+-1//4*pi+d*x,2)*sec(c+d*x))
@test integrate((e*tan(c+d*x))^-7//2*(a+a*sec(c+d*x)), x) == :(-1//5*d^-1*e^-1*(e*tan(c+d*x))^-5//2*(2a+2*a*sec(c+d*x))+1//5*d^-1*e^-3*(e*tan(c+d*x))^-1//2*(10a+6*a*sec(c+d*x))+(1/2)*a*2^(1/2)*d^-1*e^-7//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-6//5*a*d^-1*e^-5*(e*tan(c+d*x))^3//2*cos(c+d*x)+-1//2*a*2^(1/2)*d^-1*e^-7//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*a*2^(1/2)*d^-1*e^-7//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+1//4*a*2^(1/2)*d^-1*e^-7//2*log(e^(1/2)+e^(1/2)*tan(c+d*x)+-1*2^(1/2)*(e*tan(c+d*x))^(1/2))+6//5*a*d^-1*e^-4*(e*tan(c+d*x))^(1/2)*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*cos(c+d*x))
@test integrate((e*tan(c+d*x))^5//2*(a+a*sec(c+d*x))^2, x) == :(2//3*e*a^2*d^-1*(e*tan(c+d*x))^3//2+2//7*a^2*d^-1*e^-1*(e*tan(c+d*x))^7//2+(1/2)*2^(1/2)*a^2*d^-1*e^5//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-12//5*e*a^2*d^-1*(e*tan(c+d*x))^3//2*cos(c+d*x)+-1//2*2^(1/2)*a^2*d^-1*e^5//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*a^2*d^-1*e^5//2*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)*a^2*d^-1*e^5//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+4//5*e*a^2*d^-1*(e*tan(c+d*x))^3//2*sec(c+d*x)+12//5*a^2*d^-1*e^2*(e*tan(c+d*x))^(1/2)*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*cos(c+d*x))
@test integrate((e*tan(c+d*x))^3//2*(a+a*sec(c+d*x))^2, x) == :(2*e*a^2*d^-1*(e*tan(c+d*x))^(1/2)+2//5*a^2*d^-1*e^-1*(e*tan(c+d*x))^5//2+(1/2)*2^(1/2)*a^2*d^-1*e^3//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//2*2^(1/2)*a^2*d^-1*e^3//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*a^2*d^-1*e^3//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+1//4*2^(1/2)*a^2*d^-1*e^3//2*log(e^(1/2)+e^(1/2)*tan(c+d*x)+-1*2^(1/2)*(e*tan(c+d*x))^(1/2))+4//3*e*a^2*d^-1*(e*tan(c+d*x))^(1/2)*sec(c+d*x)+-2//3*a^2*d^-1*e^2*(e*tan(c+d*x))^-1//2*sin(2c+2*d*x)^(1/2)*Elliptic.F(c+-1//4*pi+d*x,2)*sec(c+d*x))
@test integrate((e*tan(c+d*x))^(1/2)*(a+a*sec(c+d*x))^2, x) == :(2//3*a^2*d^-1*e^-1*(e*tan(c+d*x))^3//2+(1/2)*2^(1/2)*a^2*d^-1*e^(1/2)*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+4*a^2*d^-1*e^-1*(e*tan(c+d*x))^3//2*cos(c+d*x)+-1//2*2^(1/2)*a^2*d^-1*e^(1/2)*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*a^2*d^-1*e^(1/2)*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+1//4*2^(1/2)*a^2*d^-1*e^(1/2)*log(e^(1/2)+e^(1/2)*tan(c+d*x)+-1*2^(1/2)*(e*tan(c+d*x))^(1/2))+-4*a^2*d^-1*(e*tan(c+d*x))^(1/2)*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*cos(c+d*x))
@test integrate((e*tan(c+d*x))^-1//2*(a+a*sec(c+d*x))^2, x) == :(2*a^2*d^-1*e^-1*(e*tan(c+d*x))^(1/2)+(1/2)*2^(1/2)*a^2*d^-1*e^-1//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//2*2^(1/2)*a^2*d^-1*e^-1//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*a^2*d^-1*e^-1//2*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)*a^2*d^-1*e^-1//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+2*a^2*d^-1*(e*tan(c+d*x))^-1//2*sin(2c+2*d*x)^(1/2)*Elliptic.F(c+-1//4*pi+d*x,2)*sec(c+d*x))
@test integrate((e*tan(c+d*x))^-3//2*(a+a*sec(c+d*x))^2, x) == :(-4*a^2*d^-1*e^-1*(e*tan(c+d*x))^-1//2+(1/2)*2^(1/2)*a^2*d^-1*e^-3//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-4*a^2*d^-1*e^-1*(e*tan(c+d*x))^-1//2*cos(c+d*x)+-1//2*2^(1/2)*a^2*d^-1*e^-3//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*a^2*d^-1*e^-3//2*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)*a^2*d^-1*e^-3//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+-4*a^2*d^-1*e^-2*(e*tan(c+d*x))^(1/2)*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*cos(c+d*x))
@test integrate((e*tan(c+d*x))^-5//2*(a+a*sec(c+d*x))^2, x) == :(-4//3*a^2*d^-1*e^-1*(e*tan(c+d*x))^-3//2+(1/2)*2^(1/2)*a^2*d^-1*e^-5//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-4//3*a^2*d^-1*e^-1*(e*tan(c+d*x))^-3//2*sec(c+d*x)+-1//2*2^(1/2)*a^2*d^-1*e^-5//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*a^2*d^-1*e^-5//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+1//4*2^(1/2)*a^2*d^-1*e^-5//2*log(e^(1/2)+e^(1/2)*tan(c+d*x)+-1*2^(1/2)*(e*tan(c+d*x))^(1/2))+-2//3*a^2*d^-1*e^-2*(e*tan(c+d*x))^-1//2*sin(2c+2*d*x)^(1/2)*Elliptic.F(c+-1//4*pi+d*x,2)*sec(c+d*x))
@test integrate((e*tan(c+d*x))^-7//2*(a+a*sec(c+d*x))^2, x) == :(2*a^2*d^-1*e^-3*(e*tan(c+d*x))^-1//2+-4//5*a^2*d^-1*e^-1*(e*tan(c+d*x))^-5//2+(1/2)*2^(1/2)*a^2*d^-1*e^-7//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-4//5*a^2*d^-1*e^-1*(e*tan(c+d*x))^-5//2*sec(c+d*x)+-1//2*2^(1/2)*a^2*d^-1*e^-7//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*a^2*d^-1*e^-7//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+1//4*2^(1/2)*a^2*d^-1*e^-7//2*log(e^(1/2)+e^(1/2)*tan(c+d*x)+-1*2^(1/2)*(e*tan(c+d*x))^(1/2))+12//5*a^2*d^-1*e^-3*(e*tan(c+d*x))^-1//2*cos(c+d*x)+12//5*a^2*d^-1*e^-4*(e*tan(c+d*x))^(1/2)*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*cos(c+d*x))
@test integrate((e*tan(c+d*x))^11//2*(a+a*sec(c+d*x))^-1, x) == :((1/2)*2^(1/2)*a^-1*d^-1*e^11//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-2//35*a^-1*d^-1*e^3*(e*tan(c+d*x))^5//2*(7+-5*sec(c+d*x))+-1//2*2^(1/2)*a^-1*d^-1*e^11//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*a^-1*d^-1*e^11//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+1//4*2^(1/2)*a^-1*d^-1*e^11//2*log(e^(1/2)+e^(1/2)*tan(c+d*x)+-1*2^(1/2)*(e*tan(c+d*x))^(1/2))+2//21*a^-1*d^-1*e^5*(e*tan(c+d*x))^(1/2)*(21+-5*sec(c+d*x))+5//21*a^-1*d^-1*e^6*(e*tan(c+d*x))^-1//2*sin(2c+2*d*x)^(1/2)*Elliptic.F(c+-1//4*pi+d*x,2)*sec(c+d*x))
@test integrate((e*tan(c+d*x))^9//2*(a+a*sec(c+d*x))^-1, x) == :((1/2)*2^(1/2)*a^-1*d^-1*e^9//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-6//5*a^-1*d^-1*e^3*(e*tan(c+d*x))^3//2*cos(c+d*x)+-2//15*a^-1*d^-1*e^3*(e*tan(c+d*x))^3//2*(5+-3*sec(c+d*x))+-1//2*2^(1/2)*a^-1*d^-1*e^9//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*a^-1*d^-1*e^9//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+1//4*2^(1/2)*a^-1*d^-1*e^9//2*log(e^(1/2)+e^(1/2)*tan(c+d*x)+-1*2^(1/2)*(e*tan(c+d*x))^(1/2))+6//5*a^-1*d^-1*e^4*(e*tan(c+d*x))^(1/2)*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*cos(c+d*x))
@test integrate((e*tan(c+d*x))^7//2*(a+a*sec(c+d*x))^-1, x) == :((1/2)*2^(1/2)*a^-1*d^-1*e^7//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-2//3*a^-1*d^-1*e^3*(e*tan(c+d*x))^(1/2)*(3+-1*sec(c+d*x))+-1//2*2^(1/2)*a^-1*d^-1*e^7//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*a^-1*d^-1*e^7//2*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)*a^-1*d^-1*e^7//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+-1//3*a^-1*d^-1*e^4*(e*tan(c+d*x))^-1//2*sin(2c+2*d*x)^(1/2)*Elliptic.F(c+-1//4*pi+d*x,2)*sec(c+d*x))
@test integrate((e*tan(c+d*x))^5//2*(a+a*sec(c+d*x))^-1, x) == :((1/2)*2^(1/2)*a^-1*d^-1*e^5//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+2*e*a^-1*d^-1*(e*tan(c+d*x))^3//2*cos(c+d*x)+-1//2*2^(1/2)*a^-1*d^-1*e^5//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*a^-1*d^-1*e^5//2*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)*a^-1*d^-1*e^5//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+-2*a^-1*d^-1*e^2*(e*tan(c+d*x))^(1/2)*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*cos(c+d*x))
@test integrate((e*tan(c+d*x))^3//2*(a+a*sec(c+d*x))^-1, x) == :((1/2)*2^(1/2)*a^-1*d^-1*e^3//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//2*2^(1/2)*a^-1*d^-1*e^3//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*a^-1*d^-1*e^3//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+1//4*2^(1/2)*a^-1*d^-1*e^3//2*log(e^(1/2)+e^(1/2)*tan(c+d*x)+-1*2^(1/2)*(e*tan(c+d*x))^(1/2))+a^-1*d^-1*e^2*(e*tan(c+d*x))^-1//2*sin(2c+2*d*x)^(1/2)*Elliptic.F(c+-1//4*pi+d*x,2)*sec(c+d*x))
@test integrate((e*tan(c+d*x))^(1/2)*(a+a*sec(c+d*x))^-1, x) == :((1/2)*2^(1/2)*a^-1*d^-1*e^(1/2)*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+2*e*a^-1*d^-1*(e*tan(c+d*x))^-1//2*(1+-1*sec(c+d*x))+2*a^-1*d^-1*e^-1*(e*tan(c+d*x))^3//2*cos(c+d*x)+-1//2*2^(1/2)*a^-1*d^-1*e^(1/2)*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*a^-1*d^-1*e^(1/2)*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+1//4*2^(1/2)*a^-1*d^-1*e^(1/2)*log(e^(1/2)+e^(1/2)*tan(c+d*x)+-1*2^(1/2)*(e*tan(c+d*x))^(1/2))+-2*a^-1*d^-1*(e*tan(c+d*x))^(1/2)*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*cos(c+d*x))
@test integrate((e*tan(c+d*x))^-1//2*(a+a*sec(c+d*x))^-1, x) == :((1/2)*2^(1/2)*a^-1*d^-1*e^-1//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//2*2^(1/2)*a^-1*d^-1*e^-1//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*a^-1*d^-1*e^-1//2*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)*a^-1*d^-1*e^-1//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+2//3*e*a^-1*d^-1*(e*tan(c+d*x))^-3//2*(1+-1*sec(c+d*x))+-1//3*a^-1*d^-1*(e*tan(c+d*x))^-1//2*sin(2c+2*d*x)^(1/2)*Elliptic.F(c+-1//4*pi+d*x,2)*sec(c+d*x))
@test integrate((e*tan(c+d*x))^-3//2*(a+a*sec(c+d*x))^-1, x) == :((1/2)*2^(1/2)*a^-1*d^-1*e^-3//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-6//5*a^-1*d^-1*e^-3*(e*tan(c+d*x))^3//2*cos(c+d*x)+-1//2*2^(1/2)*a^-1*d^-1*e^-3//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*a^-1*d^-1*e^-3//2*log(e^(1/2)+e^(1/2)*tan(c+d*x)+-1*2^(1/2)*(e*tan(c+d*x))^(1/2))+-1//5*a^-1*d^-1*e^-1*(e*tan(c+d*x))^-1//2*(10+-6*sec(c+d*x))+1//4*2^(1/2)*a^-1*d^-1*e^-3//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+2//5*e*a^-1*d^-1*(e*tan(c+d*x))^-5//2*(1+-1*sec(c+d*x))+6//5*a^-1*d^-1*e^-2*(e*tan(c+d*x))^(1/2)*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*cos(c+d*x))
@test integrate((e*tan(c+d*x))^-5//2*(a+a*sec(c+d*x))^-1, x) == :((1/2)*2^(1/2)*a^-1*d^-1*e^-5//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//2*2^(1/2)*a^-1*d^-1*e^-5//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*a^-1*d^-1*e^-5//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+-1//21*a^-1*d^-1*e^-1*(e*tan(c+d*x))^-3//2*(14+-10*sec(c+d*x))+1//4*2^(1/2)*a^-1*d^-1*e^-5//2*log(e^(1/2)+e^(1/2)*tan(c+d*x)+-1*2^(1/2)*(e*tan(c+d*x))^(1/2))+2//7*e*a^-1*d^-1*(e*tan(c+d*x))^-7//2*(1+-1*sec(c+d*x))+5//21*a^-1*d^-1*e^-2*(e*tan(c+d*x))^-1//2*sin(2c+2*d*x)^(1/2)*Elliptic.F(c+-1//4*pi+d*x,2)*sec(c+d*x))
@test integrate((e*tan(c+d*x))^13//2*(a+a*sec(c+d*x))^-2, x) == :(2//3*a^-2*d^-1*e^5*(e*tan(c+d*x))^3//2+2//7*a^-2*d^-1*e^3*(e*tan(c+d*x))^7//2+(1/2)*2^(1/2)*a^-2*d^-1*e^13//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-4//5*a^-2*d^-1*e^5*(e*tan(c+d*x))^3//2*sec(c+d*x)+-1//2*2^(1/2)*a^-2*d^-1*e^13//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*a^-2*d^-1*e^13//2*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)*a^-2*d^-1*e^13//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+12//5*a^-2*d^-1*e^5*(e*tan(c+d*x))^3//2*cos(c+d*x)+-12//5*a^-2*d^-1*e^6*(e*tan(c+d*x))^(1/2)*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*cos(c+d*x))
@test integrate((e*tan(c+d*x))^11//2*(a+a*sec(c+d*x))^-2, x) == :(2*a^-2*d^-1*e^5*(e*tan(c+d*x))^(1/2)+2//5*a^-2*d^-1*e^3*(e*tan(c+d*x))^5//2+(1/2)*2^(1/2)*a^-2*d^-1*e^11//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-4//3*a^-2*d^-1*e^5*(e*tan(c+d*x))^(1/2)*sec(c+d*x)+-1//2*2^(1/2)*a^-2*d^-1*e^11//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*a^-2*d^-1*e^11//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+1//4*2^(1/2)*a^-2*d^-1*e^11//2*log(e^(1/2)+e^(1/2)*tan(c+d*x)+-1*2^(1/2)*(e*tan(c+d*x))^(1/2))+2//3*a^-2*d^-1*e^6*(e*tan(c+d*x))^-1//2*sin(2c+2*d*x)^(1/2)*Elliptic.F(c+-1//4*pi+d*x,2)*sec(c+d*x))
@test integrate((e*tan(c+d*x))^9//2*(a+a*sec(c+d*x))^-2, x) == :(2//3*a^-2*d^-1*e^3*(e*tan(c+d*x))^3//2+(1/2)*2^(1/2)*a^-2*d^-1*e^9//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-4*a^-2*d^-1*e^3*(e*tan(c+d*x))^3//2*cos(c+d*x)+-1//2*2^(1/2)*a^-2*d^-1*e^9//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*a^-2*d^-1*e^9//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+1//4*2^(1/2)*a^-2*d^-1*e^9//2*log(e^(1/2)+e^(1/2)*tan(c+d*x)+-1*2^(1/2)*(e*tan(c+d*x))^(1/2))+4*a^-2*d^-1*e^4*(e*tan(c+d*x))^(1/2)*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*cos(c+d*x))
@test integrate((e*tan(c+d*x))^7//2*(a+a*sec(c+d*x))^-2, x) == :(2*a^-2*d^-1*e^3*(e*tan(c+d*x))^(1/2)+(1/2)*2^(1/2)*a^-2*d^-1*e^7//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//2*2^(1/2)*a^-2*d^-1*e^7//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*a^-2*d^-1*e^7//2*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)*a^-2*d^-1*e^7//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+-2*a^-2*d^-1*e^4*(e*tan(c+d*x))^-1//2*sin(2c+2*d*x)^(1/2)*Elliptic.F(c+-1//4*pi+d*x,2)*sec(c+d*x))
@test integrate((e*tan(c+d*x))^5//2*(a+a*sec(c+d*x))^-2, x) == :(-4*a^-2*d^-1*e^3*(e*tan(c+d*x))^-1//2+(1/2)*2^(1/2)*a^-2*d^-1*e^5//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+4*a^-2*d^-1*e^3*(e*tan(c+d*x))^-1//2*cos(c+d*x)+-1//2*2^(1/2)*a^-2*d^-1*e^5//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*a^-2*d^-1*e^5//2*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)*a^-2*d^-1*e^5//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+4*a^-2*d^-1*e^2*(e*tan(c+d*x))^(1/2)*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*cos(c+d*x))
@test integrate((e*tan(c+d*x))^3//2*(a+a*sec(c+d*x))^-2, x) == :(-4//3*a^-2*d^-1*e^3*(e*tan(c+d*x))^-3//2+(1/2)*2^(1/2)*a^-2*d^-1*e^3//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//2*2^(1/2)*a^-2*d^-1*e^3//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*a^-2*d^-1*e^3//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+1//4*2^(1/2)*a^-2*d^-1*e^3//2*log(e^(1/2)+e^(1/2)*tan(c+d*x)+-1*2^(1/2)*(e*tan(c+d*x))^(1/2))+4//3*a^-2*d^-1*e^3*(e*tan(c+d*x))^-3//2*sec(c+d*x)+2//3*a^-2*d^-1*e^2*(e*tan(c+d*x))^-1//2*sin(2c+2*d*x)^(1/2)*Elliptic.F(c+-1//4*pi+d*x,2)*sec(c+d*x))
@test integrate((e*tan(c+d*x))^(1/2)*(a+a*sec(c+d*x))^-2, x) == :(2*e*a^-2*d^-1*(e*tan(c+d*x))^-1//2+-4//5*a^-2*d^-1*e^3*(e*tan(c+d*x))^-5//2+(1/2)*2^(1/2)*a^-2*d^-1*e^(1/2)*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-12//5*e*a^-2*d^-1*(e*tan(c+d*x))^-1//2*cos(c+d*x)+-1//2*2^(1/2)*a^-2*d^-1*e^(1/2)*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*a^-2*d^-1*e^(1/2)*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+1//4*2^(1/2)*a^-2*d^-1*e^(1/2)*log(e^(1/2)+e^(1/2)*tan(c+d*x)+-1*2^(1/2)*(e*tan(c+d*x))^(1/2))+4//5*a^-2*d^-1*e^3*(e*tan(c+d*x))^-5//2*sec(c+d*x)+-12//5*a^-2*d^-1*(e*tan(c+d*x))^(1/2)*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*cos(c+d*x))
@test integrate((e*tan(c+d*x))^-1//2*(a+a*sec(c+d*x))^-2, x) == :(-4//7*a^-2*d^-1*e^3*(e*tan(c+d*x))^-7//2+2//3*e*a^-2*d^-1*(e*tan(c+d*x))^-3//2+(1/2)*2^(1/2)*a^-2*d^-1*e^-1//2*arctan(1+2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-20//21*e*a^-2*d^-1*(e*tan(c+d*x))^-3//2*sec(c+d*x)+-1//2*2^(1/2)*a^-2*d^-1*e^-1//2*arctan(1+-1*2^(1/2)*e^-1//2*(e*tan(c+d*x))^(1/2))+-1//4*2^(1/2)*a^-2*d^-1*e^-1//2*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)*a^-2*d^-1*e^-1//2*log(e^(1/2)+2^(1/2)*(e*tan(c+d*x))^(1/2)+e^(1/2)*tan(c+d*x))+4//7*a^-2*d^-1*e^3*(e*tan(c+d*x))^-7//2*sec(c+d*x)+-10//21*a^-2*d^-1*(e*tan(c+d*x))^-1//2*sin(2c+2*d*x)^(1/2)*Elliptic.F(c+-1//4*pi+d*x,2)*sec(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*tan(c+d*x)^5, x) == :(2*d^-1*(a+a*sec(c+d*x))^(1/2)+-2*a^(1/2)*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+-6//7*a^-3*d^-1*(a+a*sec(c+d*x))^7//2+2//3*a^-1*d^-1*(a+a*sec(c+d*x))^3//2+2//5*a^-2*d^-1*(a+a*sec(c+d*x))^5//2+2//9*a^-4*d^-1*(a+a*sec(c+d*x))^9//2)
@test integrate((a+a*sec(c+d*x))^(1/2)*tan(c+d*x)^3, x) == :(-2*d^-1*(a+a*sec(c+d*x))^(1/2)+2*a^(1/2)*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+-2//3*a^-1*d^-1*(a+a*sec(c+d*x))^3//2+2//5*a^-2*d^-1*(a+a*sec(c+d*x))^5//2)
@test integrate((a+a*sec(c+d*x))^(1/2)*tan(c+d*x), x) == :(2*d^-1*(a+a*sec(c+d*x))^(1/2)+-2*a^(1/2)*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2)))
@test integrate((a+a*sec(c+d*x))^(1/2)*cot(c+d*x), x) == :(2*a^(1/2)*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+-1*2^(1/2)*a^(1/2)*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+a*sec(c+d*x))^(1/2)))
@test integrate((a+a*sec(c+d*x))^(1/2)*cot(c+d*x)^3, x) == :(-2*a^(1/2)*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+1//4*a*d^-1*(a+a*sec(c+d*x))^-1//2+(1/2)*a*d^-1*(1+-1*sec(c+d*x))^-1*(a+a*sec(c+d*x))^-1//2+7//8*2^(1/2)*a^(1/2)*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+a*sec(c+d*x))^(1/2)))
@test integrate((a+a*sec(c+d*x))^(1/2)*cot(c+d*x)^5, x) == :(2*a^(1/2)*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+-21//64*a*d^-1*(a+a*sec(c+d*x))^-1//2+43//96*a^2*d^-1*(a+a*sec(c+d*x))^-3//2+-107//128*2^(1/2)*a^(1/2)*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+a*sec(c+d*x))^(1/2))+-15//16*a^2*d^-1*(1+-1*sec(c+d*x))^-1*(a+a*sec(c+d*x))^-3//2+-1//4*a^2*d^-1*(1+-1*sec(c+d*x))^-2*(a+a*sec(c+d*x))^-3//2)
@test integrate((a+a*sec(c+d*x))^(1/2)*tan(c+d*x)^6, x) == :(-2*a^(1/2)*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2*a*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+2*a^4*d^-1*(a+a*sec(c+d*x))^-7//2*tan(c+d*x)^7+-2//3*a^2*d^-1*(a+a*sec(c+d*x))^-3//2*tan(c+d*x)^3+2//5*a^3*d^-1*(a+a*sec(c+d*x))^-5//2*tan(c+d*x)^5+2//11*a^6*d^-1*(a+a*sec(c+d*x))^-11//2*tan(c+d*x)^11+10//9*a^5*d^-1*(a+a*sec(c+d*x))^-9//2*tan(c+d*x)^9)
@test integrate((a+a*sec(c+d*x))^(1/2)*tan(c+d*x)^4, x) == :(2*a^(1/2)*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-2*a*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+2//3*a^2*d^-1*(a+a*sec(c+d*x))^-3//2*tan(c+d*x)^3+2//7*a^4*d^-1*(a+a*sec(c+d*x))^-7//2*tan(c+d*x)^7+6//5*a^3*d^-1*(a+a*sec(c+d*x))^-5//2*tan(c+d*x)^5)
@test integrate((a+a*sec(c+d*x))^(1/2)*tan(c+d*x)^2, x) == :(-2*a^(1/2)*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2*a*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+2//3*a^2*d^-1*(a+a*sec(c+d*x))^-3//2*tan(c+d*x)^3)
@test integrate((a+a*sec(c+d*x))^(1/2)*cot(c+d*x)^2, x) == :(-1*d^-1*(a+a*sec(c+d*x))^(1/2)*cot(c+d*x)+-2*a^(1/2)*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*2^(1/2)*a^(1/2)*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^(1/2)*cot(c+d*x)^4, x) == :(2*a^(1/2)*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+7//8*d^-1*(a+a*sec(c+d*x))^(1/2)*cot(c+d*x)+-9//16*2^(1/2)*a^(1/2)*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//12*a^-1*d^-1*(a+a*sec(c+d*x))^3//2*cot(c+d*x)^3+-1//4*a^-1*d^-1*(a+a*sec(c+d*x))^3//2*cot(c+d*x)^3*sec((1/2)*c+(1/2)*d*x)^2*cos(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cot(c+d*x)^6, x) == :(-2*a^(1/2)*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-105//128*d^-1*(a+a*sec(c+d*x))^(1/2)*cot(c+d*x)+-23//192*a^-1*d^-1*(a+a*sec(c+d*x))^3//2*cot(c+d*x)^3+87//160*a^-2*d^-1*(a+a*sec(c+d*x))^5//2*cot(c+d*x)^5+151//256*2^(1/2)*a^(1/2)*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-17//32*a^-2*d^-1*(a+a*sec(c+d*x))^5//2*cot(c+d*x)^5*sec((1/2)*c+(1/2)*d*x)^2*cos(c+d*x)+-1//16*a^-2*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^2*cot(c+d*x)^5*sec((1/2)*c+(1/2)*d*x)^4)
@test integrate((a+a*sec(c+d*x))^3//2*tan(c+d*x)^5, x) == :(2//3*d^-1*(a+a*sec(c+d*x))^3//2+-2*a^3//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+2*a*d^-1*(a+a*sec(c+d*x))^(1/2)+-2//3*a^-3*d^-1*(a+a*sec(c+d*x))^9//2+2//5*a^-1*d^-1*(a+a*sec(c+d*x))^5//2+2//7*a^-2*d^-1*(a+a*sec(c+d*x))^7//2+2//11*a^-4*d^-1*(a+a*sec(c+d*x))^11//2)
@test integrate((a+a*sec(c+d*x))^3//2*tan(c+d*x)^3, x) == :(-2//3*d^-1*(a+a*sec(c+d*x))^3//2+-2*a*d^-1*(a+a*sec(c+d*x))^(1/2)+2*a^3//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+-2//5*a^-1*d^-1*(a+a*sec(c+d*x))^5//2+2//7*a^-2*d^-1*(a+a*sec(c+d*x))^7//2)
@test integrate((a+a*sec(c+d*x))^3//2*tan(c+d*x), x) == :(2//3*d^-1*(a+a*sec(c+d*x))^3//2+-2*a^3//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+2*a*d^-1*(a+a*sec(c+d*x))^(1/2))
@test integrate((a+a*sec(c+d*x))^3//2*cot(c+d*x), x) == :(2*a^3//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+-2*2^(1/2)*a^3//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+a*sec(c+d*x))^(1/2)))
@test integrate((a+a*sec(c+d*x))^3//2*cot(c+d*x)^3, x) == :(-2*a^3//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+(1/2)*a*d^-1*(1+-1*sec(c+d*x))^-1*(a+a*sec(c+d*x))^(1/2)+5//4*2^(1/2)*a^3//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+a*sec(c+d*x))^(1/2)))
@test integrate((a+a*sec(c+d*x))^3//2*cot(c+d*x)^5, x) == :(2*a^3//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+7//32*a^2*d^-1*(a+a*sec(c+d*x))^-1//2+-71//64*2^(1/2)*a^3//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+a*sec(c+d*x))^(1/2))+-13//16*a^2*d^-1*(1+-1*sec(c+d*x))^-1*(a+a*sec(c+d*x))^-1//2+-1//4*a^2*d^-1*(1+-1*sec(c+d*x))^-2*(a+a*sec(c+d*x))^-1//2)
@test integrate((a+a*sec(c+d*x))^3//2*tan(c+d*x)^6, x) == :(-2*a^3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+-2//3*a^3*d^-1*(a+a*sec(c+d*x))^-3//2*tan(c+d*x)^3+2//5*a^4*d^-1*(a+a*sec(c+d*x))^-5//2*tan(c+d*x)^5+2//13*a^8*d^-1*(a+a*sec(c+d*x))^-13//2*tan(c+d*x)^13+14//11*a^7*d^-1*(a+a*sec(c+d*x))^-11//2*tan(c+d*x)^11+30//7*a^5*d^-1*(a+a*sec(c+d*x))^-7//2*tan(c+d*x)^7+34//9*a^6*d^-1*(a+a*sec(c+d*x))^-9//2*tan(c+d*x)^9)
@test integrate((a+a*sec(c+d*x))^3//2*tan(c+d*x)^4, x) == :(2*a^3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-2*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+2//3*a^3*d^-1*(a+a*sec(c+d*x))^-3//2*tan(c+d*x)^3+2//9*a^6*d^-1*(a+a*sec(c+d*x))^-9//2*tan(c+d*x)^9+10//7*a^5*d^-1*(a+a*sec(c+d*x))^-7//2*tan(c+d*x)^7+14//5*a^4*d^-1*(a+a*sec(c+d*x))^-5//2*tan(c+d*x)^5)
@test integrate((a+a*sec(c+d*x))^3//2*tan(c+d*x)^2, x) == :(-2*a^3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+2*a^3*d^-1*(a+a*sec(c+d*x))^-3//2*tan(c+d*x)^3+2//5*a^4*d^-1*(a+a*sec(c+d*x))^-5//2*tan(c+d*x)^5)
@test integrate((a+a*sec(c+d*x))^3//2*cot(c+d*x)^2, x) == :(-2*a^3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-2*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cot(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cot(c+d*x)^4, x) == :(2*a^3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//3*d^-1*(a+a*sec(c+d*x))^3//2*cot(c+d*x)^3+-1//4*2^(1/2)*a^3//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+3//2*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cot(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cot(c+d*x)^6, x) == :(-2*a^3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+5//24*d^-1*(a+a*sec(c+d*x))^3//2*cot(c+d*x)^3+-21//16*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cot(c+d*x)+3//20*a^-1*d^-1*(a+a*sec(c+d*x))^5//2*cot(c+d*x)^5+11//32*2^(1/2)*a^3//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*a^-1*d^-1*(a+a*sec(c+d*x))^5//2*cot(c+d*x)^5*sec((1/2)*c+(1/2)*d*x)^2*cos(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*tan(c+d*x)^5, x) == :(2//5*d^-1*(a+a*sec(c+d*x))^5//2+-2*a^5//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+2*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)+-6//11*a^-3*d^-1*(a+a*sec(c+d*x))^11//2+2//3*a*d^-1*(a+a*sec(c+d*x))^3//2+2//7*a^-1*d^-1*(a+a*sec(c+d*x))^7//2+2//9*a^-2*d^-1*(a+a*sec(c+d*x))^9//2+2//13*a^-4*d^-1*(a+a*sec(c+d*x))^13//2)
@test integrate((a+a*sec(c+d*x))^5//2*tan(c+d*x)^3, x) == :(-2//5*d^-1*(a+a*sec(c+d*x))^5//2+-2*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)+2*a^5//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+-2//3*a*d^-1*(a+a*sec(c+d*x))^3//2+-2//7*a^-1*d^-1*(a+a*sec(c+d*x))^7//2+2//9*a^-2*d^-1*(a+a*sec(c+d*x))^9//2)
@test integrate((a+a*sec(c+d*x))^5//2*tan(c+d*x), x) == :(2//5*d^-1*(a+a*sec(c+d*x))^5//2+-2*a^5//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+2*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)+2//3*a*d^-1*(a+a*sec(c+d*x))^3//2)
@test integrate((a+a*sec(c+d*x))^5//2*cot(c+d*x), x) == :(2*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)+2*a^5//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+-4*2^(1/2)*a^5//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+a*sec(c+d*x))^(1/2)))
@test integrate((a+a*sec(c+d*x))^5//2*cot(c+d*x)^3, x) == :(-2*a^5//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+a^2*d^-1*(1+-1*sec(c+d*x))^-1*(a+a*sec(c+d*x))^(1/2)+3//2*2^(1/2)*a^5//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+a*sec(c+d*x))^(1/2)))
@test integrate((a+a*sec(c+d*x))^5//2*cot(c+d*x)^5, x) == :(2*a^5//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+-43//32*2^(1/2)*a^5//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+a*sec(c+d*x))^(1/2))+-11//16*a^2*d^-1*(1+-1*sec(c+d*x))^-1*(a+a*sec(c+d*x))^(1/2)+-1//4*a^2*d^-1*(1+-1*sec(c+d*x))^-2*(a+a*sec(c+d*x))^(1/2))
@test integrate((a+a*sec(c+d*x))^5//2*tan(c+d*x)^6, x) == :(-2*a^5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+-2//3*a^4*d^-1*(a+a*sec(c+d*x))^-3//2*tan(c+d*x)^3+2//5*a^5*d^-1*(a+a*sec(c+d*x))^-5//2*tan(c+d*x)^5+2//15*a^10*d^-1*(a+a*sec(c+d*x))^-15//2*tan(c+d*x)^15+18//13*a^9*d^-1*(a+a*sec(c+d*x))^-13//2*tan(c+d*x)^13+62//7*a^6*d^-1*(a+a*sec(c+d*x))^-7//2*tan(c+d*x)^7+62//11*a^8*d^-1*(a+a*sec(c+d*x))^-11//2*tan(c+d*x)^11+98//9*a^7*d^-1*(a+a*sec(c+d*x))^-9//2*tan(c+d*x)^9)
@test integrate((a+a*sec(c+d*x))^5//2*tan(c+d*x)^4, x) == :(2*a^5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-2*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+6*a^5*d^-1*(a+a*sec(c+d*x))^-5//2*tan(c+d*x)^5+2//3*a^4*d^-1*(a+a*sec(c+d*x))^-3//2*tan(c+d*x)^3+2//11*a^8*d^-1*(a+a*sec(c+d*x))^-11//2*tan(c+d*x)^11+14//9*a^7*d^-1*(a+a*sec(c+d*x))^-9//2*tan(c+d*x)^9+34//7*a^6*d^-1*(a+a*sec(c+d*x))^-7//2*tan(c+d*x)^7)
@test integrate((a+a*sec(c+d*x))^5//2*tan(c+d*x)^2, x) == :(-2*a^5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+2*a^5*d^-1*(a+a*sec(c+d*x))^-5//2*tan(c+d*x)^5+2//7*a^6*d^-1*(a+a*sec(c+d*x))^-7//2*tan(c+d*x)^7+14//3*a^4*d^-1*(a+a*sec(c+d*x))^-3//2*tan(c+d*x)^3)
@test integrate((a+a*sec(c+d*x))^5//2*cot(c+d*x)^2, x) == :(-2*a^5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-4*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cot(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cot(c+d*x)^4, x) == :(2*a^5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cot(c+d*x)+-2//3*a*d^-1*(a+a*sec(c+d*x))^3//2*cot(c+d*x)^3)
@test integrate((a+a*sec(c+d*x))^5//2*cot(c+d*x)^6, x) == :(-2*a^5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//5*d^-1*(a+a*sec(c+d*x))^5//2*cot(c+d*x)^5+(1/2)*a*d^-1*(a+a*sec(c+d*x))^3//2*cot(c+d*x)^3+-7//4*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cot(c+d*x)+1//8*2^(1/2)*a^5//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*tan(c+d*x)^5, x) == :(-2*a^-1//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+2*a^-1*d^-1*(a+a*sec(c+d*x))^(1/2)+-6//5*a^-3*d^-1*(a+a*sec(c+d*x))^5//2+2//3*a^-2*d^-1*(a+a*sec(c+d*x))^3//2+2//7*a^-4*d^-1*(a+a*sec(c+d*x))^7//2)
@test integrate((a+a*sec(c+d*x))^-1//2*tan(c+d*x)^3, x) == :(-2*a^-1*d^-1*(a+a*sec(c+d*x))^(1/2)+2*a^-1//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+2//3*a^-2*d^-1*(a+a*sec(c+d*x))^3//2)
@test integrate((a+a*sec(c+d*x))^-1//2*tan(c+d*x), x) == :(-2*a^-1//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2)))
@test integrate((a+a*sec(c+d*x))^-1//2*cot(c+d*x), x) == :(-1*d^-1*(a+a*sec(c+d*x))^-1//2+2*a^-1//2*d^-1*arctanh(a^-1//2*(a+a*sec(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+a*sec(c+d*x))^(1/2)))
@test integrate((a+a*sec(c+d*x))^-1//2*cot(c+d*x)^3, x) == :(7//8*d^-1*(a+a*sec(c+d*x))^-1//2+-2*a^-1//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+-1//12*a*d^-1*(a+a*sec(c+d*x))^-3//2+(1/2)*a*d^-1*(1+-1*sec(c+d*x))^-1*(a+a*sec(c+d*x))^-3//2+9//16*2^(1/2)*a^-1//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+a*sec(c+d*x))^(1/2)))
@test integrate((a+a*sec(c+d*x))^-1//2*cot(c+d*x)^5, x) == :(-105//128*d^-1*(a+a*sec(c+d*x))^-1//2+2*a^-1//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+23//192*a*d^-1*(a+a*sec(c+d*x))^-3//2+87//160*a^2*d^-1*(a+a*sec(c+d*x))^-5//2+-151//256*2^(1/2)*a^-1//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+a*sec(c+d*x))^(1/2))+-17//16*a^2*d^-1*(1+-1*sec(c+d*x))^-1*(a+a*sec(c+d*x))^-5//2+-1//4*a^2*d^-1*(1+-1*sec(c+d*x))^-2*(a+a*sec(c+d*x))^-5//2)
@test integrate((a+a*sec(c+d*x))^-1//2*tan(c+d*x)^6, x) == :(-2*a^-1//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+-2//3*a*d^-1*(a+a*sec(c+d*x))^-3//2*tan(c+d*x)^3+2//5*a^2*d^-1*(a+a*sec(c+d*x))^-5//2*tan(c+d*x)^5+2//9*a^4*d^-1*(a+a*sec(c+d*x))^-9//2*tan(c+d*x)^9+6//7*a^3*d^-1*(a+a*sec(c+d*x))^-7//2*tan(c+d*x)^7)
@test integrate((a+a*sec(c+d*x))^-1//2*tan(c+d*x)^4, x) == :(-2*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+2*a^-1//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//3*a*d^-1*(a+a*sec(c+d*x))^-3//2*tan(c+d*x)^3+2//5*a^2*d^-1*(a+a*sec(c+d*x))^-5//2*tan(c+d*x)^5)
@test integrate((a+a*sec(c+d*x))^-1//2*tan(c+d*x)^2, x) == :(-2*a^-1//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*cot(c+d*x)^2, x) == :(-2*a^-1//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*a^-1*d^-1*(a+a*sec(c+d*x))^(1/2)*cot(c+d*x)+7//8*2^(1/2)*a^-1//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*a^-1*d^-1*(a+a*sec(c+d*x))^(1/2)*sec((1/2)*c+(1/2)*d*x)^2*cos(c+d*x)*cot(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*cot(c+d*x)^4, x) == :(2*a^-1//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-107//128*2^(1/2)*a^-1//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+21//64*a^-1*d^-1*(a+a*sec(c+d*x))^(1/2)*cot(c+d*x)+43//96*a^-2*d^-1*(a+a*sec(c+d*x))^3//2*cot(c+d*x)^3+-15//32*a^-2*d^-1*(a+a*sec(c+d*x))^3//2*cot(c+d*x)^3*sec((1/2)*c+(1/2)*d*x)^2*cos(c+d*x)+-1//16*a^-2*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^2*cot(c+d*x)^3*sec((1/2)*c+(1/2)*d*x)^4)
@test integrate((a+a*sec(c+d*x))^-1//2*cot(c+d*x)^6, x) == :(-2*a^-1//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-323//768*a^-2*d^-1*(a+a*sec(c+d*x))^3//2*cot(c+d*x)^3+-189//512*a^-1*d^-1*(a+a*sec(c+d*x))^(1/2)*cot(c+d*x)+579//640*a^-3*d^-1*(a+a*sec(c+d*x))^5//2*cot(c+d*x)^5+835//1024*2^(1/2)*a^-1//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-101//128*a^-3*d^-1*(a+a*sec(c+d*x))^5//2*cot(c+d*x)^5*sec((1/2)*c+(1/2)*d*x)^2*cos(c+d*x)+-23//192*a^-3*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^2*cot(c+d*x)^5*sec((1/2)*c+(1/2)*d*x)^4+-1//48*a^-3*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^3*cot(c+d*x)^5*sec((1/2)*c+(1/2)*d*x)^6)
@test integrate((a+a*sec(c+d*x))^-3//2*tan(c+d*x)^5, x) == :(-2*a^-3*d^-1*(a+a*sec(c+d*x))^3//2+-2*a^-3//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+2*a^-2*d^-1*(a+a*sec(c+d*x))^(1/2)+2//5*a^-4*d^-1*(a+a*sec(c+d*x))^5//2)
@test integrate((a+a*sec(c+d*x))^-3//2*tan(c+d*x)^3, x) == :(2*a^-2*d^-1*(a+a*sec(c+d*x))^(1/2)+2*a^-3//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2)))
@test integrate((a+a*sec(c+d*x))^-3//2*tan(c+d*x), x) == :(-2*a^-3//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+2*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2)
@test integrate((a+a*sec(c+d*x))^-3//2*cot(c+d*x), x) == :(-1//3*d^-1*(a+a*sec(c+d*x))^-3//2+2*a^-3//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+-3//2*a^-1*d^-1*(a+a*sec(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+a*sec(c+d*x))^(1/2)))
@test integrate((a+a*sec(c+d*x))^-3//2*cot(c+d*x)^3, x) == :(5//24*d^-1*(a+a*sec(c+d*x))^-3//2+-2*a^-3//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+-3//20*a*d^-1*(a+a*sec(c+d*x))^-5//2+21//16*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2+(1/2)*a*d^-1*(1+-1*sec(c+d*x))^-1*(a+a*sec(c+d*x))^-5//2+11//32*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+a*sec(c+d*x))^(1/2)))
@test integrate((a+a*sec(c+d*x))^-3//2*cot(c+d*x)^5, x) == :(-53//384*d^-1*(a+a*sec(c+d*x))^-3//2+2*a^-3//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+-309//256*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2+15//64*a*d^-1*(a+a*sec(c+d*x))^-5//2+139//224*a^2*d^-1*(a+a*sec(c+d*x))^-7//2+-203//512*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+a*sec(c+d*x))^(1/2))+-19//16*a^2*d^-1*(1+-1*sec(c+d*x))^-1*(a+a*sec(c+d*x))^-7//2+-1//4*a^2*d^-1*(1+-1*sec(c+d*x))^-2*(a+a*sec(c+d*x))^-7//2)
@test integrate((a+a*sec(c+d*x))^-3//2*tan(c+d*x)^6, x) == :(-2*a^-3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-2//3*d^-1*(a+a*sec(c+d*x))^-3//2*tan(c+d*x)^3+2*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+2//5*a*d^-1*(a+a*sec(c+d*x))^-5//2*tan(c+d*x)^5+2//7*a^2*d^-1*(a+a*sec(c+d*x))^-7//2*tan(c+d*x)^7)
@test integrate((a+a*sec(c+d*x))^-3//2*tan(c+d*x)^4, x) == :(2*a^-3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//3*d^-1*(a+a*sec(c+d*x))^-3//2*tan(c+d*x)^3+-2*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*tan(c+d*x)^2, x) == :(-2*a^-3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2*2^(1/2)*a^-3//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cot(c+d*x)^2, x) == :(-2*a^-3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+7//32*a^-2*d^-1*(a+a*sec(c+d*x))^(1/2)*cot(c+d*x)+71//64*2^(1/2)*a^-3//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-13//32*a^-2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec((1/2)*c+(1/2)*d*x)^2*cos(c+d*x)*cot(c+d*x)+-1//16*a^-2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^2*sec((1/2)*c+(1/2)*d*x)^4*cot(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*cot(c+d*x)^4, x) == :(2*a^-3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-533//512*2^(1/2)*a^-3//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-21//256*a^-2*d^-1*(a+a*sec(c+d*x))^(1/2)*cot(c+d*x)+277//384*a^-3*d^-1*(a+a*sec(c+d*x))^3//2*cot(c+d*x)^3+-81//128*a^-3*d^-1*(a+a*sec(c+d*x))^3//2*cot(c+d*x)^3*sec((1/2)*c+(1/2)*d*x)^2*cos(c+d*x)+-7//64*a^-3*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^2*cot(c+d*x)^3*sec((1/2)*c+(1/2)*d*x)^4+-1//48*a^-3*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^3*cot(c+d*x)^3*sec((1/2)*c+(1/2)*d*x)^6)
@test integrate((a+a*sec(c+d*x))^-3//2*cot(c+d*x)^6, x) == :(-2*a^-3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-8171//12288*a^-3*d^-1*(a+a*sec(c+d*x))^3//2*cot(c+d*x)^3+-21//8192*a^-2*d^-1*(a+a*sec(c+d*x))^(1/2)*cot(c+d*x)+12267//10240*a^-4*d^-1*(a+a*sec(c+d*x))^5//2*cot(c+d*x)^5+16363//16384*2^(1/2)*a^-3//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-2045//2048*a^-4*d^-1*(a+a*sec(c+d*x))^5//2*cot(c+d*x)^5*sec((1/2)*c+(1/2)*d*x)^2*cos(c+d*x)+-511//3072*a^-4*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^2*cot(c+d*x)^5*sec((1/2)*c+(1/2)*d*x)^4+-29//768*a^-4*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^3*cot(c+d*x)^5*sec((1/2)*c+(1/2)*d*x)^6+-1//128*a^-4*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^4*cot(c+d*x)^5*sec((1/2)*c+(1/2)*d*x)^8)
@test integrate((a+a*sec(c+d*x))^-5//2*tan(c+d*x)^5, x) == :(-6*a^-3*d^-1*(a+a*sec(c+d*x))^(1/2)+-2*a^-5//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+2//3*a^-4*d^-1*(a+a*sec(c+d*x))^3//2)
@test integrate((a+a*sec(c+d*x))^-5//2*tan(c+d*x)^3, x) == :(-4*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2+2*a^-5//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2)))
@test integrate((a+a*sec(c+d*x))^-5//2*tan(c+d*x), x) == :(-2*a^-5//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+2*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2+2//3*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2)
@test integrate((a+a*sec(c+d*x))^-5//2*cot(c+d*x), x) == :(-1//5*d^-1*(a+a*sec(c+d*x))^-5//2+2*a^-5//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+-7//4*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2+-1//2*a^-1*d^-1*(a+a*sec(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+a*sec(c+d*x))^(1/2)))
@test integrate((a+a*sec(c+d*x))^-5//2*cot(c+d*x)^3, x) == :(3//40*d^-1*(a+a*sec(c+d*x))^-5//2+-2*a^-5//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+-5//28*a*d^-1*(a+a*sec(c+d*x))^-7//2+19//48*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2+51//32*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2+(1/2)*a*d^-1*(1+-1*sec(c+d*x))^-1*(a+a*sec(c+d*x))^-7//2+13//64*2^(1/2)*a^-5//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+a*sec(c+d*x))^(1/2)))
@test integrate((a+a*sec(c+d*x))^-5//2*cot(c+d*x)^5, x) == :(7//640*d^-1*(a+a*sec(c+d*x))^-5//2+2*a^-5//2*d^-1*arctanh(a^-1//2*(a+a*sec(c+d*x))^(1/2))+-761//512*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2+-83//256*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2+135//448*a*d^-1*(a+a*sec(c+d*x))^-7//2+199//288*a^2*d^-1*(a+a*sec(c+d*x))^-9//2+-263//1024*2^(1/2)*a^-5//2*d^-1*arctanh((1/2)*2^(1/2)*a^-1//2*(a+a*sec(c+d*x))^(1/2))+-21//16*a^2*d^-1*(1+-1*sec(c+d*x))^-1*(a+a*sec(c+d*x))^-9//2+-1//4*a^2*d^-1*(1+-1*sec(c+d*x))^-2*(a+a*sec(c+d*x))^-9//2)
@test integrate((a+a*sec(c+d*x))^-5//2*tan(c+d*x)^6, x) == :(-2*a^-5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//5*d^-1*(a+a*sec(c+d*x))^-5//2*tan(c+d*x)^5+2*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+-2//3*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*tan(c+d*x)^3)
@test integrate((a+a*sec(c+d*x))^-5//2*tan(c+d*x)^4, x) == :(2*a^-5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-4*2^(1/2)*a^-5//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*tan(c+d*x)^2, x) == :(-2*a^-5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+3//2*2^(1/2)*a^-5//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec((1/2)*c+(1/2)*d*x)^2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*cot(c+d*x)^2, x) == :(-2*a^-5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+63//128*a^-3*d^-1*(a+a*sec(c+d*x))^(1/2)*cot(c+d*x)+319//256*2^(1/2)*a^-5//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-191//384*a^-3*d^-1*(a+a*sec(c+d*x))^(1/2)*sec((1/2)*c+(1/2)*d*x)^2*cos(c+d*x)*cot(c+d*x)+-19//192*a^-3*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^2*sec((1/2)*c+(1/2)*d*x)^4*cot(c+d*x)+-1//48*a^-3*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^3*sec((1/2)*c+(1/2)*d*x)^6*cot(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*cot(c+d*x)^4, x) == :(2*a^-5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-9683//8192*2^(1/2)*a^-5//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1491//4096*a^-3*d^-1*(a+a*sec(c+d*x))^(1/2)*cot(c+d*x)+5587//6144*a^-4*d^-1*(a+a*sec(c+d*x))^3//2*cot(c+d*x)^3+-1527//2048*a^-4*d^-1*(a+a*sec(c+d*x))^3//2*cot(c+d*x)^3*sec((1/2)*c+(1/2)*d*x)^2*cos(c+d*x)+-145//1024*a^-4*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^2*cot(c+d*x)^3*sec((1/2)*c+(1/2)*d*x)^4+-9//256*a^-4*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^3*cot(c+d*x)^3*sec((1/2)*c+(1/2)*d*x)^6+-1//128*a^-4*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^4*cot(c+d*x)^3*sec((1/2)*c+(1/2)*d*x)^8)
@test integrate((a+a*sec(c+d*x))^-5//2*cot(c+d*x)^6, x) == :(-2*a^-5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-41693//49152*a^-4*d^-1*(a+a*sec(c+d*x))^3//2*cot(c+d*x)^3+8925//32768*a^-3*d^-1*(a+a*sec(c+d*x))^(1/2)*cot(c+d*x)+58077//40960*a^-5*d^-1*(a+a*sec(c+d*x))^5//2*cot(c+d*x)^5+74461//65536*2^(1/2)*a^-5//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-9467//8192*a^-5*d^-1*(a+a*sec(c+d*x))^5//2*cot(c+d*x)^5*sec((1/2)*c+(1/2)*d*x)^2*cos(c+d*x)+-2473//12288*a^-5*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^2*cot(c+d*x)^5*sec((1/2)*c+(1/2)*d*x)^4+-155//3072*a^-5*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^3*cot(c+d*x)^5*sec((1/2)*c+(1/2)*d*x)^6+-7//512*a^-5*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^4*cot(c+d*x)^5*sec((1/2)*c+(1/2)*d*x)^8+-1//320*a^-5*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^5*cot(c+d*x)^5*sec((1/2)*c+(1/2)*d*x)^10)
@test integrate((a+a*sec(e+f*x))^-9//2*tan(e+f*x)^2, x) == :(-2*a^-9//2*f^-1*arctan(a^(1/2)*(a+a*sec(e+f*x))^-1//2*tan(e+f*x))+1//3*a^-1*f^-1*(a+a*sec(e+f*x))^-7//2*tan(e+f*x)+11//24*a^-2*f^-1*(a+a*sec(e+f*x))^-5//2*tan(e+f*x)+27//32*a^-3*f^-1*(a+a*sec(e+f*x))^-3//2*tan(e+f*x)+91//64*2^(1/2)*a^-9//2*f^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(e+f*x))^-1//2*tan(e+f*x)))
@test integrate((e*cot(c+d*x))^5//2*(a+a*sec(c+d*x)), x) == :(-2//3*d^-1*(e*cot(c+d*x))^5//2*(a+a*sec(c+d*x))*tan(c+d*x)+(1/2)*a*2^(1/2)*d^-1*(e*cot(c+d*x))^5//2*tan(c+d*x)^5//2*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*a*2^(1/2)*d^-1*(e*cot(c+d*x))^5//2*tan(c+d*x)^5//2*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*a*2^(1/2)*d^-1*(e*cot(c+d*x))^5//2*tan(c+d*x)^5//2*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*a*2^(1/2)*d^-1*(e*cot(c+d*x))^5//2*tan(c+d*x)^5//2*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+-1//3*a*d^-1*(e*cot(c+d*x))^5//2*sin(2c+2*d*x)^(1/2)*tan(c+d*x)^2*Elliptic.F(c+-1//4*pi+d*x,2)*sec(c+d*x))
@test integrate((e*cot(c+d*x))^3//2*(a+a*sec(c+d*x)), x) == :(-2*d^-1*(e*cot(c+d*x))^3//2*(a+a*sec(c+d*x))*tan(c+d*x)+2*a*d^-1*(e*cot(c+d*x))^3//2*tan(c+d*x)^2*sin(c+d*x)+(1/2)*a*2^(1/2)*d^-1*(e*cot(c+d*x))^3//2*tan(c+d*x)^3//2*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*a*2^(1/2)*d^-1*(e*cot(c+d*x))^3//2*tan(c+d*x)^3//2*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*a*2^(1/2)*d^-1*(e*cot(c+d*x))^3//2*tan(c+d*x)^3//2*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*a*2^(1/2)*d^-1*(e*cot(c+d*x))^3//2*tan(c+d*x)^3//2*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+-2*a*d^-1*(e*cot(c+d*x))^3//2*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*sin(c+d*x)*tan(c+d*x))
@test integrate((e*cot(c+d*x))^(1/2)*(a+a*sec(c+d*x)), x) == :(a*d^-1*(e*cot(c+d*x))^(1/2)*sin(2c+2*d*x)^(1/2)*Elliptic.F(c+-1//4*pi+d*x,2)*sec(c+d*x)+(1/2)*a*2^(1/2)*d^-1*(e*cot(c+d*x))^(1/2)*tan(c+d*x)^(1/2)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//2*a*2^(1/2)*d^-1*(e*cot(c+d*x))^(1/2)*tan(c+d*x)^(1/2)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*a*2^(1/2)*d^-1*(e*cot(c+d*x))^(1/2)*tan(c+d*x)^(1/2)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*a*2^(1/2)*d^-1*(e*cot(c+d*x))^(1/2)*tan(c+d*x)^(1/2)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((e*cot(c+d*x))^-1//2*(a+a*sec(c+d*x)), x) == :(2*a*d^-1*(e*cot(c+d*x))^-1//2*sin(c+d*x)+(1/2)*a*2^(1/2)*d^-1*(e*cot(c+d*x))^-1//2*tan(c+d*x)^-1//2*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-2*a*d^-1*(e*cot(c+d*x))^-1//2*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*cos(c+d*x)+-1//2*a*2^(1/2)*d^-1*(e*cot(c+d*x))^-1//2*tan(c+d*x)^-1//2*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*a*2^(1/2)*d^-1*(e*cot(c+d*x))^-1//2*tan(c+d*x)^-1//2*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*a*2^(1/2)*d^-1*(e*cot(c+d*x))^-1//2*tan(c+d*x)^-1//2*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((e*cot(c+d*x))^-3//2*(a+a*sec(c+d*x)), x) == :(2//3*d^-1*(e*cot(c+d*x))^-3//2*(3a+a*sec(c+d*x))*cot(c+d*x)+(1/2)*a*2^(1/2)*d^-1*(e*cot(c+d*x))^-3//2*tan(c+d*x)^-3//2*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*a*2^(1/2)*d^-1*(e*cot(c+d*x))^-3//2*tan(c+d*x)^-3//2*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*a*2^(1/2)*d^-1*(e*cot(c+d*x))^-3//2*tan(c+d*x)^-3//2*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*a*2^(1/2)*d^-1*(e*cot(c+d*x))^-3//2*tan(c+d*x)^-3//2*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+-1//3*a*d^-1*(e*cot(c+d*x))^-3//2*sin(2c+2*d*x)^(1/2)*Elliptic.F(c+-1//4*pi+d*x,2)*cot(c+d*x)*csc(c+d*x))
@test integrate((e*cot(c+d*x))^5//2*(a+a*sec(c+d*x))^2, x) == :(-4//3*a^2*d^-1*(e*cot(c+d*x))^5//2*tan(c+d*x)+-4//3*a^2*d^-1*(e*cot(c+d*x))^5//2*sec(c+d*x)*tan(c+d*x)+(1/2)*2^(1/2)*a^2*d^-1*(e*cot(c+d*x))^5//2*tan(c+d*x)^5//2*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*a^2*d^-1*(e*cot(c+d*x))^5//2*tan(c+d*x)^5//2*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*a^2*d^-1*(e*cot(c+d*x))^5//2*tan(c+d*x)^5//2*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*a^2*d^-1*(e*cot(c+d*x))^5//2*tan(c+d*x)^5//2*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+-2//3*a^2*d^-1*(e*cot(c+d*x))^5//2*sin(2c+2*d*x)^(1/2)*tan(c+d*x)^2*Elliptic.F(c+-1//4*pi+d*x,2)*sec(c+d*x))
@test integrate((e*cot(c+d*x))^3//2*(a+a*sec(c+d*x))^2, x) == :(-4*a^2*d^-1*(e*cot(c+d*x))^3//2*sin(c+d*x)+-4*a^2*d^-1*(e*cot(c+d*x))^3//2*tan(c+d*x)+(1/2)*2^(1/2)*a^2*d^-1*(e*cot(c+d*x))^3//2*tan(c+d*x)^3//2*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*a^2*d^-1*(e*cot(c+d*x))^3//2*tan(c+d*x)^3//2*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*a^2*d^-1*(e*cot(c+d*x))^3//2*tan(c+d*x)^3//2*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*a^2*d^-1*(e*cot(c+d*x))^3//2*tan(c+d*x)^3//2*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+-4*a^2*d^-1*(e*cot(c+d*x))^3//2*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*sin(c+d*x)*tan(c+d*x))
@test integrate((e*cot(c+d*x))^(1/2)*(a+a*sec(c+d*x))^2, x) == :(2*a^2*d^-1*(e*cot(c+d*x))^(1/2)*tan(c+d*x)+(1/2)*2^(1/2)*a^2*d^-1*(e*cot(c+d*x))^(1/2)*tan(c+d*x)^(1/2)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+2*a^2*d^-1*(e*cot(c+d*x))^(1/2)*sin(2c+2*d*x)^(1/2)*Elliptic.F(c+-1//4*pi+d*x,2)*sec(c+d*x)+-1//2*2^(1/2)*a^2*d^-1*(e*cot(c+d*x))^(1/2)*tan(c+d*x)^(1/2)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*a^2*d^-1*(e*cot(c+d*x))^(1/2)*tan(c+d*x)^(1/2)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*a^2*d^-1*(e*cot(c+d*x))^(1/2)*tan(c+d*x)^(1/2)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((e*cot(c+d*x))^-1//2*(a+a*sec(c+d*x))^2, x) == :(4*a^2*d^-1*(e*cot(c+d*x))^-1//2*sin(c+d*x)+2//3*a^2*d^-1*(e*cot(c+d*x))^-1//2*tan(c+d*x)+(1/2)*2^(1/2)*a^2*d^-1*(e*cot(c+d*x))^-1//2*tan(c+d*x)^-1//2*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-4*a^2*d^-1*(e*cot(c+d*x))^-1//2*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*cos(c+d*x)+-1//2*2^(1/2)*a^2*d^-1*(e*cot(c+d*x))^-1//2*tan(c+d*x)^-1//2*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*a^2*d^-1*(e*cot(c+d*x))^-1//2*tan(c+d*x)^-1//2*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*a^2*d^-1*(e*cot(c+d*x))^-1//2*tan(c+d*x)^-1//2*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((e*cot(c+d*x))^-3//2*(a+a*sec(c+d*x))^2, x) == :(2*a^2*d^-1*(e*cot(c+d*x))^-3//2*cot(c+d*x)+2//5*a^2*d^-1*(e*cot(c+d*x))^-3//2*tan(c+d*x)+4//3*a^2*d^-1*(e*cot(c+d*x))^-3//2*csc(c+d*x)+(1/2)*2^(1/2)*a^2*d^-1*(e*cot(c+d*x))^-3//2*tan(c+d*x)^-3//2*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*a^2*d^-1*(e*cot(c+d*x))^-3//2*tan(c+d*x)^-3//2*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*a^2*d^-1*(e*cot(c+d*x))^-3//2*tan(c+d*x)^-3//2*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*a^2*d^-1*(e*cot(c+d*x))^-3//2*tan(c+d*x)^-3//2*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+-2//3*a^2*d^-1*(e*cot(c+d*x))^-3//2*sin(2c+2*d*x)^(1/2)*Elliptic.F(c+-1//4*pi+d*x,2)*cot(c+d*x)*csc(c+d*x))
@test integrate((e*cot(c+d*x))^3//2*(a+a*sec(c+d*x))^-1, x) == :(-6//5*a^-1*d^-1*(e*cot(c+d*x))^3//2*tan(c+d*x)^2*sin(c+d*x)+-2//5*a^-1*d^-1*(e*cot(c+d*x))^3//2*(5+-3*sec(c+d*x))*tan(c+d*x)+2//5*a^-1*d^-1*(e*cot(c+d*x))^3//2*(1+-1*sec(c+d*x))*cot(c+d*x)+(1/2)*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^3//2*tan(c+d*x)^3//2*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^3//2*tan(c+d*x)^3//2*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^3//2*tan(c+d*x)^3//2*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^3//2*tan(c+d*x)^3//2*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+6//5*a^-1*d^-1*(e*cot(c+d*x))^3//2*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*sin(c+d*x)*tan(c+d*x))
@test integrate((e*cot(c+d*x))^(1/2)*(a+a*sec(c+d*x))^-1, x) == :(2//3*a^-1*d^-1*(e*cot(c+d*x))^(1/2)*(1+-1*sec(c+d*x))*cot(c+d*x)+(1/2)*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^(1/2)*tan(c+d*x)^(1/2)*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^(1/2)*tan(c+d*x)^(1/2)*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//3*a^-1*d^-1*(e*cot(c+d*x))^(1/2)*sin(2c+2*d*x)^(1/2)*Elliptic.F(c+-1//4*pi+d*x,2)*sec(c+d*x)+-1//4*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^(1/2)*tan(c+d*x)^(1/2)*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^(1/2)*tan(c+d*x)^(1/2)*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((e*cot(c+d*x))^-1//2*(a+a*sec(c+d*x))^-1, x) == :(2*a^-1*d^-1*(e*cot(c+d*x))^-1//2*sin(c+d*x)+2*a^-1*d^-1*(e*cot(c+d*x))^-1//2*(1+-1*sec(c+d*x))*cot(c+d*x)+(1/2)*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^-1//2*tan(c+d*x)^-1//2*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-2*a^-1*d^-1*(e*cot(c+d*x))^-1//2*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*cos(c+d*x)+-1//2*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^-1//2*tan(c+d*x)^-1//2*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^-1//2*tan(c+d*x)^-1//2*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^-1//2*tan(c+d*x)^-1//2*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((e*cot(c+d*x))^-3//2*(a+a*sec(c+d*x))^-1, x) == :((1/2)*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^-3//2*tan(c+d*x)^-3//2*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^-3//2*tan(c+d*x)^-3//2*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^-3//2*tan(c+d*x)^-3//2*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^-3//2*tan(c+d*x)^-3//2*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+a^-1*d^-1*(e*cot(c+d*x))^-3//2*sin(2c+2*d*x)^(1/2)*Elliptic.F(c+-1//4*pi+d*x,2)*cot(c+d*x)*csc(c+d*x))
@test integrate((e*cot(c+d*x))^-5//2*(a+a*sec(c+d*x))^-1, x) == :(2*a^-1*d^-1*(e*cot(c+d*x))^-5//2*cos(c+d*x)*cot(c+d*x)+(1/2)*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^-5//2*tan(c+d*x)^-5//2*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^-5//2*tan(c+d*x)^-5//2*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^-5//2*tan(c+d*x)^-5//2*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^-5//2*tan(c+d*x)^-5//2*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+-2*a^-1*d^-1*(e*cot(c+d*x))^-5//2*cot(c+d*x)^2*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*cos(c+d*x))
@test integrate((e*cot(c+d*x))^-7//2*(a+a*sec(c+d*x))^-1, x) == :(-2//3*a^-1*d^-1*(e*cot(c+d*x))^-7//2*cot(c+d*x)^3*(3+-1*sec(c+d*x))+(1/2)*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^-7//2*tan(c+d*x)^-7//2*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^-7//2*tan(c+d*x)^-7//2*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^-7//2*tan(c+d*x)^-7//2*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^-7//2*tan(c+d*x)^-7//2*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+-1//3*a^-1*d^-1*(e*cot(c+d*x))^-7//2*cot(c+d*x)^3*sin(2c+2*d*x)^(1/2)*Elliptic.F(c+-1//4*pi+d*x,2)*csc(c+d*x))
@test integrate((e*cot(c+d*x))^-9//2*(a+a*sec(c+d*x))^-1, x) == :(-6//5*a^-1*d^-1*(e*cot(c+d*x))^-9//2*cot(c+d*x)^3*cos(c+d*x)+-2//15*a^-1*d^-1*(e*cot(c+d*x))^-9//2*cot(c+d*x)^3*(5+-3*sec(c+d*x))+(1/2)*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^-9//2*tan(c+d*x)^-9//2*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^-9//2*tan(c+d*x)^-9//2*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^-9//2*tan(c+d*x)^-9//2*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*a^-1*d^-1*(e*cot(c+d*x))^-9//2*tan(c+d*x)^-9//2*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+6//5*a^-1*d^-1*(e*cot(c+d*x))^-9//2*cot(c+d*x)^4*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*cos(c+d*x))
@test integrate((e*cot(c+d*x))^-1//2*(a+a*sec(c+d*x))^-2, x) == :(2*a^-2*d^-1*(e*cot(c+d*x))^-1//2*cot(c+d*x)+-4//5*a^-2*d^-1*(e*cot(c+d*x))^-1//2*cot(c+d*x)^3+-12//5*a^-2*d^-1*(e*cot(c+d*x))^-1//2*cos(c+d*x)*cot(c+d*x)+4//5*a^-2*d^-1*(e*cot(c+d*x))^-1//2*cot(c+d*x)^2*csc(c+d*x)+(1/2)*2^(1/2)*a^-2*d^-1*(e*cot(c+d*x))^-1//2*tan(c+d*x)^-1//2*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-12//5*a^-2*d^-1*(e*cot(c+d*x))^-1//2*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*cos(c+d*x)+-1//2*2^(1/2)*a^-2*d^-1*(e*cot(c+d*x))^-1//2*tan(c+d*x)^-1//2*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*a^-2*d^-1*(e*cot(c+d*x))^-1//2*tan(c+d*x)^-1//2*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*a^-2*d^-1*(e*cot(c+d*x))^-1//2*tan(c+d*x)^-1//2*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x)))
@test integrate((e*cot(c+d*x))^-3//2*(a+a*sec(c+d*x))^-2, x) == :(-4//3*a^-2*d^-1*(e*cot(c+d*x))^-3//2*cot(c+d*x)^3+4//3*a^-2*d^-1*(e*cot(c+d*x))^-3//2*cot(c+d*x)^2*csc(c+d*x)+(1/2)*2^(1/2)*a^-2*d^-1*(e*cot(c+d*x))^-3//2*tan(c+d*x)^-3//2*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*a^-2*d^-1*(e*cot(c+d*x))^-3//2*tan(c+d*x)^-3//2*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*a^-2*d^-1*(e*cot(c+d*x))^-3//2*tan(c+d*x)^-3//2*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*a^-2*d^-1*(e*cot(c+d*x))^-3//2*tan(c+d*x)^-3//2*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+2//3*a^-2*d^-1*(e*cot(c+d*x))^-3//2*sin(2c+2*d*x)^(1/2)*Elliptic.F(c+-1//4*pi+d*x,2)*cot(c+d*x)*csc(c+d*x))
@test integrate((e*cot(c+d*x))^-5//2*(a+a*sec(c+d*x))^-2, x) == :(-4*a^-2*d^-1*(e*cot(c+d*x))^-5//2*cot(c+d*x)^3+4*a^-2*d^-1*(e*cot(c+d*x))^-5//2*cot(c+d*x)^3*cos(c+d*x)+(1/2)*2^(1/2)*a^-2*d^-1*(e*cot(c+d*x))^-5//2*tan(c+d*x)^-5//2*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*a^-2*d^-1*(e*cot(c+d*x))^-5//2*tan(c+d*x)^-5//2*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*a^-2*d^-1*(e*cot(c+d*x))^-5//2*tan(c+d*x)^-5//2*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*a^-2*d^-1*(e*cot(c+d*x))^-5//2*tan(c+d*x)^-5//2*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+4*a^-2*d^-1*(e*cot(c+d*x))^-5//2*cot(c+d*x)^2*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*cos(c+d*x))
@test integrate((e*cot(c+d*x))^-7//2*(a+a*sec(c+d*x))^-2, x) == :(2*a^-2*d^-1*(e*cot(c+d*x))^-7//2*cot(c+d*x)^3+(1/2)*2^(1/2)*a^-2*d^-1*(e*cot(c+d*x))^-7//2*tan(c+d*x)^-7//2*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*a^-2*d^-1*(e*cot(c+d*x))^-7//2*tan(c+d*x)^-7//2*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*a^-2*d^-1*(e*cot(c+d*x))^-7//2*tan(c+d*x)^-7//2*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*a^-2*d^-1*(e*cot(c+d*x))^-7//2*tan(c+d*x)^-7//2*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+-2*a^-2*d^-1*(e*cot(c+d*x))^-7//2*cot(c+d*x)^3*sin(2c+2*d*x)^(1/2)*Elliptic.F(c+-1//4*pi+d*x,2)*csc(c+d*x))
@test integrate((e*cot(c+d*x))^-9//2*(a+a*sec(c+d*x))^-2, x) == :(2//3*a^-2*d^-1*(e*cot(c+d*x))^-9//2*cot(c+d*x)^3+-4*a^-2*d^-1*(e*cot(c+d*x))^-9//2*cot(c+d*x)^3*cos(c+d*x)+(1/2)*2^(1/2)*a^-2*d^-1*(e*cot(c+d*x))^-9//2*tan(c+d*x)^-9//2*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*a^-2*d^-1*(e*cot(c+d*x))^-9//2*tan(c+d*x)^-9//2*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*a^-2*d^-1*(e*cot(c+d*x))^-9//2*tan(c+d*x)^-9//2*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*a^-2*d^-1*(e*cot(c+d*x))^-9//2*tan(c+d*x)^-9//2*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+4*a^-2*d^-1*(e*cot(c+d*x))^-9//2*cot(c+d*x)^4*sin(2c+2*d*x)^-1//2*Elliptic.E(c+-1//4*pi+d*x,2)*cos(c+d*x))
@test integrate((e*cot(c+d*x))^-11//2*(a+a*sec(c+d*x))^-2, x) == :(2*a^-2*d^-1*(e*cot(c+d*x))^-11//2*cot(c+d*x)^5+2//5*a^-2*d^-1*(e*cot(c+d*x))^-11//2*cot(c+d*x)^3+-4//3*a^-2*d^-1*(e*cot(c+d*x))^-11//2*cot(c+d*x)^4*csc(c+d*x)+(1/2)*2^(1/2)*a^-2*d^-1*(e*cot(c+d*x))^-11//2*tan(c+d*x)^-11//2*arctan(1+-1*2^(1/2)*tan(c+d*x)^(1/2))+-1//2*2^(1/2)*a^-2*d^-1*(e*cot(c+d*x))^-11//2*tan(c+d*x)^-11//2*arctan(1+2^(1/2)*tan(c+d*x)^(1/2))+-1//4*2^(1/2)*a^-2*d^-1*(e*cot(c+d*x))^-11//2*tan(c+d*x)^-11//2*log(1+2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+1//4*2^(1/2)*a^-2*d^-1*(e*cot(c+d*x))^-11//2*tan(c+d*x)^-11//2*log(1+-1*2^(1/2)*tan(c+d*x)^(1/2)+tan(c+d*x))+2//3*a^-2*d^-1*(e*cot(c+d*x))^-11//2*cot(c+d*x)^5*sin(2c+2*d*x)^(1/2)*Elliptic.F(c+-1//4*pi+d*x,2)*csc(c+d*x))
@test integrate(tan(c+d*x)^7*(a+b*sec(c+d*x)), x) == :(a*d^-1*log(cos(c+d*x))+-16//35*b*d^-1*sec(c+d*x)+-1//140*d^-1*tan(c+d*x)^4*(35a+24*b*sec(c+d*x))+1//42*d^-1*tan(c+d*x)^6*(7a+6*b*sec(c+d*x))+1//70*d^-1*tan(c+d*x)^2*(35a+16*b*sec(c+d*x)))
@test integrate(tan(c+d*x)^5*(a+b*sec(c+d*x)), x) == :(-1*a*d^-1*log(cos(c+d*x))+-1//30*d^-1*tan(c+d*x)^2*(15a+8*b*sec(c+d*x))+1//20*d^-1*tan(c+d*x)^4*(5a+4*b*sec(c+d*x))+8//15*b*d^-1*sec(c+d*x))
@test integrate(tan(c+d*x)^3*(a+b*sec(c+d*x)), x) == :(a*d^-1*log(cos(c+d*x))+-2//3*b*d^-1*sec(c+d*x)+1//6*d^-1*tan(c+d*x)^2*(3a+2*b*sec(c+d*x)))
@test integrate((a+b*sec(c+d*x))*tan(c+d*x), x) == :(b*d^-1*sec(c+d*x)+-1*a*d^-1*log(cos(c+d*x)))
@test integrate((a+b*sec(c+d*x))*cot(c+d*x), x) == :((1/2)*d^-1*(a+b)*log(1+-1*cos(c+d*x))+(1/2)*d^-1*(a+-1b)*log(1+cos(c+d*x)))
@test integrate(cot(c+d*x)^3*(a+b*sec(c+d*x)), x) == :(-1//2*d^-1*cot(c+d*x)^2*(a+b*sec(c+d*x))+-1//4*d^-1*(b+2a)*log(1+-1*cos(c+d*x))+-1//4*d^-1*(-1b+2a)*log(1+cos(c+d*x)))
@test integrate(cot(c+d*x)^5*(a+b*sec(c+d*x)), x) == :(-1//4*d^-1*cot(c+d*x)^4*(a+b*sec(c+d*x))+1//8*d^-1*cot(c+d*x)^2*(4a+3*b*sec(c+d*x))+1//16*d^-1*(-3b+8a)*log(1+cos(c+d*x))+1//16*d^-1*(3b+8a)*log(1+-1*cos(c+d*x)))
@test integrate(cot(c+d*x)^7*(a+b*sec(c+d*x)), x) == :(-1//6*d^-1*cot(c+d*x)^6*(a+b*sec(c+d*x))+-1//16*d^-1*cot(c+d*x)^2*(8a+5*b*sec(c+d*x))+-1//32*d^-1*(-5b+16a)*log(1+cos(c+d*x))+-1//32*d^-1*(5b+16a)*log(1+-1*cos(c+d*x))+1//24*d^-1*cot(c+d*x)^4*(6a+5*b*sec(c+d*x)))
@test integrate(tan(c+d*x)^6*(a+b*sec(c+d*x)), x) == :(-1*a*x+-5//16*b*d^-1*arctanh(sin(c+d*x))+-1//24*d^-1*tan(c+d*x)^3*(8a+5*b*sec(c+d*x))+1//16*d^-1*(16a+5*b*sec(c+d*x))*tan(c+d*x)+1//30*d^-1*tan(c+d*x)^5*(6a+5*b*sec(c+d*x)))
@test integrate(tan(c+d*x)^4*(a+b*sec(c+d*x)), x) == :(a*x+-1//8*d^-1*(8a+3*b*sec(c+d*x))*tan(c+d*x)+1//12*d^-1*tan(c+d*x)^3*(4a+3*b*sec(c+d*x))+3//8*b*d^-1*arctanh(sin(c+d*x)))
@test integrate(tan(c+d*x)^2*(a+b*sec(c+d*x)), x) == :(-1*a*x+(1/2)*d^-1*(2a+b*sec(c+d*x))*tan(c+d*x)+-1//2*b*d^-1*arctanh(sin(c+d*x)))
@test integrate(cot(c+d*x)^2*(a+b*sec(c+d*x)), x) == :(-1*a*x+-1*d^-1*(a+b*sec(c+d*x))*cot(c+d*x))
@test integrate(cot(c+d*x)^4*(a+b*sec(c+d*x)), x) == :(a*x+-1//3*d^-1*cot(c+d*x)^3*(a+b*sec(c+d*x))+1//3*d^-1*(3a+2*b*sec(c+d*x))*cot(c+d*x))
@test integrate(cot(c+d*x)^6*(a+b*sec(c+d*x)), x) == :(-1*a*x+-1//5*d^-1*cot(c+d*x)^5*(a+b*sec(c+d*x))+-1//15*d^-1*(15a+8*b*sec(c+d*x))*cot(c+d*x)+1//15*d^-1*cot(c+d*x)^3*(5a+4*b*sec(c+d*x)))
@test integrate(cot(c+d*x)^8*(a+b*sec(c+d*x)), x) == :(a*x+-1//7*d^-1*cot(c+d*x)^7*(a+b*sec(c+d*x))+-1//105*d^-1*cot(c+d*x)^3*(35a+24*b*sec(c+d*x))+1//35*d^-1*cot(c+d*x)^5*(7a+6*b*sec(c+d*x))+1//35*d^-1*(35a+16*b*sec(c+d*x))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*tan(c+d*x)^3, x) == :(a^2*d^-1*log(cos(c+d*x))+(1/2)*d^-1*sec(c+d*x)^2*(a^2+-1*b^2)+1//4*b^2*d^-1*sec(c+d*x)^4+-2*a*b*d^-1*sec(c+d*x)+2//3*a*b*d^-1*sec(c+d*x)^3)
@test integrate((a+b*sec(c+d*x))^2*tan(c+d*x), x) == :((1/2)*b^2*d^-1*sec(c+d*x)^2+-1*a^2*d^-1*log(cos(c+d*x))+2*a*b*d^-1*sec(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cot(c+d*x), x) == :(a^2*d^-1*log(cos(c+d*x))+(1/2)*d^-1*(a+b)^2*log(1+-1*sec(c+d*x))+(1/2)*d^-1*(a+-1b)^2*log(1+sec(c+d*x)))
@test integrate((a+b*sec(c+d*x))^2*cot(c+d*x)^3, x) == :(-1*a^2*d^-1*log(cos(c+d*x))+-1//2*d^-1*cot(c+d*x)^2*(a^2+b^2+2*a*b*sec(c+d*x))+-1//2*a*d^-1*(a+b)*log(1+-1*sec(c+d*x))+-1//2*a*d^-1*(a+-1b)*log(1+sec(c+d*x)))
@test integrate((a+b*sec(c+d*x))^2*cot(c+d*x)^5, x) == :(a^2*d^-1*log(cos(c+d*x))+-1//4*d^-1*cot(c+d*x)^4*(a^2+b^2+2*a*b*sec(c+d*x))+1//4*a*d^-1*cot(c+d*x)^2*(2a+3*b*sec(c+d*x))+1//8*a*d^-1*(-3b+4a)*log(1+sec(c+d*x))+1//8*a*d^-1*(3b+4a)*log(1+-1*sec(c+d*x)))
@test integrate((a+b*sec(c+d*x))^2*tan(c+d*x)^6, x) == :(-1*x*a^2+a^2*d^-1*tan(c+d*x)+-1//3*a^2*d^-1*tan(c+d*x)^3+1//5*a^2*d^-1*tan(c+d*x)^5+1//7*b^2*d^-1*tan(c+d*x)^7+-5//8*a*b*d^-1*arctanh(sin(c+d*x))+-5//12*a*b*d^-1*tan(c+d*x)^3*sec(c+d*x)+1//3*a*b*d^-1*tan(c+d*x)^5*sec(c+d*x)+5//8*a*b*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*tan(c+d*x)^4, x) == :(x*a^2+-1*a^2*d^-1*tan(c+d*x)+1//3*a^2*d^-1*tan(c+d*x)^3+1//5*b^2*d^-1*tan(c+d*x)^5+3//4*a*b*d^-1*arctanh(sin(c+d*x))+(1/2)*a*b*d^-1*tan(c+d*x)^3*sec(c+d*x)+-3//4*a*b*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*tan(c+d*x)^2, x) == :(-1*x*a^2+a^2*d^-1*tan(c+d*x)+1//3*b^2*d^-1*tan(c+d*x)^3+-1*a*b*d^-1*arctanh(sin(c+d*x))+a*b*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cot(c+d*x)^2, x) == :(-1*x*a^2+-1*a^2*d^-1*cot(c+d*x)+-1*b^2*d^-1*cot(c+d*x)+-2*a*b*d^-1*csc(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cot(c+d*x)^4, x) == :(x*a^2+a^2*d^-1*cot(c+d*x)+-1//3*a^2*d^-1*cot(c+d*x)^3+-1//3*b^2*d^-1*cot(c+d*x)^3+2*a*b*d^-1*csc(c+d*x)+-2//3*a*b*d^-1*csc(c+d*x)^3)
@test integrate((a+b*sec(c+d*x))^2*cot(c+d*x)^6, x) == :(-1*x*a^2+-1*a^2*d^-1*cot(c+d*x)+-1//5*a^2*d^-1*cot(c+d*x)^5+-1//5*b^2*d^-1*cot(c+d*x)^5+1//3*a^2*d^-1*cot(c+d*x)^3+-2*a*b*d^-1*csc(c+d*x)+-2//5*a*b*d^-1*csc(c+d*x)^5+4//3*a*b*d^-1*csc(c+d*x)^3)
@test integrate((a+b*sec(c+d*x))^2*cot(c+d*x)^8, x) == :(x*a^2+a^2*d^-1*cot(c+d*x)+-1//3*a^2*d^-1*cot(c+d*x)^3+-1//7*a^2*d^-1*cot(c+d*x)^7+-1//7*b^2*d^-1*cot(c+d*x)^7+1//5*a^2*d^-1*cot(c+d*x)^5+-2*a*b*d^-1*csc(c+d*x)^3+2*a*b*d^-1*csc(c+d*x)+-2//7*a*b*d^-1*csc(c+d*x)^7+6//5*a*b*d^-1*csc(c+d*x)^5)
@test integrate((a+b*sec(c+d*x))^-1*tan(c+d*x)^9, x) == :(-1*a^-1*d^-1*log(cos(c+d*x))+1//7*b^-1*d^-1*sec(c+d*x)^7+b^-7*d^-1*(a^6+-4*b^6+-4*a^4*b^2+6*a^2*b^4)*sec(c+d*x)+-1//6*a*b^-2*d^-1*sec(c+d*x)^6+1//3*b^-5*d^-1*sec(c+d*x)^3*(a^4+6*b^4+-4*a^2*b^2)+1//5*b^-3*d^-1*sec(c+d*x)^5*(a^2+-4*b^2)+-1*a^-1*b^-8*d^-1*(a^2+-1*b^2)^4*log(a+b*sec(c+d*x))+-1//2*a*b^-6*d^-1*sec(c+d*x)^2*(a^4+6*b^4+-4*a^2*b^2)+-1//4*a*b^-4*d^-1*sec(c+d*x)^4*(a^2+-4*b^2))
@test integrate((a+b*sec(c+d*x))^-1*tan(c+d*x)^7, x) == :(a^-1*d^-1*log(cos(c+d*x))+1//5*b^-1*d^-1*sec(c+d*x)^5+b^-5*d^-1*(a^4+3*b^4+-3*a^2*b^2)*sec(c+d*x)+-1//4*a*b^-2*d^-1*sec(c+d*x)^4+1//3*b^-3*d^-1*sec(c+d*x)^3*(a^2+-3*b^2)+-1*a^-1*b^-6*d^-1*(a^2+-1*b^2)^3*log(a+b*sec(c+d*x))+-1//2*a*b^-4*d^-1*sec(c+d*x)^2*(a^2+-3*b^2))
@test integrate((a+b*sec(c+d*x))^-1*tan(c+d*x)^5, x) == :(-1*a^-1*d^-1*log(cos(c+d*x))+1//3*b^-1*d^-1*sec(c+d*x)^3+b^-3*d^-1*(a^2+-2*b^2)*sec(c+d*x)+-1//2*a*b^-2*d^-1*sec(c+d*x)^2+-1*a^-1*b^-4*d^-1*(a^2+-1*b^2)^2*log(a+b*sec(c+d*x)))
@test integrate((a+b*sec(c+d*x))^-1*tan(c+d*x)^3, x) == :(a^-1*d^-1*log(cos(c+d*x))+b^-1*d^-1*sec(c+d*x)+-1*a^-1*b^-2*d^-1*(a^2+-1*b^2)*log(a+b*sec(c+d*x)))
@test integrate((a+b*sec(c+d*x))^-1*tan(c+d*x), x) == :(-1*a^-1*d^-1*log(a+b*sec(c+d*x))+-1*a^-1*d^-1*log(cos(c+d*x)))
@test integrate((a+b*sec(c+d*x))^-1*cot(c+d*x), x) == :(a^-1*d^-1*log(cos(c+d*x))+d^-1*(-2b+2a)^-1*log(1+sec(c+d*x))+d^-1*(2a+2b)^-1*log(1+-1*sec(c+d*x))+-1*a^-1*b^2*d^-1*(a^2+-1*b^2)^-1*log(a+b*sec(c+d*x)))
@test integrate((a+b*sec(c+d*x))^-1*cot(c+d*x)^3, x) == :(d^-1*(1+-1*sec(c+d*x))^-1*(4a+4b)^-1+d^-1*(1+sec(c+d*x))^-1*(-4b+4a)^-1+-1*a^-1*d^-1*log(cos(c+d*x))+-1//4*d^-1*(a+b)^-2*(2a+3b)*log(1+-1*sec(c+d*x))+-1//4*d^-1*(a+-1b)^-2*(-3b+2a)*log(1+sec(c+d*x))+-1*a^-1*b^4*d^-1*(a^2+-1*b^2)^-2*log(a+b*sec(c+d*x)))
@test integrate((a+b*sec(c+d*x))^-1*cot(c+d*x)^5, x) == :(a^-1*d^-1*log(cos(c+d*x))+-1*d^-1*(1+-1*sec(c+d*x))^-2*(16a+16b)^-1+-1*d^-1*(1+sec(c+d*x))^-2*(-16b+16a)^-1+-1//16*d^-1*(1+-1*sec(c+d*x))^-1*(a+b)^-2*(5a+7b)+-1//16*d^-1*(1+sec(c+d*x))^-1*(a+-1b)^-2*(-7b+5a)+1//16*d^-1*(a+b)^-3*(8*a^2+15*b^2+21*a*b)*log(1+-1*sec(c+d*x))+1//16*d^-1*(a+-1b)^-3*(8*a^2+15*b^2+-21*a*b)*log(1+sec(c+d*x))+-1*a^-1*b^6*d^-1*(a^2+-1*b^2)^-3*log(a+b*sec(c+d*x)))
@test integrate((a+b*sec(c+d*x))^-1*tan(c+d*x)^4, x) == :(x*a^-1+(1/2)*b^-1*d^-1*sec(c+d*x)*tan(c+d*x)+(1/2)*b^-3*d^-1*(-3*b^2+2*a^2)*arctanh(sin(c+d*x))+-1*a*b^-2*d^-1*tan(c+d*x)+-2*a^-1*b^-3*d^-1*(a+b)^3//2*(a+-1b)^3//2*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*tan(c+d*x)^2, x) == :(-1*x*a^-1+b^-1*d^-1*arctanh(sin(c+d*x))+-2*a^-1*b^-1*d^-1*(a+b)^(1/2)*(a+-1b)^(1/2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-2*tan(c+d*x)^9, x) == :(-1*a^-2*d^-1*log(cos(c+d*x))+1//6*b^-2*d^-1*sec(c+d*x)^6+(1/2)*b^-6*d^-1*sec(c+d*x)^2*(5*a^4+6*b^4+-12*a^2*b^2)+-2//5*a*b^-3*d^-1*sec(c+d*x)^5+1//4*b^-4*d^-1*sec(c+d*x)^4*(-4*b^2+3*a^2)+a^-1*b^-8*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^4+-2*a*b^-7*d^-1*(3*a^4+6*b^4+-8*a^2*b^2)*sec(c+d*x)+-4//3*a*b^-5*d^-1*sec(c+d*x)^3*(a^2+-2*b^2)+a^-2*b^-8*d^-1*(a^2+-1*b^2)^3*(b^2+7*a^2)*log(a+b*sec(c+d*x)))
@test integrate((a+b*sec(c+d*x))^-2*tan(c+d*x)^7, x) == :(a^-2*d^-1*log(cos(c+d*x))+1//4*b^-2*d^-1*sec(c+d*x)^4+(1/2)*b^-4*d^-1*sec(c+d*x)^2*(-3*b^2+3*a^2)+-2//3*a*b^-3*d^-1*sec(c+d*x)^3+a^-1*b^-6*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^3+-2*a*b^-5*d^-1*(-3*b^2+2*a^2)*sec(c+d*x)+a^-2*b^-6*d^-1*(a^2+-1*b^2)^2*(b^2+5*a^2)*log(a+b*sec(c+d*x)))
@test integrate((a+b*sec(c+d*x))^-2*tan(c+d*x)^5, x) == :((1/2)*b^-2*d^-1*sec(c+d*x)^2+-1*a^-2*d^-1*log(cos(c+d*x))+-2*a*b^-3*d^-1*sec(c+d*x)+a^-1*b^-4*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^2+a^-2*b^-4*d^-1*(a^2+-1*b^2)*(b^2+3*a^2)*log(a+b*sec(c+d*x)))
@test integrate((a+b*sec(c+d*x))^-2*tan(c+d*x)^3, x) == :(a^-2*d^-1*log(cos(c+d*x))+a^-1*b^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)+a^-2*b^-2*d^-1*(a^2+b^2)*log(a+b*sec(c+d*x)))
@test integrate((a+b*sec(c+d*x))^-2*tan(c+d*x), x) == :(a^-1*d^-1*(a+b*sec(c+d*x))^-1+-1*a^-2*d^-1*log(a+b*sec(c+d*x))+-1*a^-2*d^-1*log(cos(c+d*x)))
@test integrate((a+b*sec(c+d*x))^-2*cot(c+d*x), x) == :(a^-2*d^-1*log(cos(c+d*x))+(1/2)*d^-1*(a+b)^-2*log(1+-1*sec(c+d*x))+(1/2)*d^-1*(a+-1b)^-2*log(1+sec(c+d*x))+a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1+-1*a^-2*b^2*d^-1*(a^2+-1*b^2)^-2*(-1*b^2+3*a^2)*log(a+b*sec(c+d*x)))
@test integrate((a+b*sec(c+d*x))^-2*cot(c+d*x)^3, x) == :(-1*a^-2*d^-1*log(cos(c+d*x))+1//4*d^-1*(1+-1*sec(c+d*x))^-1*(a+b)^-2+1//4*d^-1*(1+sec(c+d*x))^-1*(a+-1b)^-2+-1//2*d^-1*(a+b)^-3*(a+2b)*log(1+-1*sec(c+d*x))+-1//2*d^-1*(a+-1b)^-3*(a+-2b)*log(1+sec(c+d*x))+a^-1*b^4*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2+-1*a^-2*b^4*d^-1*(a^2+-1*b^2)^-3*(-1*b^2+5*a^2)*log(a+b*sec(c+d*x)))
@test integrate((a+b*sec(c+d*x))^-2*cot(c+d*x)^5, x) == :(a^-2*d^-1*log(cos(c+d*x))+-1//16*d^-1*(1+-1*sec(c+d*x))^-2*(a+b)^-2+-1//16*d^-1*(1+sec(c+d*x))^-2*(a+-1b)^-2+-1//16*d^-1*(1+-1*sec(c+d*x))^-1*(a+b)^-3*(5a+9b)+-1//16*d^-1*(1+sec(c+d*x))^-1*(a+-1b)^-3*(-9b+5a)+1//8*d^-1*(a+b)^-4*(4*a^2+12*b^2+13*a*b)*log(1+-1*sec(c+d*x))+1//8*d^-1*(a+-1b)^-4*(4*a^2+12*b^2+-13*a*b)*log(1+sec(c+d*x))+a^-1*b^6*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3+-1*a^-2*b^6*d^-1*(a^2+-1*b^2)^-4*(-1*b^2+7*a^2)*log(a+b*sec(c+d*x)))
@test integrate((a+b*sec(c+d*x))^-2*tan(c+d*x)^4, x) == :(x*a^-2+b^-1*d^-1*(b+a*cos(c+d*x))^-1*tan(c+d*x)+-2*a*b^-3*d^-1*arctanh(sin(c+d*x))+a^-1*b^-2*d^-1*(b+a*cos(c+d*x))^-1*(-1*b^2+2*a^2)*sin(c+d*x)+2*a^-2*b^-3*d^-1*(a+b)^(1/2)*(a+-1b)^(1/2)*(b^2+2*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-2*tan(c+d*x)^2, x) == :(-1*x*a^-2+a^-1*d^-1*(a+b*sec(c+d*x))^-1*tan(c+d*x)+2*b*a^-2*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-2*cot(c+d*x)^2, x) == :(-1*x*a^-2+(1/2)*d^-1*(1+cos(c+d*x))^-1*(a+-1b)^-2*sin(c+d*x)+-1//2*d^-1*(1+-1*cos(c+d*x))^-1*(a+b)^-2*sin(c+d*x)+a^-1*b^4*d^-1*(b+a*cos(c+d*x))^-1*(a^2+-1*b^2)^-2*sin(c+d*x)+-2*a^-2*b^5*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-4*a^-2*b^3*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(-1*b^2+2*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-2*cot(c+d*x)^4, x) == :(x*a^-2+-1//12*d^-1*(1+-1*cos(c+d*x))^-1*(a+b)^-2*sin(c+d*x)+-1//12*d^-1*(1+-1*cos(c+d*x))^-2*(a+b)^-2*sin(c+d*x)+1//12*d^-1*(1+cos(c+d*x))^-1*(a+-1b)^-2*sin(c+d*x)+1//12*d^-1*(1+cos(c+d*x))^-2*(a+-1b)^-2*sin(c+d*x)+-1//4*d^-1*(1+cos(c+d*x))^-1*(a+-1b)^-3*(-5b+3a)*sin(c+d*x)+1//4*d^-1*(1+-1*cos(c+d*x))^-1*(a+b)^-3*(3a+5b)*sin(c+d*x)+a^-1*b^6*d^-1*(b+a*cos(c+d*x))^-1*(a^2+-1*b^2)^-3*sin(c+d*x)+-2*a^-2*b^7*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-4*a^-2*b^5*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(-1*b^2+3*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^(1/2)*tan(c+d*x)^5, x) == :(2*d^-1*(a+b*sec(c+d*x))^(1/2)+-2*a^(1/2)*d^-1*arctanh(a^-1//2*(a+b*sec(c+d*x))^(1/2))+2//9*b^-4*d^-1*(a+b*sec(c+d*x))^9//2+-6//7*a*b^-4*d^-1*(a+b*sec(c+d*x))^7//2+1//5*b^-4*d^-1*(a+b*sec(c+d*x))^5//2*(-4*b^2+6*a^2)+-2//3*a*b^-4*d^-1*(a+b*sec(c+d*x))^3//2*(a^2+-2*b^2))
@test integrate((a+b*sec(c+d*x))^(1/2)*tan(c+d*x)^3, x) == :(-2*d^-1*(a+b*sec(c+d*x))^(1/2)+2*a^(1/2)*d^-1*arctanh(a^-1//2*(a+b*sec(c+d*x))^(1/2))+2//5*b^-2*d^-1*(a+b*sec(c+d*x))^5//2+-2//3*a*b^-2*d^-1*(a+b*sec(c+d*x))^3//2)
@test integrate((a+b*sec(c+d*x))^(1/2)*tan(c+d*x), x) == :(2*d^-1*(a+b*sec(c+d*x))^(1/2)+-2*a^(1/2)*d^-1*arctanh(a^-1//2*(a+b*sec(c+d*x))^(1/2)))
@test integrate((a+b*sec(c+d*x))^(1/2)*cot(c+d*x), x) == :(-1*d^-1*(a+b)^(1/2)*arctanh((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2))+-1*d^-1*(a+-1b)^(1/2)*arctanh((a+-1b)^-1//2*(a+b*sec(c+d*x))^(1/2))+2*a^(1/2)*d^-1*arctanh(a^-1//2*(a+b*sec(c+d*x))^(1/2)))
@test integrate((a+b*sec(c+d*x))^(1/2)*cot(c+d*x)^3, x) == :(-2*a^(1/2)*d^-1*arctanh(a^-1//2*(a+b*sec(c+d*x))^(1/2))+-1//2*d^-1*(a+b*sec(c+d*x))^(1/2)*cot(c+d*x)^2+a*d^-1*(a+b)^-1//2*arctanh((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2))+a*d^-1*(a+-1b)^-1//2*arctanh((a+-1b)^-1//2*(a+b*sec(c+d*x))^(1/2))+-3//4*b*d^-1*(a+-1b)^-1//2*arctanh((a+-1b)^-1//2*(a+b*sec(c+d*x))^(1/2))+3//4*b*d^-1*(a+b)^-1//2*arctanh((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)))
@test integrate((a+b*sec(c+d*x))^-1//2*tan(c+d*x)^5, x) == :(-2*a^-1//2*d^-1*arctanh(a^-1//2*(a+b*sec(c+d*x))^(1/2))+2//7*b^-4*d^-1*(a+b*sec(c+d*x))^7//2+-6//5*a*b^-4*d^-1*(a+b*sec(c+d*x))^5//2+1//3*b^-4*d^-1*(a+b*sec(c+d*x))^3//2*(-4*b^2+6*a^2)+-2*a*b^-4*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-2*b^2))
@test integrate((a+b*sec(c+d*x))^-1//2*tan(c+d*x)^3, x) == :(2*a^-1//2*d^-1*arctanh(a^-1//2*(a+b*sec(c+d*x))^(1/2))+2//3*b^-2*d^-1*(a+b*sec(c+d*x))^3//2+-2*a*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2))
@test integrate((a+b*sec(c+d*x))^-1//2*tan(c+d*x), x) == :(-2*a^-1//2*d^-1*arctanh(a^-1//2*(a+b*sec(c+d*x))^(1/2)))
@test integrate((a+b*sec(c+d*x))^-1//2*cot(c+d*x), x) == :(-1*d^-1*(a+b)^-1//2*arctanh((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2))+-1*d^-1*(a+-1b)^-1//2*arctanh((a+-1b)^-1//2*(a+b*sec(c+d*x))^(1/2))+2*a^-1//2*d^-1*arctanh(a^-1//2*(a+b*sec(c+d*x))^(1/2)))
@test integrate((a+b*sec(c+d*x))^-1//2*cot(c+d*x)^3, x) == :(d^-1*(a+b)^-1//2*arctanh((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2))+d^-1*(a+-1b)^-1//2*arctanh((a+-1b)^-1//2*(a+b*sec(c+d*x))^(1/2))+-2*a^-1//2*d^-1*arctanh(a^-1//2*(a+b*sec(c+d*x))^(1/2))+d^-1*(1+-1*sec(c+d*x))^-1*(a+b*sec(c+d*x))^(1/2)*(4a+4b)^-1+d^-1*(1+sec(c+d*x))^-1*(a+b*sec(c+d*x))^(1/2)*(-4b+4a)^-1+-1//4*b*d^-1*(a+-1b)^-3//2*arctanh((a+-1b)^-1//2*(a+b*sec(c+d*x))^(1/2))+1//4*b*d^-1*(a+b)^-3//2*arctanh((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)))
@test integrate((a+b*sec(c+d*x))^-3//2*tan(c+d*x)^5, x) == :(-2*a^-3//2*d^-1*arctanh(a^-1//2*(a+b*sec(c+d*x))^(1/2))+2//5*b^-4*d^-1*(a+b*sec(c+d*x))^5//2+b^-4*d^-1*(a+b*sec(c+d*x))^(1/2)*(-4*b^2+6*a^2)+-2*a*b^-4*d^-1*(a+b*sec(c+d*x))^3//2+2*a^-1*b^-4*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^2)
@test integrate((a+b*sec(c+d*x))^-3//2*tan(c+d*x)^3, x) == :(2*a^-3//2*d^-1*arctanh(a^-1//2*(a+b*sec(c+d*x))^(1/2))+2*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)+a^-1*b^-2*d^-1*(a+b*sec(c+d*x))^-1//2*(-2*b^2+2*a^2))
@test integrate((a+b*sec(c+d*x))^-3//2*tan(c+d*x), x) == :(-2*a^-3//2*d^-1*arctanh(a^-1//2*(a+b*sec(c+d*x))^(1/2))+2*a^-1*d^-1*(a+b*sec(c+d*x))^-1//2)
@test integrate((a+b*sec(c+d*x))^-3//2*cot(c+d*x), x) == :(-1*d^-1*(a+b)^-3//2*arctanh((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2))+-1*d^-1*(a+-1b)^-3//2*arctanh((a+-1b)^-1//2*(a+b*sec(c+d*x))^(1/2))+2*a^-3//2*d^-1*arctanh(a^-1//2*(a+b*sec(c+d*x))^(1/2))+2*a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1)

max_stars_repo_path: test/4 Trig functions/4.5 Secant/4.5.1.4 (d tan)^n (a+b sec)^m.jl