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

@test integrate(sec(c+d*x)^4*(a+a*sec(c+d*x)), x) == :(a*d^-1*tan(c+d*x)+1//3*a*d^-1*tan(c+d*x)^3+3//8*a*d^-1*arctanh(sin(c+d*x))+1//4*a*d^-1*sec(c+d*x)^3*tan(c+d*x)+3//8*a*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate(sec(c+d*x)^3*(a+a*sec(c+d*x)), x) == :(a*d^-1*tan(c+d*x)+(1/2)*a*d^-1*arctanh(sin(c+d*x))+1//3*a*d^-1*tan(c+d*x)^3+(1/2)*a*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate(sec(c+d*x)^2*(a+a*sec(c+d*x)), x) == :(a*d^-1*tan(c+d*x)+(1/2)*a*d^-1*arctanh(sin(c+d*x))+(1/2)*a*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))*sec(c+d*x), x) == :(a*d^-1*arctanh(sin(c+d*x))+a*d^-1*tan(c+d*x))
@test integrate(a+a*sec(c+d*x), x) == :(a*x+a*d^-1*arctanh(sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))*cos(c+d*x), x) == :(a*x+a*d^-1*sin(c+d*x))
@test integrate(cos(c+d*x)^2*(a+a*sec(c+d*x)), x) == :((1/2)*a*x+a*d^-1*sin(c+d*x)+(1/2)*a*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^3*(a+a*sec(c+d*x)), x) == :((1/2)*a*x+a*d^-1*sin(c+d*x)+-1//3*a*d^-1*sin(c+d*x)^3+(1/2)*a*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^4*(a+a*sec(c+d*x)), x) == :(3//8*a*x+a*d^-1*sin(c+d*x)+-1//3*a*d^-1*sin(c+d*x)^3+1//4*a*d^-1*cos(c+d*x)^3*sin(c+d*x)+3//8*a*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^4, x) == :(3//4*a^2*d^-1*arctanh(sin(c+d*x))+3//5*a^2*d^-1*tan(c+d*x)^3+9//5*a^2*d^-1*tan(c+d*x)+(1/2)*a^2*d^-1*sec(c+d*x)^3*tan(c+d*x)+1//5*a^2*d^-1*sec(c+d*x)^4*tan(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*sec(c+d*x)^3, x) == :(2*a^2*d^-1*tan(c+d*x)+2//3*a^2*d^-1*tan(c+d*x)^3+7//8*a^2*d^-1*arctanh(sin(c+d*x))+1//4*a^2*d^-1*sec(c+d*x)^3*tan(c+d*x)+7//8*a^2*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^2, x) == :(a^2*d^-1*arctanh(sin(c+d*x))+5//3*a^2*d^-1*tan(c+d*x)+a^2*d^-1*sec(c+d*x)*tan(c+d*x)+1//3*a^2*d^-1*sec(c+d*x)^2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x), x) == :(2*a^2*d^-1*tan(c+d*x)+3//2*a^2*d^-1*arctanh(sin(c+d*x))+(1/2)*a^2*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^2, 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*cos(c+d*x), x) == :(2*x*a^2+a^2*d^-1*arctanh(sin(c+d*x))+a^2*d^-1*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^2, x) == :(3//2*x*a^2+2*a^2*d^-1*sin(c+d*x)+(1/2)*a^2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^3, x) == :(x*a^2+2*a^2*d^-1*sin(c+d*x)+-1//3*a^2*d^-1*sin(c+d*x)^3+a^2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^4, x) == :(7//8*x*a^2+2*a^2*d^-1*sin(c+d*x)+-2//3*a^2*d^-1*sin(c+d*x)^3+1//4*a^2*d^-1*cos(c+d*x)^3*sin(c+d*x)+7//8*a^2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^5, x) == :(3//4*x*a^2+-1*a^2*d^-1*sin(c+d*x)^3+2*a^2*d^-1*sin(c+d*x)+1//5*a^2*d^-1*sin(c+d*x)^5+(1/2)*a^2*d^-1*cos(c+d*x)^3*sin(c+d*x)+3//4*a^2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^3, x) == :(4*a^3*d^-1*tan(c+d*x)+1//5*a^3*d^-1*tan(c+d*x)^5+5//3*a^3*d^-1*tan(c+d*x)^3+13//8*a^3*d^-1*arctanh(sin(c+d*x))+3//4*a^3*d^-1*sec(c+d*x)^3*tan(c+d*x)+13//8*a^3*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^2, x) == :(a^3*d^-1*tan(c+d*x)^3+4*a^3*d^-1*tan(c+d*x)+15//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)+15//8*a^3*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x), x) == :(4*a^3*d^-1*tan(c+d*x)+1//3*a^3*d^-1*tan(c+d*x)^3+5//2*a^3*d^-1*arctanh(sin(c+d*x))+3//2*a^3*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3, x) == :(x*a^3+(1/2)*d^-1*(a^3+a^3*sec(c+d*x))*tan(c+d*x)+5//2*a^3*d^-1*tan(c+d*x)+7//2*a^3*d^-1*arctanh(sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x), x) == :(3*x*a^3+a^3*d^-1*sin(c+d*x)+a^3*d^-1*tan(c+d*x)+3*a^3*d^-1*arctanh(sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^2, x) == :(7//2*x*a^3+a^3*d^-1*arctanh(sin(c+d*x))+3*a^3*d^-1*sin(c+d*x)+(1/2)*a^3*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^3, x) == :(5//2*x*a^3+4*a^3*d^-1*sin(c+d*x)+-1//3*a^3*d^-1*sin(c+d*x)^3+3//2*a^3*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^4, x) == :(15//8*x*a^3+-1*a^3*d^-1*sin(c+d*x)^3+4*a^3*d^-1*sin(c+d*x)+1//4*a^3*d^-1*cos(c+d*x)^3*sin(c+d*x)+15//8*a^3*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^5, x) == :(13//8*x*a^3+4*a^3*d^-1*sin(c+d*x)+-5//3*a^3*d^-1*sin(c+d*x)^3+1//5*a^3*d^-1*sin(c+d*x)^5+3//4*a^3*d^-1*cos(c+d*x)^3*sin(c+d*x)+13//8*a^3*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^6, x) == :(23//16*x*a^3+4*a^3*d^-1*sin(c+d*x)+-7//3*a^3*d^-1*sin(c+d*x)^3+3//5*a^3*d^-1*sin(c+d*x)^5+1//6*a^3*d^-1*cos(c+d*x)^5*sin(c+d*x)+23//16*a^3*d^-1*cos(c+d*x)*sin(c+d*x)+23//24*a^3*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*sec(c+d*x)^3, x) == :(4*a^4*d^-1*tan(c+d*x)^3+8*a^4*d^-1*tan(c+d*x)+4//5*a^4*d^-1*tan(c+d*x)^5+49//16*a^4*d^-1*arctanh(sin(c+d*x))+1//6*a^4*d^-1*sec(c+d*x)^5*tan(c+d*x)+41//24*a^4*d^-1*sec(c+d*x)^3*tan(c+d*x)+49//16*a^4*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*sec(c+d*x)^2, x) == :(8*a^4*d^-1*tan(c+d*x)+1//5*a^4*d^-1*tan(c+d*x)^5+7//2*a^4*d^-1*arctanh(sin(c+d*x))+8//3*a^4*d^-1*tan(c+d*x)^3+a^4*d^-1*sec(c+d*x)^3*tan(c+d*x)+7//2*a^4*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*sec(c+d*x), x) == :(8*a^4*d^-1*tan(c+d*x)+4//3*a^4*d^-1*tan(c+d*x)^3+35//8*a^4*d^-1*arctanh(sin(c+d*x))+1//4*a^4*d^-1*sec(c+d*x)^3*tan(c+d*x)+27//8*a^4*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^4, x) == :(x*a^4+5*a^4*d^-1*tan(c+d*x)+6*a^4*d^-1*arctanh(sin(c+d*x))+1//3*d^-1*(a^2+a^2*sec(c+d*x))^2*tan(c+d*x)+1//3*d^-1*(4*a^4+4*a^4*sec(c+d*x))*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x), x) == :(4*x*a^4+a^4*d^-1*sin(c+d*x)+4*a^4*d^-1*tan(c+d*x)+13//2*a^4*d^-1*arctanh(sin(c+d*x))+(1/2)*a^4*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^2, x) == :(13//2*x*a^4+a^4*d^-1*tan(c+d*x)+4*a^4*d^-1*arctanh(sin(c+d*x))+4*a^4*d^-1*sin(c+d*x)+(1/2)*a^4*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^3, x) == :(6*x*a^4+a^4*d^-1*arctanh(sin(c+d*x))+7*a^4*d^-1*sin(c+d*x)+-1//3*a^4*d^-1*sin(c+d*x)^3+2*a^4*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^4, x) == :(35//8*x*a^4+8*a^4*d^-1*sin(c+d*x)+-4//3*a^4*d^-1*sin(c+d*x)^3+1//4*a^4*d^-1*cos(c+d*x)^3*sin(c+d*x)+27//8*a^4*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^5, x) == :(7//2*x*a^4+8*a^4*d^-1*sin(c+d*x)+-8//3*a^4*d^-1*sin(c+d*x)^3+1//5*a^4*d^-1*sin(c+d*x)^5+a^4*d^-1*cos(c+d*x)^3*sin(c+d*x)+7//2*a^4*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^6, x) == :(49//16*x*a^4+-4*a^4*d^-1*sin(c+d*x)^3+8*a^4*d^-1*sin(c+d*x)+4//5*a^4*d^-1*sin(c+d*x)^5+1//6*a^4*d^-1*cos(c+d*x)^5*sin(c+d*x)+41//24*a^4*d^-1*cos(c+d*x)^3*sin(c+d*x)+49//16*a^4*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^7, x) == :(11//4*x*a^4+8*a^4*d^-1*sin(c+d*x)+-16//3*a^4*d^-1*sin(c+d*x)^3+-1//7*a^4*d^-1*sin(c+d*x)^7+9//5*a^4*d^-1*sin(c+d*x)^5+2//3*a^4*d^-1*cos(c+d*x)^5*sin(c+d*x)+11//4*a^4*d^-1*cos(c+d*x)*sin(c+d*x)+11//6*a^4*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5*sec(c+d*x)^3, x) == :(16*a^5*d^-1*tan(c+d*x)+1//7*a^5*d^-1*tan(c+d*x)^7+13//5*a^5*d^-1*tan(c+d*x)^5+28//3*a^5*d^-1*tan(c+d*x)^3+93//16*a^5*d^-1*arctanh(sin(c+d*x))+5//6*a^5*d^-1*sec(c+d*x)^5*tan(c+d*x)+85//24*a^5*d^-1*sec(c+d*x)^3*tan(c+d*x)+93//16*a^5*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^5, x) == :(4*a^-1*d^-1*tan(c+d*x)+-3//2*a^-1*d^-1*arctanh(sin(c+d*x))+4//3*a^-1*d^-1*tan(c+d*x)^3+-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^3*tan(c+d*x)+-3//2*a^-1*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^4, x) == :(-2*a^-1*d^-1*tan(c+d*x)+3//2*a^-1*d^-1*arctanh(sin(c+d*x))+-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^2*tan(c+d*x)+3//2*a^-1*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^3, x) == :(a^-1*d^-1*tan(c+d*x)+d^-1*(a+a*sec(c+d*x))^-1*tan(c+d*x)+-1*a^-1*d^-1*arctanh(sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^2, x) == :(a^-1*d^-1*arctanh(sin(c+d*x))+-1*d^-1*(a+a*sec(c+d*x))^-1*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x), x) == :(d^-1*(a+a*sec(c+d*x))^-1*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1, x) == :(x*a^-1+-1*d^-1*(a+a*sec(c+d*x))^-1*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x), x) == :(-1*x*a^-1+-1*d^-1*(a+a*sec(c+d*x))^-1*sin(c+d*x)+2*a^-1*d^-1*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^2, x) == :(3//2*x*a^-1+-2*a^-1*d^-1*sin(c+d*x)+-1*d^-1*(a+a*sec(c+d*x))^-1*cos(c+d*x)*sin(c+d*x)+3//2*a^-1*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^3, x) == :(-3//2*x*a^-1+4*a^-1*d^-1*sin(c+d*x)+-4//3*a^-1*d^-1*sin(c+d*x)^3+-1*d^-1*(a+a*sec(c+d*x))^-1*cos(c+d*x)^2*sin(c+d*x)+-3//2*a^-1*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^4, x) == :(15//8*x*a^-1+-4*a^-1*d^-1*sin(c+d*x)+4//3*a^-1*d^-1*sin(c+d*x)^3+-1*d^-1*(a+a*sec(c+d*x))^-1*cos(c+d*x)^3*sin(c+d*x)+5//4*a^-1*d^-1*cos(c+d*x)^3*sin(c+d*x)+15//8*a^-1*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^5, x) == :(-16//3*a^-2*d^-1*tan(c+d*x)+7//2*a^-2*d^-1*arctanh(sin(c+d*x))+-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^3*tan(c+d*x)+7//2*a^-2*d^-1*sec(c+d*x)*tan(c+d*x)+-8//3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^4, x) == :(-2*a^-2*d^-1*arctanh(sin(c+d*x))+4//3*a^-2*d^-1*tan(c+d*x)+2*a^-2*d^-1*(1+sec(c+d*x))^-1*tan(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^3, x) == :(a^-2*d^-1*arctanh(sin(c+d*x))+1//3*d^-1*(a+a*sec(c+d*x))^-2*tan(c+d*x)+-5//3*a^-2*d^-1*(1+sec(c+d*x))^-1*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^2, x) == :(-1//3*d^-1*(a+a*sec(c+d*x))^-2*tan(c+d*x)+2//3*d^-1*(a^2+a^2*sec(c+d*x))^-1*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x), x) == :(1//3*d^-1*(a+a*sec(c+d*x))^-2*tan(c+d*x)+1//3*d^-1*(a^2+a^2*sec(c+d*x))^-1*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2, x) == :(x*a^-2+-1//3*d^-1*(a+a*sec(c+d*x))^-2*tan(c+d*x)+-4//3*a^-2*d^-1*(1+sec(c+d*x))^-1*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x), x) == :(-2*x*a^-2+-1//3*d^-1*(a+a*sec(c+d*x))^-2*sin(c+d*x)+10//3*a^-2*d^-1*sin(c+d*x)+-2*a^-2*d^-1*(1+sec(c+d*x))^-1*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^2, x) == :(7//2*x*a^-2+-16//3*a^-2*d^-1*sin(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)*sin(c+d*x)+7//2*a^-2*d^-1*cos(c+d*x)*sin(c+d*x)+-8//3*a^-2*d^-1*(1+sec(c+d*x))^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^3, x) == :(-5*x*a^-2+-4*a^-2*d^-1*sin(c+d*x)^3+12*a^-2*d^-1*sin(c+d*x)+-5*a^-2*d^-1*cos(c+d*x)*sin(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)^2*sin(c+d*x)+-10//3*a^-2*d^-1*(1+sec(c+d*x))^-1*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^6, x) == :(-152//15*a^-3*d^-1*tan(c+d*x)+13//2*a^-3*d^-1*arctanh(sin(c+d*x))+-76//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^2*tan(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^4*tan(c+d*x)+13//2*a^-3*d^-1*sec(c+d*x)*tan(c+d*x)+-11//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^5, x) == :(-3*a^-3*d^-1*arctanh(sin(c+d*x))+3*d^-1*(a^3+a^3*sec(c+d*x))^-1*tan(c+d*x)+9//5*a^-3*d^-1*tan(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^3*tan(c+d*x)+-3//5*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^4, x) == :(a^-3*d^-1*arctanh(sin(c+d*x))+-29//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*tan(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^2*tan(c+d*x)+7//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^3, x) == :(1//5*d^-1*(a+a*sec(c+d*x))^-3*tan(c+d*x)+7//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*tan(c+d*x)+-8//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^2, x) == :(-1//5*d^-1*(a+a*sec(c+d*x))^-3*tan(c+d*x)+1//5*d^-1*(a^3+a^3*sec(c+d*x))^-1*tan(c+d*x)+1//5*a^-1*d^-1*(a+a*sec(c+d*x))^-2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x), x) == :(1//5*d^-1*(a+a*sec(c+d*x))^-3*tan(c+d*x)+2//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*tan(c+d*x)+2//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3, x) == :(x*a^-3+-22//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*tan(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*tan(c+d*x)+-7//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x), x) == :(-3*x*a^-3+-3*d^-1*(a^3+a^3*sec(c+d*x))^-1*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*sin(c+d*x)+24//5*a^-3*d^-1*sin(c+d*x)+-3//5*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^2, x) == :(13//2*x*a^-3+-152//15*a^-3*d^-1*sin(c+d*x)+-76//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*cos(c+d*x)*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*cos(c+d*x)*sin(c+d*x)+13//2*a^-3*d^-1*cos(c+d*x)*sin(c+d*x)+-11//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*sec(c+d*x)^7, x) == :(-576//35*a^-4*d^-1*tan(c+d*x)+21//2*a^-4*d^-1*arctanh(sin(c+d*x))+-1//7*d^-1*(a+a*sec(c+d*x))^-4*sec(c+d*x)^5*tan(c+d*x)+21//2*a^-4*d^-1*sec(c+d*x)*tan(c+d*x)+-288//35*a^-4*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^2*tan(c+d*x)+-43//35*a^-4*d^-1*(1+sec(c+d*x))^-2*sec(c+d*x)^3*tan(c+d*x)+-2//5*a^-1*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^4*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*sec(c+d*x)^6, x) == :(-4*a^-4*d^-1*arctanh(sin(c+d*x))+244//105*a^-4*d^-1*tan(c+d*x)+4*a^-4*d^-1*(1+sec(c+d*x))^-1*tan(c+d*x)+-1//7*d^-1*(a+a*sec(c+d*x))^-4*sec(c+d*x)^4*tan(c+d*x)+-88//105*a^-4*d^-1*(1+sec(c+d*x))^-2*sec(c+d*x)^2*tan(c+d*x)+-12//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*sec(c+d*x)^5, x) == :(a^-4*d^-1*arctanh(sin(c+d*x))+-43//21*a^-4*d^-1*(1+sec(c+d*x))^-1*tan(c+d*x)+-1//7*d^-1*(a+a*sec(c+d*x))^-4*sec(c+d*x)^3*tan(c+d*x)+11//21*a^-4*d^-1*(1+sec(c+d*x))^-2*tan(c+d*x)+-2//7*a^-1*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*sec(c+d*x)^4, x) == :(-8//35*d^-1*(a^2+a^2*sec(c+d*x))^-2*tan(c+d*x)+1//5*d^-1*(a^4+a^4*sec(c+d*x))^-1*tan(c+d*x)+1//7*d^-1*(a+a*sec(c+d*x))^-4*sec(c+d*x)^3*tan(c+d*x)+3//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*sec(c+d*x)^3, x) == :(1//7*d^-1*(a+a*sec(c+d*x))^-4*tan(c+d*x)+13//105*d^-1*(a^2+a^2*sec(c+d*x))^-2*tan(c+d*x)+13//105*d^-1*(a^4+a^4*sec(c+d*x))^-1*tan(c+d*x)+-11//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*sec(c+d*x)^2, x) == :(-1//7*d^-1*(a+a*sec(c+d*x))^-4*tan(c+d*x)+8//105*d^-1*(a^2+a^2*sec(c+d*x))^-2*tan(c+d*x)+8//105*d^-1*(a^4+a^4*sec(c+d*x))^-1*tan(c+d*x)+4//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*sec(c+d*x), x) == :(1//7*d^-1*(a+a*sec(c+d*x))^-4*tan(c+d*x)+2//35*d^-1*(a^2+a^2*sec(c+d*x))^-2*tan(c+d*x)+2//35*d^-1*(a^4+a^4*sec(c+d*x))^-1*tan(c+d*x)+3//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4, x) == :(x*a^-4+-1//7*d^-1*(a+a*sec(c+d*x))^-4*tan(c+d*x)+-32//21*a^-4*d^-1*(1+sec(c+d*x))^-1*tan(c+d*x)+-11//21*a^-4*d^-1*(1+sec(c+d*x))^-2*tan(c+d*x)+-2//7*a^-1*d^-1*(a+a*sec(c+d*x))^-3*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*cos(c+d*x), x) == :(-4*x*a^-4+-1//7*d^-1*(a+a*sec(c+d*x))^-4*sin(c+d*x)+664//105*a^-4*d^-1*sin(c+d*x)+-4*a^-4*d^-1*(1+sec(c+d*x))^-1*sin(c+d*x)+-88//105*a^-4*d^-1*(1+sec(c+d*x))^-2*sin(c+d*x)+-12//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*cos(c+d*x)^2, x) == :(21//2*x*a^-4+-576//35*a^-4*d^-1*sin(c+d*x)+-1//7*d^-1*(a+a*sec(c+d*x))^-4*cos(c+d*x)*sin(c+d*x)+21//2*a^-4*d^-1*cos(c+d*x)*sin(c+d*x)+-288//35*a^-4*d^-1*(1+sec(c+d*x))^-1*cos(c+d*x)*sin(c+d*x)+-43//35*a^-4*d^-1*(1+sec(c+d*x))^-2*cos(c+d*x)*sin(c+d*x)+-2//5*a^-1*d^-1*(a+a*sec(c+d*x))^-3*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5*sec(c+d*x)^7, x) == :(-5*a^-5*d^-1*arctanh(sin(c+d*x))+5*d^-1*(a^5+a^5*sec(c+d*x))^-1*tan(c+d*x)+181//63*a^-5*d^-1*tan(c+d*x)+-1//9*d^-1*(a+a*sec(c+d*x))^-5*sec(c+d*x)^5*tan(c+d*x)+-67//63*a^-3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^2*tan(c+d*x)+-29//63*a^-2*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^3*tan(c+d*x)+-5//21*a^-1*d^-1*(a+a*sec(c+d*x))^-4*sec(c+d*x)^4*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5*sec(c+d*x)^6, x) == :(a^-5*d^-1*arctanh(sin(c+d*x))+-661//315*d^-1*(a^5+a^5*sec(c+d*x))^-1*tan(c+d*x)+-1//9*d^-1*(a+a*sec(c+d*x))^-5*sec(c+d*x)^4*tan(c+d*x)+173//315*a^-3*d^-1*(a+a*sec(c+d*x))^-2*tan(c+d*x)+-34//105*a^-2*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^2*tan(c+d*x)+-13//63*a^-1*d^-1*(a+a*sec(c+d*x))^-4*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5*sec(c+d*x)^5, x) == :(4//45*d^-1*(a^5+a^5*sec(c+d*x))^-1*tan(c+d*x)+-32//315*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^-2*tan(c+d*x)+1//9*d^-1*(a+a*sec(c+d*x))^-5*sec(c+d*x)^4*tan(c+d*x)+4//105*a^-2*d^-1*(a+a*sec(c+d*x))^-3*tan(c+d*x)+4//63*a^-1*d^-1*(a+a*sec(c+d*x))^-4*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5*sec(c+d*x)^4, x) == :(1//9*d^-1*(a^5+a^5*sec(c+d*x))^-1*tan(c+d*x)+-8//63*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^-2*tan(c+d*x)+-1//9*d^-1*(a+a*sec(c+d*x))^-5*sec(c+d*x)^4*tan(c+d*x)+1//21*a^-2*d^-1*(a+a*sec(c+d*x))^-3*tan(c+d*x)+5//63*a^-1*d^-1*(a+a*sec(c+d*x))^-4*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5*sec(c+d*x)^3, x) == :(1//9*d^-1*(a+a*sec(c+d*x))^-5*tan(c+d*x)+2//45*d^-1*(a^5+a^5*sec(c+d*x))^-1*tan(c+d*x)+-2//9*a^-1*d^-1*(a+a*sec(c+d*x))^-4*tan(c+d*x)+1//15*a^-2*d^-1*(a+a*sec(c+d*x))^-3*tan(c+d*x)+2//45*a^-3*d^-1*(a+a*sec(c+d*x))^-2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5*sec(c+d*x)^2, x) == :(-1//9*d^-1*(a+a*sec(c+d*x))^-5*tan(c+d*x)+2//63*d^-1*(a^5+a^5*sec(c+d*x))^-1*tan(c+d*x)+1//21*a^-2*d^-1*(a+a*sec(c+d*x))^-3*tan(c+d*x)+2//63*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^-2*tan(c+d*x)+5//63*a^-1*d^-1*(a+a*sec(c+d*x))^-4*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5*sec(c+d*x), x) == :(1//9*d^-1*(a+a*sec(c+d*x))^-5*tan(c+d*x)+8//315*d^-1*(a^5+a^5*sec(c+d*x))^-1*tan(c+d*x)+4//63*a^-1*d^-1*(a+a*sec(c+d*x))^-4*tan(c+d*x)+4//105*a^-2*d^-1*(a+a*sec(c+d*x))^-3*tan(c+d*x)+8//315*a^-1*d^-1*(a^2+a^2*sec(c+d*x))^-2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5, x) == :(x*a^-5+-488//315*d^-1*(a^5+a^5*sec(c+d*x))^-1*tan(c+d*x)+-1//9*d^-1*(a+a*sec(c+d*x))^-5*tan(c+d*x)+-173//315*a^-3*d^-1*(a+a*sec(c+d*x))^-2*tan(c+d*x)+-34//105*a^-2*d^-1*(a+a*sec(c+d*x))^-3*tan(c+d*x)+-13//63*a^-1*d^-1*(a+a*sec(c+d*x))^-4*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5*cos(c+d*x), x) == :(-5*x*a^-5+-5*d^-1*(a^5+a^5*sec(c+d*x))^-1*sin(c+d*x)+-1//9*d^-1*(a+a*sec(c+d*x))^-5*sin(c+d*x)+496//63*a^-5*d^-1*sin(c+d*x)+-67//63*a^-3*d^-1*(a+a*sec(c+d*x))^-2*sin(c+d*x)+-29//63*a^-2*d^-1*(a+a*sec(c+d*x))^-3*sin(c+d*x)+-5//21*a^-1*d^-1*(a+a*sec(c+d*x))^-4*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5*cos(c+d*x)^2, x) == :(31//2*x*a^-5+-7664//315*a^-5*d^-1*sin(c+d*x)+-3832//315*d^-1*(a^5+a^5*sec(c+d*x))^-1*cos(c+d*x)*sin(c+d*x)+-1//9*d^-1*(a+a*sec(c+d*x))^-5*cos(c+d*x)*sin(c+d*x)+31//2*a^-5*d^-1*cos(c+d*x)*sin(c+d*x)+-577//315*a^-3*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)*sin(c+d*x)+-28//45*a^-2*d^-1*(a+a*sec(c+d*x))^-3*cos(c+d*x)*sin(c+d*x)+-17//63*a^-1*d^-1*(a+a*sec(c+d*x))^-4*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^4, x) == :(-8//35*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x)+4//5*a*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+12//35*a^-1*d^-1*(a+a*sec(c+d*x))^3//2*tan(c+d*x)+2//7*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3, x) == :(-4//15*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x)+2//5*a^-1*d^-1*(a+a*sec(c+d*x))^3//2*tan(c+d*x)+14//15*a*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^2, x) == :(2//3*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x)+2//3*a*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x), x) == :(2*a*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2), x) == :(2*a^(1/2)*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x), x) == :(a^(1/2)*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+a*d^-1*(a+a*sec(c+d*x))^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^2, x) == :(3//4*a^(1/2)*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+3//4*a*d^-1*(a+a*sec(c+d*x))^-1//2*sin(c+d*x)+(1/2)*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^3, x) == :(5//8*a^(1/2)*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+5//8*a*d^-1*(a+a*sec(c+d*x))^-1//2*sin(c+d*x)+1//3*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*sin(c+d*x)+5//12*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^4, x) == :(35//64*a^(1/2)*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+35//64*a*d^-1*(a+a*sec(c+d*x))^-1//2*sin(c+d*x)+1//4*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3*sin(c+d*x)+7//24*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*sin(c+d*x)+35//96*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^4, x) == :(68//105*d^-1*(a+a*sec(c+d*x))^3//2*tan(c+d*x)+-136//315*a*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x)+68//45*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+2//9*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^4*tan(c+d*x)+34//63*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^3, x) == :(-4//35*d^-1*(a+a*sec(c+d*x))^3//2*tan(c+d*x)+2//7*a^-1*d^-1*(a+a*sec(c+d*x))^5//2*tan(c+d*x)+38//105*a*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x)+152//105*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^2, x) == :(2//5*d^-1*(a+a*sec(c+d*x))^3//2*tan(c+d*x)+2//5*a*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x)+8//5*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x), x) == :(2//3*a*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x)+8//3*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//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))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x), x) == :(3*a^3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^2, x) == :(7//4*a^3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+7//4*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sin(c+d*x)+(1/2)*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^3, x) == :(11//8*a^3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+11//8*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sin(c+d*x)+1//3*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*sin(c+d*x)+11//12*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^4, x) == :(-568//693*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x)+284//99*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+284//231*a*d^-1*(a+a*sec(c+d*x))^3//2*tan(c+d*x)+2//11*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^4*tan(c+d*x)+46//99*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^4*tan(c+d*x)+710//693*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^3, x) == :(-4//63*d^-1*(a+a*sec(c+d*x))^5//2*tan(c+d*x)+2//9*a^-1*d^-1*(a+a*sec(c+d*x))^7//2*tan(c+d*x)+26//105*a*d^-1*(a+a*sec(c+d*x))^3//2*tan(c+d*x)+208//315*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x)+832//315*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^2, x) == :(2//7*d^-1*(a+a*sec(c+d*x))^5//2*tan(c+d*x)+2//7*a*d^-1*(a+a*sec(c+d*x))^3//2*tan(c+d*x)+16//21*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x)+64//21*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x), x) == :(2//5*a*d^-1*(a+a*sec(c+d*x))^3//2*tan(c+d*x)+16//15*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x)+64//15*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//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//3*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x)+14//3*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x), x) == :(5*a^5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sin(c+d*x)+2*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^2, x) == :(19//4*a^5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+9//4*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sin(c+d*x)+(1/2)*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^3, x) == :(25//8*a^5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+25//8*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sin(c+d*x)+1//3*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^2*sin(c+d*x)+13//12*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^4, x) == :(163//64*a^5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+163//64*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sin(c+d*x)+1//4*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^3*sin(c+d*x)+17//24*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*sin(c+d*x)+163//96*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+-1*a*sec(c+d*x))^(1/2)*sec(c+d*x), x) == :(-2*a*d^-1*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x))
@test integrate((a+-1*a*sec(c+d*x))^(1/2), x) == :(2*a^(1/2)*d^-1*arctan(a^(1/2)*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+-1*a*sec(c+d*x))^(1/2)*cos(c+d*x), x) == :(-1*a^(1/2)*d^-1*arctan(a^(1/2)*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x))+a*d^-1*(a+-1*a*sec(c+d*x))^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^4, x) == :(28//15*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+-1*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))+-2//15*a^-1*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x)+2//5*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3, x) == :(-4//3*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+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))+2//3*a^-1*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2, x) == :(2*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+-1*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*sec(c+d*x), x) == :(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, 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^(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*cos(c+d*x), x) == :(d^-1*(a+a*sec(c+d*x))^-1//2*sin(c+d*x)+-1*a^-1//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2^(1/2)*a^-1//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2, x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-1//2*sin(c+d*x)+7//4*a^-1//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)*sin(c+d*x)+-1*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))^-3//2*sec(c+d*x)^5, x) == :(-15//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))+-13//10*a^-2*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x)+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3*tan(c+d*x)+31//5*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+9//10*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^4, x) == :(-13//3*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^2*tan(c+d*x)+7//6*a^-2*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x)+11//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)))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3, x) == :((1/2)*d^-1*(a+a*sec(c+d*x))^-3//2*tan(c+d*x)+2*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+-7//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)))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^2, x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*tan(c+d*x)+3//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)))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x), x) == :((1/2)*d^-1*(a+a*sec(c+d*x))^-3//2*tan(c+d*x)+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)))
@test integrate((a+a*sec(c+d*x))^-3//2, x) == :(2*a^-3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*tan(c+d*x)+-5//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)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x), x) == :(-3*a^-3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sin(c+d*x)+3//2*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sin(c+d*x)+9//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)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^2, x) == :(19//4*a^-3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-13//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))+-7//4*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sin(c+d*x)+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)*sin(c+d*x)+a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^5, x) == :(-197//24*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^3*tan(c+d*x)+95//48*a^-3*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x)+163//32*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))+-17//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^4, x) == :(-75//32*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//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^2*tan(c+d*x)+9//4*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+13//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^3, x) == :(1//4*d^-1*(a+a*sec(c+d*x))^-5//2*tan(c+d*x)+-13//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*tan(c+d*x)+19//32*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))^-5//2*sec(c+d*x)^2, x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*tan(c+d*x)+5//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*tan(c+d*x)+5//32*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))^-5//2*sec(c+d*x), x) == :(1//4*d^-1*(a+a*sec(c+d*x))^-5//2*tan(c+d*x)+3//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*tan(c+d*x)+3//32*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))^-5//2, x) == :(2*a^-5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*tan(c+d*x)+-43//32*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))+-11//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x), x) == :(-5*a^-5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sin(c+d*x)+-15//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sin(c+d*x)+35//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sin(c+d*x)+115//32*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+-1*a*sec(c+d*x))^-1//2*sec(c+d*x), x) == :(-1*2^(1/2)*a^-1//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+-1*a*sec(c+d*x))^-1//2, x) == :(2*a^-1//2*d^-1*arctan(a^(1/2)*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x))+-1*2^(1/2)*a^-1//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^2//3*sec(c+d*x)^3, x) == :(-9//40*d^-1*(a+a*sec(c+d*x))^2//3*tan(c+d*x)+3//8*a^-1*d^-1*(a+a*sec(c+d*x))^5//3*tan(c+d*x)+57//80*d^-1*(1+sec(c+d*x))^-1*(a+a*sec(c+d*x))^2//3*tan(c+d*x)+-19//160*2^2//3*3^3//4*d^-1*((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^2//3+(1+sec(c+d*x))^2//3+2^1//3*(1+sec(c+d*x))^1//3))^(1/2)*(-1*(1+sec(c+d*x))^1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^1//3+-1*(1+sec(c+d*x))^1//3))^-1//2*(1+-1*sec(c+d*x))^-1*(1+sec(c+d*x))^-1*(a+a*sec(c+d*x))^2//3*(2^1//3+-1*(1+sec(c+d*x))^1//3)*Elliptic.F(arccos((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-1*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^2//3*sec(c+d*x)^2, x) == :(3//5*d^-1*(a+a*sec(c+d*x))^2//3*tan(c+d*x)+3//5*d^-1*(1+sec(c+d*x))^-1*(a+a*sec(c+d*x))^2//3*tan(c+d*x)+-1//10*2^2//3*3^3//4*d^-1*((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^2//3+(1+sec(c+d*x))^2//3+2^1//3*(1+sec(c+d*x))^1//3))^(1/2)*(-1*(1+sec(c+d*x))^1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^1//3+-1*(1+sec(c+d*x))^1//3))^-1//2*(1+-1*sec(c+d*x))^-1*(1+sec(c+d*x))^-1*(a+a*sec(c+d*x))^2//3*(2^1//3+-1*(1+sec(c+d*x))^1//3)*Elliptic.F(arccos((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-1*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^2//3*sec(c+d*x), x) == :(3//2*d^-1*(1+sec(c+d*x))^-1*(a+a*sec(c+d*x))^2//3*tan(c+d*x)+-1//4*2^2//3*3^3//4*d^-1*((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^2//3+(1+sec(c+d*x))^2//3+2^1//3*(1+sec(c+d*x))^1//3))^(1/2)*(-1*(1+sec(c+d*x))^1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^1//3+-1*(1+sec(c+d*x))^1//3))^-1//2*(1+-1*sec(c+d*x))^-1*(1+sec(c+d*x))^-1*(a+a*sec(c+d*x))^2//3*(2^1//3+-1*(1+sec(c+d*x))^1//3)*Elliptic.F(arccos((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-1*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//3*sec(c+d*x)^3, x) == :(-9//88*d^-1*(a+a*sec(c+d*x))^5//3*tan(c+d*x)+3//11*a^-1*d^-1*(a+a*sec(c+d*x))^8//3*tan(c+d*x)+147//440*a*d^-1*(a+a*sec(c+d*x))^2//3*tan(c+d*x)+1029//880*a*d^-1*(1+sec(c+d*x))^-1*(a+a*sec(c+d*x))^2//3*tan(c+d*x)+-343//1760*a*2^2//3*3^3//4*d^-1*((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^2//3+(1+sec(c+d*x))^2//3+2^1//3*(1+sec(c+d*x))^1//3))^(1/2)*(-1*(1+sec(c+d*x))^1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^1//3+-1*(1+sec(c+d*x))^1//3))^-1//2*(1+-1*sec(c+d*x))^-1*(1+sec(c+d*x))^-1*(a+a*sec(c+d*x))^2//3*(2^1//3+-1*(1+sec(c+d*x))^1//3)*Elliptic.F(arccos((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-1*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//3*sec(c+d*x)^2, x) == :(3//8*d^-1*(a+a*sec(c+d*x))^5//3*tan(c+d*x)+3//8*a*d^-1*(a+a*sec(c+d*x))^2//3*tan(c+d*x)+21//16*a*d^-1*(1+sec(c+d*x))^-1*(a+a*sec(c+d*x))^2//3*tan(c+d*x)+-7//32*a*2^2//3*3^3//4*d^-1*((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^2//3+(1+sec(c+d*x))^2//3+2^1//3*(1+sec(c+d*x))^1//3))^(1/2)*(-1*(1+sec(c+d*x))^1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^1//3+-1*(1+sec(c+d*x))^1//3))^-1//2*(1+-1*sec(c+d*x))^-1*(1+sec(c+d*x))^-1*(a+a*sec(c+d*x))^2//3*(2^1//3+-1*(1+sec(c+d*x))^1//3)*Elliptic.F(arccos((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-1*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//3*sec(c+d*x), x) == :(3//5*a*d^-1*(a+a*sec(c+d*x))^2//3*tan(c+d*x)+21//10*a*d^-1*(1+sec(c+d*x))^-1*(a+a*sec(c+d*x))^2//3*tan(c+d*x)+-7//20*a*2^2//3*3^3//4*d^-1*((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^2//3+(1+sec(c+d*x))^2//3+2^1//3*(1+sec(c+d*x))^1//3))^(1/2)*(-1*(1+sec(c+d*x))^1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^1//3+-1*(1+sec(c+d*x))^1//3))^-1//2*(1+-1*sec(c+d*x))^-1*(1+sec(c+d*x))^-1*(a+a*sec(c+d*x))^2//3*(2^1//3+-1*(1+sec(c+d*x))^1//3)*Elliptic.F(arccos((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-1*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//3*sec(c+d*x)^4, x) == :(99//80*d^-1*(a+a*sec(c+d*x))^-1//3*tan(c+d*x)+-3//40*a^-1*d^-1*(a+a*sec(c+d*x))^2//3*tan(c+d*x)+3//8*d^-1*(a+a*sec(c+d*x))^-1//3*sec(c+d*x)^2*tan(c+d*x)+37//160*2^2//3*3^3//4*d^-1*((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^2//3+(1+sec(c+d*x))^2//3+2^1//3*(1+sec(c+d*x))^1//3))^(1/2)*(-1*(1+sec(c+d*x))^1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^1//3+-1*(1+sec(c+d*x))^1//3))^-1//2*(1+-1*sec(c+d*x))^-1*(a+a*sec(c+d*x))^-1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3)*Elliptic.F(arccos((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-1*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//3*sec(c+d*x)^3, x) == :(-9//10*d^-1*(a+a*sec(c+d*x))^-1//3*tan(c+d*x)+3//5*a^-1*d^-1*(a+a*sec(c+d*x))^2//3*tan(c+d*x)+-7//20*2^2//3*3^3//4*d^-1*((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^2//3+(1+sec(c+d*x))^2//3+2^1//3*(1+sec(c+d*x))^1//3))^(1/2)*(-1*(1+sec(c+d*x))^1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^1//3+-1*(1+sec(c+d*x))^1//3))^-1//2*(1+-1*sec(c+d*x))^-1*(a+a*sec(c+d*x))^-1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3)*Elliptic.F(arccos((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-1*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//3*sec(c+d*x)^2, x) == :(3//2*d^-1*(a+a*sec(c+d*x))^-1//3*tan(c+d*x)+1//4*2^2//3*3^3//4*d^-1*((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^2//3+(1+sec(c+d*x))^2//3+2^1//3*(1+sec(c+d*x))^1//3))^(1/2)*(-1*(1+sec(c+d*x))^1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^1//3+-1*(1+sec(c+d*x))^1//3))^-1//2*(1+-1*sec(c+d*x))^-1*(a+a*sec(c+d*x))^-1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3)*Elliptic.F(arccos((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-1*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//3*sec(c+d*x), x) == :(-1//2*2^2//3*3^3//4*d^-1*((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^2//3+(1+sec(c+d*x))^2//3+2^1//3*(1+sec(c+d*x))^1//3))^(1/2)*(-1*(1+sec(c+d*x))^1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^1//3+-1*(1+sec(c+d*x))^1//3))^-1//2*(1+-1*sec(c+d*x))^-1*(a+a*sec(c+d*x))^-1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3)*Elliptic.F(arccos((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-1*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//3*sec(c+d*x)^4, x) == :(-33//28*d^-1*(a+a*sec(c+d*x))^-5//3*tan(c+d*x)+3//4*d^-1*(a+a*sec(c+d*x))^-5//3*sec(c+d*x)^2*tan(c+d*x)+135//14*a^-1*d^-1*(a+a*sec(c+d*x))^-2//3*tan(c+d*x)+1//28*a^-2*d^-1*(1+sec(c+d*x))^-2//3*(a+a*sec(c+d*x))^1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-1*(375+375*3^(1/2))*tan(c+d*x)+-375//28*2^1//3*3^1//4*a^-2*d^-1*((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^2//3+(1+sec(c+d*x))^2//3+2^1//3*(1+sec(c+d*x))^1//3))^(1/2)*(-1*(1+sec(c+d*x))^1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^1//3+-1*(1+sec(c+d*x))^1//3))^-1//2*(1+-1*sec(c+d*x))^-1*(1+sec(c+d*x))^-2//3*(a+a*sec(c+d*x))^1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3)*Elliptic.E(arccos((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-1*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))*tan(c+d*x)+-125//56*2^1//3*3^3//4*a^-2*d^-1*((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^2//3+(1+sec(c+d*x))^2//3+2^1//3*(1+sec(c+d*x))^1//3))^(1/2)*(-1*(1+sec(c+d*x))^1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^1//3+-1*(1+sec(c+d*x))^1//3))^-1//2*(1+-1*sec(c+d*x))^-1*(1+sec(c+d*x))^-2//3*(a+a*sec(c+d*x))^1//3*(1+-1*3^(1/2))*(2^1//3+-1*(1+sec(c+d*x))^1//3)*Elliptic.F(arccos((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-1*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//3*sec(c+d*x)^3, x) == :(3//7*d^-1*(a+a*sec(c+d*x))^-5//3*tan(c+d*x)+-36//7*a^-1*d^-1*(a+a*sec(c+d*x))^-2//3*tan(c+d*x)+-1//7*a^-2*d^-1*(1+sec(c+d*x))^-2//3*(a+a*sec(c+d*x))^1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-1*(57+57*3^(1/2))*tan(c+d*x)+57//7*2^1//3*3^1//4*a^-2*d^-1*((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^2//3+(1+sec(c+d*x))^2//3+2^1//3*(1+sec(c+d*x))^1//3))^(1/2)*(-1*(1+sec(c+d*x))^1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^1//3+-1*(1+sec(c+d*x))^1//3))^-1//2*(1+-1*sec(c+d*x))^-1*(1+sec(c+d*x))^-2//3*(a+a*sec(c+d*x))^1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3)*Elliptic.E(arccos((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-1*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))*tan(c+d*x)+19//14*2^1//3*3^3//4*a^-2*d^-1*((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^2//3+(1+sec(c+d*x))^2//3+2^1//3*(1+sec(c+d*x))^1//3))^(1/2)*(-1*(1+sec(c+d*x))^1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^1//3+-1*(1+sec(c+d*x))^1//3))^-1//2*(1+-1*sec(c+d*x))^-1*(1+sec(c+d*x))^-2//3*(a+a*sec(c+d*x))^1//3*(1+-1*3^(1/2))*(2^1//3+-1*(1+sec(c+d*x))^1//3)*Elliptic.F(arccos((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-1*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//3*sec(c+d*x)^2, x) == :(-3//7*d^-1*(a+a*sec(c+d*x))^-5//3*tan(c+d*x)+15//7*a^-1*d^-1*(a+a*sec(c+d*x))^-2//3*tan(c+d*x)+1//7*a^-1*d^-1*(1+sec(c+d*x))^1//3*(a+a*sec(c+d*x))^-2//3*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-1*(15+15*3^(1/2))*tan(c+d*x)+-15//7*2^1//3*3^1//4*a^-1*d^-1*((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^2//3+(1+sec(c+d*x))^2//3+2^1//3*(1+sec(c+d*x))^1//3))^(1/2)*(-1*(1+sec(c+d*x))^1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^1//3+-1*(1+sec(c+d*x))^1//3))^-1//2*(1+-1*sec(c+d*x))^-1*(1+sec(c+d*x))^1//3*(a+a*sec(c+d*x))^-2//3*(2^1//3+-1*(1+sec(c+d*x))^1//3)*Elliptic.E(arccos((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-1*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))*tan(c+d*x)+-5//14*2^1//3*3^3//4*a^-1*d^-1*((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^2//3+(1+sec(c+d*x))^2//3+2^1//3*(1+sec(c+d*x))^1//3))^(1/2)*(-1*(1+sec(c+d*x))^1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^1//3+-1*(1+sec(c+d*x))^1//3))^-1//2*(1+-1*sec(c+d*x))^-1*(1+sec(c+d*x))^1//3*(a+a*sec(c+d*x))^-2//3*(1+-1*3^(1/2))*(2^1//3+-1*(1+sec(c+d*x))^1//3)*Elliptic.F(arccos((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-1*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//3*sec(c+d*x), x) == :(6//7*a^-1*d^-1*(a+a*sec(c+d*x))^-2//3*tan(c+d*x)+3//7*a^-1*d^-1*(1+sec(c+d*x))^-1*(a+a*sec(c+d*x))^-2//3*tan(c+d*x)+1//7*a^-1*d^-1*(1+sec(c+d*x))^1//3*(a+a*sec(c+d*x))^-2//3*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-1*(6+6*3^(1/2))*tan(c+d*x)+-6//7*2^1//3*3^1//4*a^-1*d^-1*((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^2//3+(1+sec(c+d*x))^2//3+2^1//3*(1+sec(c+d*x))^1//3))^(1/2)*(-1*(1+sec(c+d*x))^1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^1//3+-1*(1+sec(c+d*x))^1//3))^-1//2*(1+-1*sec(c+d*x))^-1*(1+sec(c+d*x))^1//3*(a+a*sec(c+d*x))^-2//3*(2^1//3+-1*(1+sec(c+d*x))^1//3)*Elliptic.E(arccos((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-1*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))*tan(c+d*x)+-1//7*2^1//3*3^3//4*a^-1*d^-1*((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^2//3+(1+sec(c+d*x))^2//3+2^1//3*(1+sec(c+d*x))^1//3))^(1/2)*(-1*(1+sec(c+d*x))^1//3*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-2*(2^1//3+-1*(1+sec(c+d*x))^1//3))^-1//2*(1+-1*sec(c+d*x))^-1*(1+sec(c+d*x))^1//3*(a+a*sec(c+d*x))^-2//3*(1+-1*3^(1/2))*(2^1//3+-1*(1+sec(c+d*x))^1//3)*Elliptic.F(arccos((2^1//3+-1*(1+sec(c+d*x))^1//3*(1+3^(1/2)))^-1*(2^1//3+-1*(1+sec(c+d*x))^1//3*(1+-1*3^(1/2)))),1/2+1//4*3^(1/2))*tan(c+d*x))
@test integrate(sec(c+d*x)^5//2*(a+a*sec(c+d*x)), x) == :(2//3*a*d^-1*sec(c+d*x)^3//2*sin(c+d*x)+2//5*a*d^-1*sec(c+d*x)^5//2*sin(c+d*x)+6//5*a*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+-6//5*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^3//2*(a+a*sec(c+d*x)), x) == :(2*a*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+2//3*a*d^-1*sec(c+d*x)^3//2*sin(c+d*x)+-2*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^(1/2)*(a+a*sec(c+d*x)), x) == :(2*a*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+-2*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^-1//2*(a+a*sec(c+d*x)), x) == :(2*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^-3//2*(a+a*sec(c+d*x)), x) == :(2//3*a*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+2*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^-5//2*(a+a*sec(c+d*x)), x) == :(2//3*a*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+2//5*a*d^-1*sec(c+d*x)^-3//2*sin(c+d*x)+2//3*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+6//5*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^-7//2*(a+a*sec(c+d*x)), x) == :(2//5*a*d^-1*sec(c+d*x)^-3//2*sin(c+d*x)+2//7*a*d^-1*sec(c+d*x)^-5//2*sin(c+d*x)+10//21*a*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+6//5*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+10//21*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^5//2, x) == :(2//7*a^2*d^-1*sec(c+d*x)^7//2*sin(c+d*x)+4//5*a^2*d^-1*sec(c+d*x)^5//2*sin(c+d*x)+8//7*a^2*d^-1*sec(c+d*x)^3//2*sin(c+d*x)+12//5*a^2*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+-12//5*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+8//7*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^3//2, x) == :(2//5*a^2*d^-1*sec(c+d*x)^5//2*sin(c+d*x)+4//3*a^2*d^-1*sec(c+d*x)^3//2*sin(c+d*x)+16//5*a^2*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+-16//5*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//3*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^(1/2), x) == :(4*a^2*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+2//3*a^2*d^-1*sec(c+d*x)^3//2*sin(c+d*x)+-4*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+8//3*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^-1//2, x) == :(2*a^2*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+4*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^-3//2, x) == :(2//3*a^2*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+4*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+8//3*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^-5//2, x) == :(2//5*a^2*d^-1*sec(c+d*x)^-3//2*sin(c+d*x)+4//3*a^2*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+4//3*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+16//5*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^-7//2, x) == :(2//7*a^2*d^-1*sec(c+d*x)^-5//2*sin(c+d*x)+4//5*a^2*d^-1*sec(c+d*x)^-3//2*sin(c+d*x)+8//7*a^2*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+8//7*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+12//5*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^3//2, x) == :(2//7*a^3*d^-1*sec(c+d*x)^7//2*sin(c+d*x)+6//5*a^3*d^-1*sec(c+d*x)^5//2*sin(c+d*x)+28//5*a^3*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+52//21*a^3*d^-1*sec(c+d*x)^3//2*sin(c+d*x)+-28//5*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+52//21*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^(1/2), x) == :(2*a^3*d^-1*sec(c+d*x)^3//2*sin(c+d*x)+2//5*a^3*d^-1*sec(c+d*x)^5//2*sin(c+d*x)+36//5*a^3*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+4*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-36//5*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^-1//2, x) == :(6*a^3*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+2//3*a^3*d^-1*sec(c+d*x)^3//2*sin(c+d*x)+-4*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+20//3*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^-3//2, x) == :(2*a^3*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+2//3*a^3*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+4*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+20//3*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^-5//2, x) == :(2*a^3*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+2//5*a^3*d^-1*sec(c+d*x)^-3//2*sin(c+d*x)+4*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+36//5*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^-7//2, x) == :(2//7*a^3*d^-1*sec(c+d*x)^-5//2*sin(c+d*x)+6//5*a^3*d^-1*sec(c+d*x)^-3//2*sin(c+d*x)+52//21*a^3*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+28//5*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+52//21*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^-9//2, x) == :(2//9*a^3*d^-1*sec(c+d*x)^-7//2*sin(c+d*x)+6//7*a^3*d^-1*sec(c+d*x)^-5//2*sin(c+d*x)+44//21*a^3*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+68//45*a^3*d^-1*sec(c+d*x)^-3//2*sin(c+d*x)+44//21*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+68//15*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^4*sec(c+d*x)^3//2, x) == :(2//9*a^4*d^-1*sec(c+d*x)^9//2*sin(c+d*x)+8//7*a^4*d^-1*sec(c+d*x)^7//2*sin(c+d*x)+32//7*a^4*d^-1*sec(c+d*x)^3//2*sin(c+d*x)+122//45*a^4*d^-1*sec(c+d*x)^5//2*sin(c+d*x)+152//15*a^4*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+-152//15*a^4*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+32//7*a^4*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^4*sec(c+d*x)^(1/2), x) == :(2//7*a^4*d^-1*sec(c+d*x)^7//2*sin(c+d*x)+8//5*a^4*d^-1*sec(c+d*x)^5//2*sin(c+d*x)+64//5*a^4*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+94//21*a^4*d^-1*sec(c+d*x)^3//2*sin(c+d*x)+-64//5*a^4*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+136//21*a^4*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^4*sec(c+d*x)^-1//2, x) == :(2//5*a^4*d^-1*sec(c+d*x)^5//2*sin(c+d*x)+8//3*a^4*d^-1*sec(c+d*x)^3//2*sin(c+d*x)+66//5*a^4*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+-56//5*a^4*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+32//3*a^4*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^4*sec(c+d*x)^-3//2, x) == :(8*a^4*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+2//3*a^4*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+2//3*a^4*d^-1*sec(c+d*x)^3//2*sin(c+d*x)+40//3*a^4*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^4*sec(c+d*x)^-5//2, x) == :(2*a^4*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+2//5*a^4*d^-1*sec(c+d*x)^-3//2*sin(c+d*x)+8//3*a^4*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+32//3*a^4*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+56//5*a^4*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^4*sec(c+d*x)^-7//2, x) == :(2//7*a^4*d^-1*sec(c+d*x)^-5//2*sin(c+d*x)+8//5*a^4*d^-1*sec(c+d*x)^-3//2*sin(c+d*x)+94//21*a^4*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+64//5*a^4*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+136//21*a^4*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^4*sec(c+d*x)^-9//2, x) == :(2//9*a^4*d^-1*sec(c+d*x)^-7//2*sin(c+d*x)+8//7*a^4*d^-1*sec(c+d*x)^-5//2*sin(c+d*x)+32//7*a^4*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+122//45*a^4*d^-1*sec(c+d*x)^-3//2*sin(c+d*x)+32//7*a^4*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+152//15*a^4*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^4*sec(c+d*x)^-11//2, x) == :(2//11*a^4*d^-1*sec(c+d*x)^-9//2*sin(c+d*x)+8//9*a^4*d^-1*sec(c+d*x)^-7//2*sin(c+d*x)+128//45*a^4*d^-1*sec(c+d*x)^-3//2*sin(c+d*x)+150//77*a^4*d^-1*sec(c+d*x)^-5//2*sin(c+d*x)+904//231*a^4*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+128//15*a^4*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+904//231*a^4*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^7//2, x) == :(-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^5//2*sin(c+d*x)+-3*a^-1*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+5//3*a^-1*d^-1*sec(c+d*x)^3//2*sin(c+d*x)+3*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+5//3*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^5//2, x) == :(-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^3//2*sin(c+d*x)+3*a^-1*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+-1*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-3*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^3//2, x) == :(-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^(1/2), x) == :(d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^-1//2, x) == :(-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+-1*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+3*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^-3//2, x) == :(-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^-1//2*sin(c+d*x)+5//3*a^-1*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+-3*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+5//3*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^-5//2, x) == :(-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^-3//2*sin(c+d*x)+-5//3*a^-1*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+7//5*a^-1*d^-1*sec(c+d*x)^-3//2*sin(c+d*x)+-5//3*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+21//5*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^9//2, x) == :(-7*a^-2*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^7//2*sin(c+d*x)+10//3*a^-2*d^-1*sec(c+d*x)^3//2*sin(c+d*x)+7*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-7//3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^5//2*sin(c+d*x)+10//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^7//2, x) == :(4*a^-2*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^5//2*sin(c+d*x)+-4*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-5//3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^3//2*sin(c+d*x)+-5//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^5//2, x) == :(-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^3//2*sin(c+d*x)+a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+2//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^3//2, x) == :(1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^3//2*sin(c+d*x)+1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^(1/2), x) == :(-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^3//2*sin(c+d*x)+a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+-1*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^-1//2, x) == :(-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^(1/2)*sin(c+d*x)+4*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-5//3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+-5//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^-3//2, x) == :(-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^-1//2*sin(c+d*x)+10//3*a^-2*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+-7*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-7//3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^-1//2*sin(c+d*x)+10//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^-5//2, x) == :(-5*a^-2*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^-3//2*sin(c+d*x)+56//15*a^-2*d^-1*sec(c+d*x)^-3//2*sin(c+d*x)+-5*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^-3//2*sin(c+d*x)+56//5*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^11//2, x) == :(-119//10*a^-3*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+-119//30*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^5//2*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^9//2*sin(c+d*x)+11//2*a^-3*d^-1*sec(c+d*x)^3//2*sin(c+d*x)+-2//3*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^7//2*sin(c+d*x)+11//2*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+119//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^9//2, x) == :(-13//6*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^3//2*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^7//2*sin(c+d*x)+49//10*a^-3*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+-49//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-13//6*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-8//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^5//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^7//2, x) == :(-9//10*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^5//2*sin(c+d*x)+(1/2)*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-2//5*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^3//2*sin(c+d*x)+9//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^5//2, x) == :(-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^3//2*sin(c+d*x)+1//6*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+-4//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^(1/2)*sin(c+d*x)+1//6*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^3//2, x) == :(1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^3//2*sin(c+d*x)+1//6*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+-1//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^(1/2)*sin(c+d*x)+1//6*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^(1/2), x) == :((1/2)*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^3//2*sin(c+d*x)+(1/2)*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-9//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//5*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^-1//2, x) == :(-13//6*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^(1/2)*sin(c+d*x)+-13//6*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-8//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^(1/2)*sin(c+d*x)+49//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^-3//2, x) == :(-119//30*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^-1//2*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^-1//2*sin(c+d*x)+11//2*a^-3*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+-119//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-2//3*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^-1//2*sin(c+d*x)+11//2*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^-5//2, x) == :(-63//10*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^-3//2*sin(c+d*x)+-21//2*a^-3*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^-3//2*sin(c+d*x)+77//10*a^-3*d^-1*sec(c+d*x)^-3//2*sin(c+d*x)+-21//2*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-4//5*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^-3//2*sin(c+d*x)+231//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^5//2, x) == :(3//4*a^(1/2)*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*sin(c+d*x)+3//4*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3//2, x) == :(a^(1/2)*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^(1/2), x) == :(2*a^(1/2)*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2, x) == :(2*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2, x) == :(2//3*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x)+4//3*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2, x) == :(2//5*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*sin(c+d*x)+8//15*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x)+16//15*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-7//2, x) == :(2//7*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-5//2*sin(c+d*x)+12//35*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*sin(c+d*x)+16//35*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x)+32//35*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^5//2, x) == :(11//8*a^3//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//3*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^7//2*sin(c+d*x)+11//8*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x)+11//12*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^3//2, x) == :(7//4*a^3//2*d^-1*arcsinh(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(c+d*x)^5//2*sin(c+d*x)+7//4*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^(1/2), x) == :(3*a^3//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^-1//2, x) == :(2*a^3//2*d^-1*arcsinh(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*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^-3//2, x) == :(2//3*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*sin(c+d*x)+8//3*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^-5//2, x) == :(2//5*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-3//2*sin(c+d*x)+2//5*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*sin(c+d*x)+8//5*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^-7//2, x) == :(2//7*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-5//2*sin(c+d*x)+26//35*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*sin(c+d*x)+104//105*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x)+208//105*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^-9//2, x) == :(2//9*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-7//2*sin(c+d*x)+34//63*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-5//2*sin(c+d*x)+68//105*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*sin(c+d*x)+272//315*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x)+544//315*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^5//2, x) == :(163//64*a^5//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//4*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^7//2*sin(c+d*x)+17//24*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^7//2*sin(c+d*x)+163//64*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x)+163//96*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^3//2, x) == :(25//8*a^5//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//3*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^5//2*sin(c+d*x)+13//12*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*sin(c+d*x)+25//8*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^(1/2), x) == :(19//4*a^5//2*d^-1*arcsinh(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(c+d*x)^3//2*sin(c+d*x)+9//4*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-1//2, x) == :(5*a^5//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*sin(c+d*x)+a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-3//2, x) == :(2*a^5//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//3*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*sin(c+d*x)+14//3*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-5//2, x) == :(2//5*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-3//2*sin(c+d*x)+16//15*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*sin(c+d*x)+64//15*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-7//2, x) == :(2//7*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^-5//2*sin(c+d*x)+2//7*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-3//2*sin(c+d*x)+16//21*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*sin(c+d*x)+64//21*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-9//2, x) == :(2//9*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-7//2*sin(c+d*x)+38//63*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-5//2*sin(c+d*x)+146//105*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*sin(c+d*x)+584//315*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x)+1168//315*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-11//2, x) == :(2//11*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-9//2*sin(c+d*x)+46//99*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-7//2*sin(c+d*x)+284//231*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*sin(c+d*x)+710//693*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-5//2*sin(c+d*x)+1136//693*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x)+2272//693*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^-1//4, x) == :(4*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//4*sin(c+d*x))
@test integrate((a+a*sec(e+f*x))^(1/2)*sec(e+f*x)^(1/2), x) == :(2*a^(1/2)*f^-1*arcsinh(a^(1/2)*(a+a*sec(e+f*x))^-1//2*tan(e+f*x)))
@test integrate((-1*sec(e+f*x))^(1/2)*(a+-1*a*sec(e+f*x))^(1/2), x) == :(2*a^(1/2)*f^-1*arcsinh(a^(1/2)*(a+-1*a*sec(e+f*x))^-1//2*tan(e+f*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2, x) == :(-1*a^-1//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+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*sec(c+d*x)^(1/2)*sin(c+d*x))+d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2, x) == :(2*a^-1//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1*2^(1/2)*a^-1//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2), x) == :(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*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2, x) == :(-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*sec(c+d*x)^(1/2)*sin(c+d*x))+2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2, x) == :(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*sec(c+d*x)^(1/2)*sin(c+d*x))+-2//3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)+2//3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-5//2, x) == :(-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*sec(c+d*x)^(1/2)*sin(c+d*x))+-2//15*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x)+2//5*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*sin(c+d*x)+26//15*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^7//2, x) == :(-3*a^-3//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^5//2*sin(c+d*x)+9//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*sec(c+d*x)^(1/2)*sin(c+d*x))+3//2*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^5//2, x) == :(2*a^-3//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-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*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3//2, x) == :((1/2)*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3//2*sin(c+d*x)+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*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^(1/2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3//2*sin(c+d*x)+3//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*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-1//2, x) == :(-7//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*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^(1/2)*sin(c+d*x)+5//2*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-3//2, x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-1//2*sin(c+d*x)+11//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*sec(c+d*x)^(1/2)*sin(c+d*x))+-19//6*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)+7//6*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-5//2, x) == :(-15//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*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-3//2*sin(c+d*x)+-13//10*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x)+9//10*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*sin(c+d*x)+49//10*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^9//2, x) == :(-5*a^-5//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^7//2*sin(c+d*x)+115//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*sec(c+d*x)^(1/2)*sin(c+d*x))+-15//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^5//2*sin(c+d*x)+35//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^7//2, x) == :(2*a^-5//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-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*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^5//2*sin(c+d*x)+-11//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^5//2, x) == :(1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^5//2*sin(c+d*x)+3//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*sec(c+d*x)^(1/2)*sin(c+d*x))+3//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^3//2, x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^5//2*sin(c+d*x)+5//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*sec(c+d*x)^(1/2)*sin(c+d*x))+5//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^(1/2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^3//2*sin(c+d*x)+19//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*sec(c+d*x)^(1/2)*sin(c+d*x))+-9//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^-1//2, x) == :(-75//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*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^(1/2)*sin(c+d*x)+-13//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^(1/2)*sin(c+d*x)+49//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^-3//2, x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^-1//2*sin(c+d*x)+163//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*sec(c+d*x)^(1/2)*sin(c+d*x))+-299//48*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)+-17//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-1//2*sin(c+d*x)+95//48*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x))
@test integrate((1+sec(c+d*x))^-1//2*sec(c+d*x)^7//2, x) == :(7//4*d^-1*arcsinh((1+sec(c+d*x))^-1//2*tan(c+d*x))+-1*2^(1/2)*d^-1*arcsinh((1+sec(c+d*x))^-1*tan(c+d*x))+(1/2)*d^-1*(1+sec(c+d*x))^-1//2*sec(c+d*x)^5//2*sin(c+d*x)+-1//4*d^-1*(1+sec(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x))
@test integrate((1+sec(c+d*x))^-1//2*sec(c+d*x)^5//2, x) == :(-1*d^-1*arcsinh((1+sec(c+d*x))^-1//2*tan(c+d*x))+2^(1/2)*d^-1*arcsinh((1+sec(c+d*x))^-1*tan(c+d*x))+d^-1*(1+sec(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x))
@test integrate((1+sec(c+d*x))^-1//2*sec(c+d*x)^3//2, x) == :(2*d^-1*arcsinh((1+sec(c+d*x))^-1//2*tan(c+d*x))+-1*2^(1/2)*d^-1*arcsinh((1+sec(c+d*x))^-1*tan(c+d*x)))
@test integrate((1+sec(c+d*x))^-1//2*sec(c+d*x)^(1/2), x) == :(2^(1/2)*d^-1*arcsinh((1+sec(c+d*x))^-1*tan(c+d*x)))
@test integrate((1+sec(c+d*x))^-1//2*sec(c+d*x)^-1//2, x) == :(-1*2^(1/2)*d^-1*arcsinh((1+sec(c+d*x))^-1*tan(c+d*x))+2*d^-1*(1+sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((1+sec(c+d*x))^-1//2*sec(c+d*x)^-3//2, x) == :(2^(1/2)*d^-1*arcsinh((1+sec(c+d*x))^-1*tan(c+d*x))+-2//3*d^-1*(1+sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)+2//3*d^-1*(1+sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x))
@test integrate((1+sec(c+d*x))^-1//2*sec(c+d*x)^-5//2, x) == :(-1*2^(1/2)*d^-1*arcsinh((1+sec(c+d*x))^-1*tan(c+d*x))+-2//15*d^-1*(1+sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x)+2//5*d^-1*(1+sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*sin(c+d*x)+26//15*d^-1*(1+sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((e*sec(c+d*x))^4//3*(a+a*sec(c+d*x))^(1/2), x) == :(6//5*a*e*d^-1*(e*sec(c+d*x))^1//3*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+4//5*e*3^3//4*a^2*d^-1*((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^2//3+(e*sec(c+d*x))^2//3+e^1//3*(e*sec(c+d*x))^1//3))^(1/2)*(e^1//3*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^1//3+-1*(e*sec(c+d*x))^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+a*sec(c+d*x))^-1//2*(a+-1*a*sec(c+d*x))^-1*(e^1//3+-1*(e*sec(c+d*x))^1//3)*Elliptic.F(arcsin((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-1*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))*tan(c+d*x))
@test integrate((e*sec(c+d*x))^1//3*(a+a*sec(c+d*x))^(1/2), x) == :(2*3^3//4*a^2*d^-1*((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^2//3+(e*sec(c+d*x))^2//3+e^1//3*(e*sec(c+d*x))^1//3))^(1/2)*(e^1//3*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^1//3+-1*(e*sec(c+d*x))^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+a*sec(c+d*x))^-1//2*(a+-1*a*sec(c+d*x))^-1*(e^1//3+-1*(e*sec(c+d*x))^1//3)*Elliptic.F(arcsin((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-1*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))*tan(c+d*x))
@test integrate((e*sec(c+d*x))^-2//3*(a+a*sec(c+d*x))^(1/2), x) == :(3//2*a*d^-1*(e*sec(c+d*x))^-2//3*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+(1/2)*3^3//4*a^2*d^-1*e^-1*((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^2//3+(e*sec(c+d*x))^2//3+e^1//3*(e*sec(c+d*x))^1//3))^(1/2)*(e^1//3*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^1//3+-1*(e*sec(c+d*x))^1//3))^-1//2*(2+3^(1/2))^(1/2)*(a+a*sec(c+d*x))^-1//2*(a+-1*a*sec(c+d*x))^-1*(e^1//3+-1*(e*sec(c+d*x))^1//3)*Elliptic.F(arcsin((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-1*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))*tan(c+d*x))
@test integrate((e*sec(c+d*x))^8//3*(a+a*sec(c+d*x))^(1/2), x) == :(-240//91*a*d^-1*e^3*(a+a*sec(c+d*x))^-1//2*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-1*tan(c+d*x)+6//13*a*e*d^-1*(e*sec(c+d*x))^5//3*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+60//91*a*d^-1*e^2*(e*sec(c+d*x))^2//3*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+-80//91*2^(1/2)*3^3//4*a^2*d^-1*e^7//3*((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^2//3+(e*sec(c+d*x))^2//3+e^1//3*(e*sec(c+d*x))^1//3))^(1/2)*(e^1//3*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^1//3+-1*(e*sec(c+d*x))^1//3))^-1//2*(a+a*sec(c+d*x))^-1//2*(a+-1*a*sec(c+d*x))^-1*(e^1//3+-1*(e*sec(c+d*x))^1//3)*Elliptic.F(arcsin((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-1*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))*tan(c+d*x)+120//91*3^1//4*a^2*d^-1*e^7//3*((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^2//3+(e*sec(c+d*x))^2//3+e^1//3*(e*sec(c+d*x))^1//3))^(1/2)*(e^1//3*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^1//3+-1*(e*sec(c+d*x))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+a*sec(c+d*x))^-1//2*(a+-1*a*sec(c+d*x))^-1*(e^1//3+-1*(e*sec(c+d*x))^1//3)*Elliptic.E(arcsin((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-1*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))*tan(c+d*x))
@test integrate((e*sec(c+d*x))^5//3*(a+a*sec(c+d*x))^(1/2), x) == :(-24//7*a*d^-1*e^2*(a+a*sec(c+d*x))^-1//2*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-1*tan(c+d*x)+6//7*a*e*d^-1*(e*sec(c+d*x))^2//3*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+-8//7*2^(1/2)*3^3//4*a^2*d^-1*e^4//3*((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^2//3+(e*sec(c+d*x))^2//3+e^1//3*(e*sec(c+d*x))^1//3))^(1/2)*(e^1//3*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^1//3+-1*(e*sec(c+d*x))^1//3))^-1//2*(a+a*sec(c+d*x))^-1//2*(a+-1*a*sec(c+d*x))^-1*(e^1//3+-1*(e*sec(c+d*x))^1//3)*Elliptic.F(arcsin((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-1*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))*tan(c+d*x)+12//7*3^1//4*a^2*d^-1*e^4//3*((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^2//3+(e*sec(c+d*x))^2//3+e^1//3*(e*sec(c+d*x))^1//3))^(1/2)*(e^1//3*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^1//3+-1*(e*sec(c+d*x))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+a*sec(c+d*x))^-1//2*(a+-1*a*sec(c+d*x))^-1*(e^1//3+-1*(e*sec(c+d*x))^1//3)*Elliptic.E(arcsin((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-1*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))*tan(c+d*x))
@test integrate((e*sec(c+d*x))^2//3*(a+a*sec(c+d*x))^(1/2), x) == :(-6*a*e*d^-1*(a+a*sec(c+d*x))^-1//2*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-1*tan(c+d*x)+-2*2^(1/2)*3^3//4*a^2*d^-1*e^1//3*((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^2//3+(e*sec(c+d*x))^2//3+e^1//3*(e*sec(c+d*x))^1//3))^(1/2)*(e^1//3*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^1//3+-1*(e*sec(c+d*x))^1//3))^-1//2*(a+a*sec(c+d*x))^-1//2*(a+-1*a*sec(c+d*x))^-1*(e^1//3+-1*(e*sec(c+d*x))^1//3)*Elliptic.F(arcsin((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-1*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))*tan(c+d*x)+3*3^1//4*a^2*d^-1*e^1//3*((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^2//3+(e*sec(c+d*x))^2//3+e^1//3*(e*sec(c+d*x))^1//3))^(1/2)*(e^1//3*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^1//3+-1*(e*sec(c+d*x))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+a*sec(c+d*x))^-1//2*(a+-1*a*sec(c+d*x))^-1*(e^1//3+-1*(e*sec(c+d*x))^1//3)*Elliptic.E(arcsin((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-1*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))*tan(c+d*x))
@test integrate((e*sec(c+d*x))^-1//3*(a+a*sec(c+d*x))^(1/2), x) == :(3*a*d^-1*(e*sec(c+d*x))^-1//3*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+3*a*d^-1*(a+a*sec(c+d*x))^-1//2*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-1*tan(c+d*x)+2^(1/2)*3^3//4*a^2*d^-1*e^-2//3*((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^2//3+(e*sec(c+d*x))^2//3+e^1//3*(e*sec(c+d*x))^1//3))^(1/2)*(e^1//3*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^1//3+-1*(e*sec(c+d*x))^1//3))^-1//2*(a+a*sec(c+d*x))^-1//2*(a+-1*a*sec(c+d*x))^-1*(e^1//3+-1*(e*sec(c+d*x))^1//3)*Elliptic.F(arcsin((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-1*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))*tan(c+d*x)+-3//2*3^1//4*a^2*d^-1*e^-2//3*((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^2//3+(e*sec(c+d*x))^2//3+e^1//3*(e*sec(c+d*x))^1//3))^(1/2)*(e^1//3*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^1//3+-1*(e*sec(c+d*x))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+a*sec(c+d*x))^-1//2*(a+-1*a*sec(c+d*x))^-1*(e^1//3+-1*(e*sec(c+d*x))^1//3)*Elliptic.E(arcsin((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-1*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))*tan(c+d*x))
@test integrate((e*sec(c+d*x))^-4//3*(a+a*sec(c+d*x))^(1/2), x) == :(3//4*a*d^-1*(e*sec(c+d*x))^-4//3*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+15//8*a*d^-1*e^-1*(e*sec(c+d*x))^-1//3*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+15//8*a*d^-1*e^-1*(a+a*sec(c+d*x))^-1//2*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-1*tan(c+d*x)+-15//16*3^1//4*a^2*d^-1*e^-5//3*((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^2//3+(e*sec(c+d*x))^2//3+e^1//3*(e*sec(c+d*x))^1//3))^(1/2)*(e^1//3*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^1//3+-1*(e*sec(c+d*x))^1//3))^-1//2*(2+-1*3^(1/2))^(1/2)*(a+a*sec(c+d*x))^-1//2*(a+-1*a*sec(c+d*x))^-1*(e^1//3+-1*(e*sec(c+d*x))^1//3)*Elliptic.E(arcsin((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-1*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))*tan(c+d*x)+5//8*2^(1/2)*3^3//4*a^2*d^-1*e^-5//3*((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^2//3+(e*sec(c+d*x))^2//3+e^1//3*(e*sec(c+d*x))^1//3))^(1/2)*(e^1//3*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-2*(e^1//3+-1*(e*sec(c+d*x))^1//3))^-1//2*(a+a*sec(c+d*x))^-1//2*(a+-1*a*sec(c+d*x))^-1*(e^1//3+-1*(e*sec(c+d*x))^1//3)*Elliptic.F(arcsin((-1*(e*sec(c+d*x))^1//3+e^1//3*(1+3^(1/2)))^-1*(-1*(e*sec(c+d*x))^1//3+e^1//3*(1+-1*3^(1/2)))),-7+-4*3^(1/2))*tan(c+d*x))
@test integrate(cos(c+d*x)^7//2*(a+a*sec(c+d*x)), x) == :(6//5*a*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+10//21*a*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*a*d^-1*cos(c+d*x)^3//2*sin(c+d*x)+2//7*a*d^-1*cos(c+d*x)^5//2*sin(c+d*x)+10//21*a*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate(cos(c+d*x)^5//2*(a+a*sec(c+d*x)), x) == :(2//3*a*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+6//5*a*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+2//5*a*d^-1*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate(cos(c+d*x)^3//2*(a+a*sec(c+d*x)), x) == :(2*a*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate(cos(c+d*x)^(1/2)*(a+a*sec(c+d*x)), x) == :(2*a*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*a*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(cos(c+d*x)^-1//2*(a+a*sec(c+d*x)), x) == :(-2*a*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*a*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*a*d^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate(cos(c+d*x)^-3//2*(a+a*sec(c+d*x)), x) == :(-2*a*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*a*d^-1*cos(c+d*x)^-1//2*sin(c+d*x)+2//3*a*d^-1*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate(cos(c+d*x)^-5//2*(a+a*sec(c+d*x)), x) == :(-6//5*a*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*cos(c+d*x)^-3//2*sin(c+d*x)+2//5*a*d^-1*cos(c+d*x)^-5//2*sin(c+d*x)+6//5*a*d^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate(cos(c+d*x)^-7//2*(a+a*sec(c+d*x)), x) == :(-6//5*a*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+10//21*a*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*a*d^-1*cos(c+d*x)^-5//2*sin(c+d*x)+2//7*a*d^-1*cos(c+d*x)^-7//2*sin(c+d*x)+6//5*a*d^-1*cos(c+d*x)^-1//2*sin(c+d*x)+10//21*a*d^-1*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^9//2, x) == :(20//21*a^2*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+32//15*a^2*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//9*a^2*d^-1*cos(c+d*x)^7//2*sin(c+d*x)+4//7*a^2*d^-1*cos(c+d*x)^5//2*sin(c+d*x)+20//21*a^2*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+32//45*a^2*d^-1*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^7//2, x) == :(8//7*a^2*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+12//5*a^2*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//7*a^2*d^-1*cos(c+d*x)^5//2*sin(c+d*x)+4//5*a^2*d^-1*cos(c+d*x)^3//2*sin(c+d*x)+8//7*a^2*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^5//2, x) == :(4//3*a^2*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+16//5*a^2*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//5*a^2*d^-1*cos(c+d*x)^3//2*sin(c+d*x)+4//3*a^2*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^3//2, x) == :(4*a^2*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+8//3*a^2*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*a^2*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^(1/2), x) == :(4*a^2*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*a^2*d^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^-1//2, x) == :(-4*a^2*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+8//3*a^2*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+4*a^2*d^-1*cos(c+d*x)^-1//2*sin(c+d*x)+2//3*a^2*d^-1*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^-3//2, x) == :(-16//5*a^2*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//3*a^2*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*a^2*d^-1*cos(c+d*x)^-5//2*sin(c+d*x)+4//3*a^2*d^-1*cos(c+d*x)^-3//2*sin(c+d*x)+16//5*a^2*d^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^-5//2, x) == :(-12//5*a^2*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+8//7*a^2*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//7*a^2*d^-1*cos(c+d*x)^-7//2*sin(c+d*x)+4//5*a^2*d^-1*cos(c+d*x)^-5//2*sin(c+d*x)+8//7*a^2*d^-1*cos(c+d*x)^-3//2*sin(c+d*x)+12//5*a^2*d^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^9//2, x) == :(44//21*a^3*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+68//15*a^3*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//9*a^3*d^-1*cos(c+d*x)^7//2*sin(c+d*x)+6//7*a^3*d^-1*cos(c+d*x)^5//2*sin(c+d*x)+44//21*a^3*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+68//45*a^3*d^-1*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^7//2, x) == :(28//5*a^3*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+52//21*a^3*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//7*a^3*d^-1*cos(c+d*x)^5//2*sin(c+d*x)+6//5*a^3*d^-1*cos(c+d*x)^3//2*sin(c+d*x)+52//21*a^3*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^5//2, x) == :(4*a^3*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+36//5*a^3*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*a^3*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+2//5*a^3*d^-1*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^3//2, x) == :(4*a^3*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+20//3*a^3*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*a^3*d^-1*cos(c+d*x)^-1//2*sin(c+d*x)+2//3*a^3*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^(1/2), x) == :(-4*a^3*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+20//3*a^3*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+6*a^3*d^-1*cos(c+d*x)^-1//2*sin(c+d*x)+2//3*a^3*d^-1*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^-1//2, x) == :(4*a^3*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-36//5*a^3*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*a^3*d^-1*cos(c+d*x)^-3//2*sin(c+d*x)+2//5*a^3*d^-1*cos(c+d*x)^-5//2*sin(c+d*x)+36//5*a^3*d^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^-3//2, x) == :(-28//5*a^3*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+52//21*a^3*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//7*a^3*d^-1*cos(c+d*x)^-7//2*sin(c+d*x)+6//5*a^3*d^-1*cos(c+d*x)^-5//2*sin(c+d*x)+28//5*a^3*d^-1*cos(c+d*x)^-1//2*sin(c+d*x)+52//21*a^3*d^-1*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^5//2, x) == :(-5//3*a^-1*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+21//5*a^-1*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1*d^-1*(a+a*sec(c+d*x))^-1*cos(c+d*x)^3//2*sin(c+d*x)+-5//3*a^-1*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+7//5*a^-1*d^-1*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^3//2, x) == :(-3*a^-1*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+5//3*a^-1*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1*d^-1*(a+a*sec(c+d*x))^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+5//3*a^-1*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^(1/2), x) == :(-1*a^-1*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+3*a^-1*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1*d^-1*(a+a*sec(c+d*x))^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^-1//2, x) == :(a^-1*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1*a^-1*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+d^-1*(a+a*sec(c+d*x))^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^-3//2, x) == :(a^-1*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+a^-1*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1*d^-1*(a+a*sec(c+d*x))^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^-5//2, x) == :(-1*a^-1*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-3*a^-1*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1*d^-1*(a+a*sec(c+d*x))^-1*cos(c+d*x)^-3//2*sin(c+d*x)+3*a^-1*d^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^-7//2, x) == :(3*a^-1*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+5//3*a^-1*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1*d^-1*(a+a*sec(c+d*x))^-1*cos(c+d*x)^-5//2*sin(c+d*x)+-3*a^-1*d^-1*cos(c+d*x)^-1//2*sin(c+d*x)+5//3*a^-1*d^-1*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^5//2, x) == :(-5*a^-2*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+56//5*a^-2*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-5*a^-2*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)^3//2*sin(c+d*x)+56//15*a^-2*d^-1*cos(c+d*x)^3//2*sin(c+d*x)+-3*a^-2*d^-1*(1+sec(c+d*x))^-1*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^3//2, x) == :(-7*a^-2*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+10//3*a^-2*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)^(1/2)*sin(c+d*x)+10//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+-7//3*a^-2*d^-1*(1+sec(c+d*x))^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^(1/2), x) == :(4*a^-2*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-5//3*a^-2*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)^-1//2*sin(c+d*x)+-5//3*a^-2*d^-1*(1+sec(c+d*x))^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^-1//2, x) == :(-1*a^-2*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a^-2*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)^-3//2*sin(c+d*x)+a^-2*d^-1*(1+sec(c+d*x))^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^-3//2, x) == :(1//3*a^-2*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^-5//2, x) == :(a^-2*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a^-2*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)^-3//2*sin(c+d*x)+-1*a^-2*d^-1*(1+sec(c+d*x))^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^-7//2, x) == :(-4*a^-2*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-5//3*a^-2*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+4*a^-2*d^-1*cos(c+d*x)^-1//2*sin(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)^-5//2*sin(c+d*x)+-5//3*a^-2*d^-1*(1+sec(c+d*x))^-1*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^-9//2, x) == :(7*a^-2*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+10//3*a^-2*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-7*a^-2*d^-1*cos(c+d*x)^-1//2*sin(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)^-7//2*sin(c+d*x)+10//3*a^-2*d^-1*cos(c+d*x)^-3//2*sin(c+d*x)+-7//3*a^-2*d^-1*(1+sec(c+d*x))^-1*cos(c+d*x)^-5//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^5//2, x) == :(-21//2*a^-3*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+231//10*a^-3*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-63//10*d^-1*(a^3+a^3*sec(c+d*x))^-1*cos(c+d*x)^3//2*sin(c+d*x)+-21//2*a^-3*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*cos(c+d*x)^3//2*sin(c+d*x)+77//10*a^-3*d^-1*cos(c+d*x)^3//2*sin(c+d*x)+-4//5*a^-1*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^3//2, x) == :(-119//10*a^-3*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+11//2*a^-3*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-119//30*d^-1*(a^3+a^3*sec(c+d*x))^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*cos(c+d*x)^(1/2)*sin(c+d*x)+11//2*a^-3*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+-2//3*a^-1*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^(1/2), x) == :(-13//6*a^-3*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+49//10*a^-3*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-13//6*d^-1*(a^3+a^3*sec(c+d*x))^-1*cos(c+d*x)^-1//2*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*cos(c+d*x)^-1//2*sin(c+d*x)+-8//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^-1//2, x) == :((1/2)*a^-3*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-9//10*a^-3*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+(1/2)*d^-1*(a^3+a^3*sec(c+d*x))^-1*cos(c+d*x)^-1//2*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*cos(c+d*x)^-3//2*sin(c+d*x)+2//5*a^-1*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^-3//2, x) == :(-1//10*a^-3*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//6*a^-3*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*(a+a*sec(c+d*x))^-3*cos(c+d*x)^-3//2*sin(c+d*x)+1//6*d^-1*(a^3+a^3*sec(c+d*x))^-1*cos(c+d*x)^-1//2*sin(c+d*x)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^-5//2, x) == :(1//6*a^-3*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//10*a^-3*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*cos(c+d*x)^-3//2*sin(c+d*x)+1//6*d^-1*(a^3+a^3*sec(c+d*x))^-1*cos(c+d*x)^-1//2*sin(c+d*x)+-4//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^-7//2, x) == :((1/2)*a^-3*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+9//10*a^-3*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-9//10*d^-1*(a^3+a^3*sec(c+d*x))^-1*cos(c+d*x)^-1//2*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*cos(c+d*x)^-5//2*sin(c+d*x)+-2//5*a^-1*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^-9//2, x) == :(-49//10*a^-3*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-13//6*a^-3*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-13//6*d^-1*(a^3+a^3*sec(c+d*x))^-1*cos(c+d*x)^-3//2*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*cos(c+d*x)^-7//2*sin(c+d*x)+49//10*a^-3*d^-1*cos(c+d*x)^-1//2*sin(c+d*x)+-8//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)^-5//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^-11//2, x) == :(11//2*a^-3*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+119//10*a^-3*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-119//10*a^-3*d^-1*cos(c+d*x)^-1//2*sin(c+d*x)+-119//30*d^-1*(a^3+a^3*sec(c+d*x))^-1*cos(c+d*x)^-5//2*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*cos(c+d*x)^-9//2*sin(c+d*x)+11//2*a^-3*d^-1*cos(c+d*x)^-3//2*sin(c+d*x)+-2//3*a^-1*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)^-7//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^7//2, x) == :(2//7*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^5//2*sin(c+d*x)+12//35*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x)+16//35*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)+32//35*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2, x) == :(2//5*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x)+8//15*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)+16//15*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2, x) == :(2//3*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)+4//3*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2), x) == :(2*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-1//2, x) == :(2*a^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-3//2, x) == :(a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+a^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-5//2, x) == :((1/2)*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x)+3//4*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+3//4*a^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^7//2, x) == :(2//7*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^5//2*sin(c+d*x)+26//35*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x)+104//105*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)+208//105*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^5//2, x) == :(2//5*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^3//2*sin(c+d*x)+2//5*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x)+8//5*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^3//2, x) == :(2//3*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x)+8//3*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^(1/2), x) == :(2*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+2*a^3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^-1//2, x) == :(a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+3*a^3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^-3//2, x) == :((1/2)*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x)+7//4*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+7//4*a^3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^-5//2, x) == :(1//3*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-7//2*sin(c+d*x)+11//8*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+11//8*a^3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+11//12*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^9//2, x) == :(2//9*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^7//2*sin(c+d*x)+38//63*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^5//2*sin(c+d*x)+146//105*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x)+584//315*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)+1168//315*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^7//2, x) == :(2//7*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^5//2*sin(c+d*x)+2//7*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^3//2*sin(c+d*x)+16//21*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x)+64//21*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^5//2, x) == :(2//5*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^3//2*sin(c+d*x)+16//15*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x)+64//15*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^3//2, x) == :(2*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//3*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x)+14//3*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^(1/2), x) == :(a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-1//2*sin(c+d*x)+a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+5*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^-1//2, x) == :((1/2)*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-3//2*sin(c+d*x)+9//4*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+19//4*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^-3//2, x) == :(1//3*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-5//2*sin(c+d*x)+13//12*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x)+25//8*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+25//8*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^-5//2, x) == :(1//4*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-7//2*sin(c+d*x)+17//24*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-7//2*sin(c+d*x)+163//64*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+163//64*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+163//96*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^5//2, x) == :(-2//15*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)+2//5*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x)+26//15*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2, x) == :(-2//3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+2//3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)+2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2), x) == :(2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2, x) == :(2*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1*2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2, x) == :(d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+-1*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-7//2, x) == :((1/2)*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x)+-1//4*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+7//4*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1*2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^5//2, x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^3//2*sin(c+d*x)+-13//10*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)+9//10*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x)+49//10*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+-15//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^3//2, x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^(1/2)*sin(c+d*x)+-19//6*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+7//6*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)+11//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^(1/2), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-1//2*sin(c+d*x)+5//2*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+-7//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-1//2, x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-3//2*sin(c+d*x)+3//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-3//2, x) == :((1/2)*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-3//2*sin(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-5//2, x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-3//2*sin(c+d*x)+2*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-5//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-7//2, x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-5//2*sin(c+d*x)+-3*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+3//2*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+9//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^3//2, x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^(1/2)*sin(c+d*x)+-299//48*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+-17//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^(1/2)*sin(c+d*x)+95//48*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)+163//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^(1/2), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-1//2*sin(c+d*x)+-13//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-1//2*sin(c+d*x)+49//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+-75//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-1//2, x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-3//2*sin(c+d*x)+-9//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-3//2*sin(c+d*x)+19//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-3//2, x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-5//2*sin(c+d*x)+5//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-3//2*sin(c+d*x)+5//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-5//2, x) == :(1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-5//2*sin(c+d*x)+3//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-3//2*sin(c+d*x)+3//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-7//2, x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-5//2*sin(c+d*x)+2*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-11//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-3//2*sin(c+d*x)+-43//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-9//2, x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-7//2*sin(c+d*x)+-5*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-15//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-5//2*sin(c+d*x)+35//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+115//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate(sec(c+d*x)^4*(a+b*sec(c+d*x)), x) == :(a*d^-1*tan(c+d*x)+1//3*a*d^-1*tan(c+d*x)^3+3//8*b*d^-1*arctanh(sin(c+d*x))+1//4*b*d^-1*sec(c+d*x)^3*tan(c+d*x)+3//8*b*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate(sec(c+d*x)^3*(a+b*sec(c+d*x)), x) == :(b*d^-1*tan(c+d*x)+(1/2)*a*d^-1*arctanh(sin(c+d*x))+1//3*b*d^-1*tan(c+d*x)^3+(1/2)*a*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate(sec(c+d*x)^2*(a+b*sec(c+d*x)), x) == :(a*d^-1*tan(c+d*x)+(1/2)*b*d^-1*arctanh(sin(c+d*x))+(1/2)*b*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))*sec(c+d*x), x) == :(a*d^-1*arctanh(sin(c+d*x))+b*d^-1*tan(c+d*x))
@test integrate(a+b*sec(c+d*x), x) == :(a*x+b*d^-1*arctanh(sin(c+d*x)))
@test integrate((a+b*sec(c+d*x))*cos(c+d*x), x) == :(b*x+a*d^-1*sin(c+d*x))
@test integrate(cos(c+d*x)^2*(a+b*sec(c+d*x)), x) == :((1/2)*a*x+b*d^-1*sin(c+d*x)+(1/2)*a*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^3*(a+b*sec(c+d*x)), x) == :((1/2)*b*x+a*d^-1*sin(c+d*x)+-1//3*a*d^-1*sin(c+d*x)^3+(1/2)*b*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^4*(a+b*sec(c+d*x)), x) == :(3//8*a*x+b*d^-1*sin(c+d*x)+-1//3*b*d^-1*sin(c+d*x)^3+1//4*a*d^-1*cos(c+d*x)^3*sin(c+d*x)+3//8*a*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^5*(a+b*sec(c+d*x)), x) == :(3//8*b*x+a*d^-1*sin(c+d*x)+-2//3*a*d^-1*sin(c+d*x)^3+1//5*a*d^-1*sin(c+d*x)^5+1//4*b*d^-1*cos(c+d*x)^3*sin(c+d*x)+3//8*b*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^4, x) == :(1//5*d^-1*(4*b^2+5*a^2)*tan(c+d*x)+1//15*d^-1*tan(c+d*x)^3*(4*b^2+5*a^2)+1//5*b^2*d^-1*sec(c+d*x)^4*tan(c+d*x)+3//4*a*b*d^-1*arctanh(sin(c+d*x))+(1/2)*a*b*d^-1*sec(c+d*x)^3*tan(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*sec(c+d*x)^3, x) == :(1//8*d^-1*(3*b^2+4*a^2)*arctanh(sin(c+d*x))+2*a*b*d^-1*tan(c+d*x)+1//4*b^2*d^-1*sec(c+d*x)^3*tan(c+d*x)+1//8*d^-1*(3*b^2+4*a^2)*sec(c+d*x)*tan(c+d*x)+2//3*a*b*d^-1*tan(c+d*x)^3)
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^2, x) == :(1//3*d^-1*(2*b^2+3*a^2)*tan(c+d*x)+a*b*d^-1*arctanh(sin(c+d*x))+1//3*b^2*d^-1*sec(c+d*x)^2*tan(c+d*x)+a*b*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x), x) == :((1/2)*d^-1*(b^2+2*a^2)*arctanh(sin(c+d*x))+(1/2)*b^2*d^-1*sec(c+d*x)*tan(c+d*x)+2*a*b*d^-1*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^2, x) == :(x*a^2+b^2*d^-1*tan(c+d*x)+2*a*b*d^-1*arctanh(sin(c+d*x)))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x), x) == :(a^2*d^-1*sin(c+d*x)+b^2*d^-1*arctanh(sin(c+d*x))+2*a*b*x)
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^2, x) == :(x*(b^2+(1/2)*a^2)+(1/2)*a^2*d^-1*cos(c+d*x)*sin(c+d*x)+2*a*b*d^-1*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^3, x) == :(a*b*x+d^-1*(a^2+b^2)*sin(c+d*x)+-1//3*a^2*d^-1*sin(c+d*x)^3+a*b*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^4, x) == :(x*((1/2)*b^2+3//8*a^2)+2*a*b*d^-1*sin(c+d*x)+-2//3*a*b*d^-1*sin(c+d*x)^3+1//4*a^2*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//8*d^-1*(3*a^2+4*b^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^5, x) == :(d^-1*(a^2+b^2)*sin(c+d*x)+-1//3*d^-1*sin(c+d*x)^3*(b^2+2*a^2)+1//5*a^2*d^-1*sin(c+d*x)^5+3//4*a*b*x+(1/2)*a*b*d^-1*cos(c+d*x)^3*sin(c+d*x)+3//4*a*b*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^3, x) == :(-1//30*b^-1*d^-1*(-16*b^4+3*a^4+-52*a^2*b^2)*tan(c+d*x)+1//5*b^-1*d^-1*(a+b*sec(c+d*x))^4*tan(c+d*x)+1//8*a*d^-1*(4*a^2+9*b^2)*arctanh(sin(c+d*x))+-1//20*a*b^-1*d^-1*(a+b*sec(c+d*x))^3*tan(c+d*x)+-1//60*b^-1*d^-1*(a+b*sec(c+d*x))^2*(-16*b^2+3*a^2)*tan(c+d*x)+-1//120*a*d^-1*(-71*b^2+6*a^2)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^2, x) == :(1//4*d^-1*(a+b*sec(c+d*x))^3*tan(c+d*x)+(1/2)*a*d^-1*(a^2+4*b^2)*tan(c+d*x)+1//4*a*d^-1*(a+b*sec(c+d*x))^2*tan(c+d*x)+3//8*b*d^-1*(b^2+4*a^2)*arctanh(sin(c+d*x))+1//8*b*d^-1*(2*a^2+3*b^2)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x), x) == :((1/2)*a*d^-1*(2*a^2+3*b^2)*arctanh(sin(c+d*x))+1//3*b*d^-1*(a+b*sec(c+d*x))^2*tan(c+d*x)+2//3*b*d^-1*(b^2+4*a^2)*tan(c+d*x)+5//6*a*b^2*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^3, x) == :(x*a^3+(1/2)*b*d^-1*(b^2+6*a^2)*arctanh(sin(c+d*x))+(1/2)*b^2*d^-1*(a+b*sec(c+d*x))*tan(c+d*x)+5//2*a*b^2*d^-1*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x), x) == :(3*b*x*a^2+a*d^-1*(a^2+-1*b^2)*sin(c+d*x)+b^2*d^-1*(a+b*sec(c+d*x))*sin(c+d*x)+3*a*b^2*d^-1*arctanh(sin(c+d*x)))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^2, x) == :(b^3*d^-1*arctanh(sin(c+d*x))+(1/2)*a*x*(a^2+6*b^2)+5//2*b*a^2*d^-1*sin(c+d*x)+(1/2)*a^2*d^-1*(a+b*sec(c+d*x))*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^3, x) == :((1/2)*b*x*(2*b^2+3*a^2)+1//3*a*d^-1*(2*a^2+9*b^2)*sin(c+d*x)+1//3*a^2*d^-1*cos(c+d*x)^2*(a+b*sec(c+d*x))*sin(c+d*x)+7//6*b*a^2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^4, x) == :(3//8*a*x*(a^2+4*b^2)+-3//4*b*a^2*d^-1*sin(c+d*x)^3+1//4*b*d^-1*(4*b^2+11*a^2)*sin(c+d*x)+1//4*a^2*d^-1*cos(c+d*x)^3*(a+b*sec(c+d*x))*sin(c+d*x)+3//8*a*d^-1*(a^2+4*b^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^5, x) == :(1//8*b*x*(4*b^2+9*a^2)+-1//15*a*d^-1*sin(c+d*x)^3*(4*a^2+15*b^2)+1//5*a*d^-1*(4*a^2+15*b^2)*sin(c+d*x)+1//5*a^2*d^-1*cos(c+d*x)^4*(a+b*sec(c+d*x))*sin(c+d*x)+1//8*b*d^-1*(4*b^2+9*a^2)*cos(c+d*x)*sin(c+d*x)+11//20*b*a^2*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^6, x) == :(1//16*a*x*(5*a^2+18*b^2)+-1//3*b*d^-1*sin(c+d*x)^3*(b^2+5*a^2)+1//6*b*d^-1*(6*b^2+17*a^2)*sin(c+d*x)+13//30*b*a^2*d^-1*sin(c+d*x)^5+1//6*a^2*d^-1*cos(c+d*x)^5*(a+b*sec(c+d*x))*sin(c+d*x)+1//16*a*d^-1*(5*a^2+18*b^2)*cos(c+d*x)*sin(c+d*x)+1//24*a*d^-1*cos(c+d*x)^3*(5*a^2+18*b^2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*sec(c+d*x)^3, x) == :(1//16*d^-1*(5*b^4+8*a^4+36*a^2*b^2)*arctanh(sin(c+d*x))+-1//240*d^-1*(-75*b^4+8*a^4+-178*a^2*b^2)*sec(c+d*x)*tan(c+d*x)+1//6*b^-1*d^-1*(a+b*sec(c+d*x))^5*tan(c+d*x)+-1//30*a*b^-1*d^-1*(a+b*sec(c+d*x))^4*tan(c+d*x)+-1//60*a*b^-1*d^-1*(-128*b^4+4*a^4+-121*a^2*b^2)*tan(c+d*x)+-1//120*b^-1*d^-1*(a+b*sec(c+d*x))^3*(-25*b^2+4*a^2)*tan(c+d*x)+-1//120*a*b^-1*d^-1*(a+b*sec(c+d*x))^2*(-53*b^2+4*a^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*sec(c+d*x)^2, x) == :(1//5*d^-1*(a+b*sec(c+d*x))^4*tan(c+d*x)+1//15*d^-1*(6*a^4+8*b^4+56*a^2*b^2)*tan(c+d*x)+1//5*a*d^-1*(a+b*sec(c+d*x))^3*tan(c+d*x)+1//15*d^-1*(a+b*sec(c+d*x))^2*(3*a^2+4*b^2)*tan(c+d*x)+(1/2)*a*b*d^-1*(3*b^2+4*a^2)*arctanh(sin(c+d*x))+1//30*a*b*d^-1*(6*a^2+29*b^2)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*sec(c+d*x), x) == :(1//8*d^-1*(3*b^4+8*a^4+24*a^2*b^2)*arctanh(sin(c+d*x))+1//4*b*d^-1*(a+b*sec(c+d*x))^3*tan(c+d*x)+1//6*a*b*d^-1*(16*b^2+19*a^2)*tan(c+d*x)+1//24*b^2*d^-1*(9*b^2+26*a^2)*sec(c+d*x)*tan(c+d*x)+7//12*a*b*d^-1*(a+b*sec(c+d*x))^2*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^4, x) == :(x*a^4+1//3*b^2*d^-1*(a+b*sec(c+d*x))^2*tan(c+d*x)+1//3*b^2*d^-1*(2*b^2+17*a^2)*tan(c+d*x)+2*a*b*d^-1*(b^2+2*a^2)*arctanh(sin(c+d*x))+4//3*a*b^3*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x), x) == :(4*b*x*a^3+(1/2)*a^2*d^-1*(-1*b^2+2*a^2)*sin(c+d*x)+(1/2)*b^2*d^-1*(a+b*sec(c+d*x))^2*sin(c+d*x)+(1/2)*b^2*d^-1*(b^2+12*a^2)*arctanh(sin(c+d*x))+3*a*b^3*d^-1*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^2, x) == :((1/2)*x*a^2*(a^2+12*b^2)+3*b*a^3*d^-1*sin(c+d*x)+4*a*b^3*d^-1*arctanh(sin(c+d*x))+-1//2*b^2*d^-1*(a^2+-2*b^2)*tan(c+d*x)+(1/2)*a^2*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^3, x) == :(b^4*d^-1*arctanh(sin(c+d*x))+2*a*b*x*(a^2+2*b^2)+1//3*a^2*d^-1*(2*a^2+17*b^2)*sin(c+d*x)+1//3*a^2*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^2*sin(c+d*x)+4//3*b*a^3*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^4, x) == :(x*(b^4+3//8*a^4+3*a^2*b^2)+1//4*a^2*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^3*sin(c+d*x)+1//8*a^2*d^-1*(3*a^2+22*b^2)*cos(c+d*x)*sin(c+d*x)+4//3*a*b*d^-1*(2*a^2+3*b^2)*sin(c+d*x)+5//6*b*a^3*d^-1*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^5, x) == :(1//5*d^-1*(4*a^4+5*b^4+29*a^2*b^2)*sin(c+d*x)+(1/2)*a*b*x*(3*a^2+4*b^2)+-1//15*a^2*d^-1*sin(c+d*x)^3*(4*a^2+27*b^2)+1//5*a^2*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^4*sin(c+d*x)+3//5*b*a^3*d^-1*cos(c+d*x)^3*sin(c+d*x)+(1/2)*a*b*d^-1*(3*a^2+4*b^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^6, x) == :(x*((1/2)*b^4+5//16*a^4+9//4*a^2*b^2)+1//16*d^-1*(5*a^4+8*b^4+36*a^2*b^2)*cos(c+d*x)*sin(c+d*x)+-4//15*a*b*d^-1*sin(c+d*x)^3*(4*a^2+5*b^2)+1//6*a^2*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^5*sin(c+d*x)+1//24*a^2*d^-1*cos(c+d*x)^3*(5*a^2+32*b^2)*sin(c+d*x)+4//5*a*b*d^-1*(4*a^2+5*b^2)*sin(c+d*x)+7//15*b*a^3*d^-1*cos(c+d*x)^4*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^5, x) == :(x*a^5+1//4*b^2*d^-1*(a+b*sec(c+d*x))^3*tan(c+d*x)+1//8*b*d^-1*(3*b^4+40*a^4+40*a^2*b^2)*arctanh(sin(c+d*x))+1//6*a*b^2*d^-1*(20*b^2+53*a^2)*tan(c+d*x)+1//24*b^3*d^-1*(9*b^2+58*a^2)*sec(c+d*x)*tan(c+d*x)+11//12*a*b^2*d^-1*(a+b*sec(c+d*x))^2*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-1*sec(c+d*x)^5, x) == :(1//3*b^-1*d^-1*sec(c+d*x)^2*tan(c+d*x)+1//3*b^-3*d^-1*(2*b^2+3*a^2)*tan(c+d*x)+-1//2*a*b^-4*d^-1*(b^2+2*a^2)*arctanh(sin(c+d*x))+-1//2*a*b^-2*d^-1*sec(c+d*x)*tan(c+d*x)+2*a^4*b^-4*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))^-1*sec(c+d*x)^4, x) == :((1/2)*b^-1*d^-1*sec(c+d*x)*tan(c+d*x)+(1/2)*b^-3*d^-1*(b^2+2*a^2)*arctanh(sin(c+d*x))+-1*a*b^-2*d^-1*tan(c+d*x)+-2*a^3*b^-3*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))^-1*sec(c+d*x)^3, x) == :(b^-1*d^-1*tan(c+d*x)+-1*a*b^-2*d^-1*arctanh(sin(c+d*x))+2*a^2*b^-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))^-1*sec(c+d*x)^2, x) == :(b^-1*d^-1*arctanh(sin(c+d*x))+-2*a*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))^-1*sec(c+d*x), x) == :(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))^-1, x) == :(x*a^-1+-2*b*a^-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))^-1*cos(c+d*x), x) == :(a^-1*d^-1*sin(c+d*x)+-1*b*x*a^-2+2*a^-2*b^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))^-1*cos(c+d*x)^2, x) == :((1/2)*x*a^-3*(a^2+2*b^2)+(1/2)*a^-1*d^-1*cos(c+d*x)*sin(c+d*x)+-1*b*a^-2*d^-1*sin(c+d*x)+-2*a^-3*b^3*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))^-1*cos(c+d*x)^3, x) == :(-1//2*b*x*a^-4*(a^2+2*b^2)+1//3*a^-1*d^-1*cos(c+d*x)^2*sin(c+d*x)+1//3*a^-3*d^-1*(2*a^2+3*b^2)*sin(c+d*x)+-1//2*b*a^-2*d^-1*cos(c+d*x)*sin(c+d*x)+2*a^-4*b^4*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))^-1*cos(c+d*x)^4, x) == :(1//8*x*a^-5*(3*a^4+8*b^4+4*a^2*b^2)+1//4*a^-1*d^-1*cos(c+d*x)^3*sin(c+d*x)+-1//3*b*a^-4*d^-1*(2*a^2+3*b^2)*sin(c+d*x)+-1//3*b*a^-2*d^-1*cos(c+d*x)^2*sin(c+d*x)+1//8*a^-3*d^-1*(3*a^2+4*b^2)*cos(c+d*x)*sin(c+d*x)+-2*a^-5*b^5*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*sec(c+d*x)^5, x) == :((1/2)*b^-4*d^-1*(b^2+6*a^2)*arctanh(sin(c+d*x))+(1/2)*b^-2*d^-1*(a^2+-1*b^2)^-1*(-1*b^2+3*a^2)*sec(c+d*x)*tan(c+d*x)+-1*a*b^-3*d^-1*(a^2+-1*b^2)^-1*(-2*b^2+3*a^2)*tan(c+d*x)+-1*a^2*b^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*sec(c+d*x)^2*tan(c+d*x)+-2*a^3*b^-4*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-4*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))^-2*sec(c+d*x)^4, x) == :(-2*a*b^-3*d^-1*arctanh(sin(c+d*x))+b^-2*d^-1*(a^2+-1*b^2)^-1*(-1*b^2+2*a^2)*tan(c+d*x)+-1*a^2*b^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*sec(c+d*x)*tan(c+d*x)+2*a^2*b^-3*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-3*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*sec(c+d*x)^3, x) == :(b^-2*d^-1*arctanh(sin(c+d*x))+-1*a^2*b^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*tan(c+d*x)+-2*a*b^-2*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(a^2+-2*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-2*sec(c+d*x)^2, x) == :(a*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*tan(c+d*x)+-2*b*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))^-2*sec(c+d*x), x) == :(-1*b*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*tan(c+d*x)+2*a*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))^-2, x) == :(x*a^-2+a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*tan(c+d*x)+-2*b*a^-2*d^-1*(a+b)^-3//2*(a+-1b)^-3//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*cos(c+d*x), x) == :(-2*b*x*a^-3+a^-2*d^-1*(a^2+-1*b^2)^-1*(a^2+-2*b^2)*sin(c+d*x)+a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*sin(c+d*x)+2*a^-3*b^2*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-2*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))^-2*cos(c+d*x)^2, x) == :((1/2)*x*a^-4*(a^2+6*b^2)+(1/2)*a^-2*d^-1*(a^2+-1*b^2)^-1*(a^2+-3*b^2)*cos(c+d*x)*sin(c+d*x)+-1*b*a^-3*d^-1*(a^2+-1*b^2)^-1*(-3*b^2+2*a^2)*sin(c+d*x)+a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*cos(c+d*x)*sin(c+d*x)+-2*a^-4*b^3*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-3*b^2+4*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-2*cos(c+d*x)^3, x) == :(-1*b*x*a^-5*(a^2+4*b^2)+1//3*a^-4*d^-1*(a^2+-1*b^2)^-1*(-12*b^4+2*a^4+7*a^2*b^2)*sin(c+d*x)+1//3*a^-2*d^-1*(a^2+-1*b^2)^-1*cos(c+d*x)^2*(a^2+-4*b^2)*sin(c+d*x)+a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*cos(c+d*x)^2*sin(c+d*x)+-1*b*a^-3*d^-1*(a^2+-1*b^2)^-1*(a^2+-2*b^2)*cos(c+d*x)*sin(c+d*x)+2*a^-5*b^4*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-4*b^2+5*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))^-3*sec(c+d*x)^5, x) == :(-3*a*b^-4*d^-1*arctanh(sin(c+d*x))+(1/2)*b^-3*d^-1*(a^2+-1*b^2)^-1*(-2*b^2+3*a^2)*tan(c+d*x)+3*a^2*b^-4*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(2*a^4+4*b^4+-5*a^2*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1//2*a^2*b^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*sec(c+d*x)^2*tan(c+d*x)+3//2*a^3*b^-3*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(a^2+-2*b^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*sec(c+d*x)^4, x) == :(b^-3*d^-1*arctanh(sin(c+d*x))+-1*a*b^-3*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(2*a^4+6*b^4+-5*a^2*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1//2*a^2*b^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*sec(c+d*x)*tan(c+d*x)+-1//2*a^2*b^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-5*b^2+2*a^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*sec(c+d*x)^3, x) == :(d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(a^2+2*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1//2*a^2*b^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*tan(c+d*x)+(1/2)*a*b^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(a^2+-4*b^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*sec(c+d*x)^2, x) == :(a*d^-1*(a+b*sec(c+d*x))^-2*(-2*b^2+2*a^2)^-1*tan(c+d*x)+(1/2)*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(a^2+2*b^2)*tan(c+d*x)+-3*a*b*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)))
@test integrate((a+b*sec(c+d*x))^-3*sec(c+d*x), x) == :(d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(b^2+2*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1*b*d^-1*(a+b*sec(c+d*x))^-2*(-2*b^2+2*a^2)^-1*tan(c+d*x)+-3//2*a*b*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3, x) == :(x*a^-3+(1/2)*a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*tan(c+d*x)+(1/2)*a^-2*b^2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-2*b^2+5*a^2)*tan(c+d*x)+-1*b*a^-3*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(2*b^4+6*a^4+-5*a^2*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-3*cos(c+d*x), x) == :(-3*b*x*a^-4+(1/2)*a^-3*d^-1*(a^2+-1*b^2)^-2*(2*a^4+6*b^4+-11*a^2*b^2)*sin(c+d*x)+(1/2)*a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*sin(c+d*x)+3*a^-4*b^2*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(2*b^4+4*a^4+-5*a^2*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+3//2*a^-2*b^2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-1*b^2+2*a^2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*cos(c+d*x)^2, x) == :((1/2)*x*a^-5*(a^2+12*b^2)+(1/2)*a^-3*d^-1*(a^2+-1*b^2)^-2*(a^4+6*b^4+-10*a^2*b^2)*cos(c+d*x)*sin(c+d*x)+-3//2*b*a^-4*d^-1*(a^2+-1*b^2)^-2*(2*a^4+4*b^4+-7*a^2*b^2)*sin(c+d*x)+(1/2)*a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*cos(c+d*x)*sin(c+d*x)+-1*a^-5*b^3*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(12*b^4+20*a^4+-29*a^2*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+(1/2)*a^-2*b^2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-4*b^2+7*a^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*sec(c+d*x)^6, x) == :(-4*a*b^-5*d^-1*arctanh(sin(c+d*x))+1//6*b^-4*d^-1*(a^2+-1*b^2)^-2*(6*b^4+12*a^4+-23*a^2*b^2)*tan(c+d*x)+a^2*b^-5*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(-20*b^6+8*a^6+-28*a^4*b^2+35*a^2*b^4)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+(1/2)*a^3*b^-4*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(4*a^4+12*b^4+-11*a^2*b^2)*tan(c+d*x)+-1//3*a^2*b^-1*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*sec(c+d*x)^3*tan(c+d*x)+-1//6*a^2*b^-2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*sec(c+d*x)^2*(-9*b^2+4*a^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*sec(c+d*x)^5, x) == :(b^-4*d^-1*arctanh(sin(c+d*x))+-1*a*b^-4*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(-8*b^6+2*a^6+-7*a^4*b^2+8*a^2*b^4)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1//3*a^2*b^-1*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*sec(c+d*x)^2*tan(c+d*x)+-1//6*a^2*b^-3*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(9*a^4+34*b^4+-28*a^2*b^2)*tan(c+d*x)+1//6*a^3*b^-3*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(-8*b^2+3*a^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*sec(c+d*x)^4, x) == :(-1*b*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(2*b^2+3*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1//3*a^2*b^-1*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*sec(c+d*x)*tan(c+d*x)+-1//6*a^2*b^-2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(-7*b^2+2*a^2)*tan(c+d*x)+1//6*a*b^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(2*a^4+18*b^4+-5*a^2*b^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*sec(c+d*x)^3, x) == :(a*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(a^2+4*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1//3*a^2*b^-1*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*tan(c+d*x)+1//6*b^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(a^4+-6*b^4+-10*a^2*b^2)*tan(c+d*x)+1//6*a*b^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(a^2+-6*b^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*sec(c+d*x)^2, x) == :(a*d^-1*(a+b*sec(c+d*x))^-3*(-3*b^2+3*a^2)^-1*tan(c+d*x)+1//6*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(2*a^2+3*b^2)*tan(c+d*x)+-1*b*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(b^2+4*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+1//6*a*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(2*a^2+13*b^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*sec(c+d*x), x) == :(-1*b*d^-1*(a+b*sec(c+d*x))^-3*(-3*b^2+3*a^2)^-1*tan(c+d*x)+a*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(2*a^2+3*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-5//6*a*b*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*tan(c+d*x)+-1//6*b*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(4*b^2+11*a^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4, x) == :(x*a^-4+1//3*a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*tan(c+d*x)+-1*b*a^-4*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(-2*b^6+8*a^6+-8*a^4*b^2+7*a^2*b^4)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+1//6*a^-3*b^2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(6*b^4+26*a^4+-17*a^2*b^2)*tan(c+d*x)+1//6*a^-2*b^2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(-3*b^2+8*a^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*cos(c+d*x), x) == :(-4*b*x*a^-5+1//6*a^-4*d^-1*(a^2+-1*b^2)^-3*(-24*b^6+6*a^6+-65*a^4*b^2+68*a^2*b^4)*sin(c+d*x)+1//3*a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*sin(c+d*x)+a^-5*b^2*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(-8*b^6+20*a^6+-35*a^4*b^2+28*a^2*b^4)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+(1/2)*a^-3*b^2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(4*b^4+12*a^4+-11*a^2*b^2)*sin(c+d*x)+1//6*a^-2*b^2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(-4*b^2+9*a^2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*cos(c+d*x)^2, x) == :((1/2)*x*a^-6*(a^2+20*b^2)+(1/2)*a^-4*d^-1*(a^2+-1*b^2)^-3*(a^6+-10*b^6+-23*a^4*b^2+27*a^2*b^4)*cos(c+d*x)*sin(c+d*x)+-1//6*b*a^-5*d^-1*(a^2+-1*b^2)^-3*(-60*b^6+24*a^6+-146*a^4*b^2+167*a^2*b^4)*sin(c+d*x)+-1*a^-6*b^3*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(-20*b^6+40*a^6+-84*a^4*b^2+69*a^2*b^4)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+1//3*a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*cos(c+d*x)*sin(c+d*x)+1//6*a^-3*b^2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(20*b^4+48*a^4+-53*a^2*b^2)*cos(c+d*x)*sin(c+d*x)+5//6*a^-2*b^2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(-1*b^2+2*a^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((3+5*sec(c+d*x))^-1, x) == :(-1//12*x+5//6*d^-1*arctan((3+cos(c+d*x))^-1*sin(c+d*x)))
@test integrate((3+5*sec(c+d*x))^-2, x) == :(29//576*x+35//288*d^-1*arctan((3+cos(c+d*x))^-1*sin(c+d*x))+-25//48*d^-1*(3+5*sec(c+d*x))^-1*tan(c+d*x))
@test integrate((3+5*sec(c+d*x))^-3, x) == :(-1007//55296*x+3055//27648*d^-1*arctan((3+cos(c+d*x))^-1*sin(c+d*x))+-125//4608*d^-1*(3+5*sec(c+d*x))^-1*tan(c+d*x)+-25//96*d^-1*(3+5*sec(c+d*x))^-2*tan(c+d*x))
@test integrate((3+5*sec(c+d*x))^-4, x) == :(21553//2654208*x+11215//1327104*d^-1*arctan((3+cos(c+d*x))^-1*sin(c+d*x))+-16925//221184*d^-1*(3+5*sec(c+d*x))^-1*tan(c+d*x)+-25//144*d^-1*(3+5*sec(c+d*x))^-3*tan(c+d*x)+-25//4608*d^-1*(3+5*sec(c+d*x))^-2*tan(c+d*x))
@test integrate((5+3*sec(c+d*x))^-1, x) == :(1//5*x+-3//20*d^-1*log(2*cos((1/2)*c+(1/2)*d*x)+sin((1/2)*c+(1/2)*d*x))+3//20*d^-1*log(-1*sin((1/2)*c+(1/2)*d*x)+2*cos((1/2)*c+(1/2)*d*x)))
@test integrate((5+3*sec(c+d*x))^-2, x) == :(1//25*x+-123//1600*d^-1*log(2*cos((1/2)*c+(1/2)*d*x)+sin((1/2)*c+(1/2)*d*x))+123//1600*d^-1*log(-1*sin((1/2)*c+(1/2)*d*x)+2*cos((1/2)*c+(1/2)*d*x))+9//80*d^-1*(5+3*sec(c+d*x))^-1*tan(c+d*x))
@test integrate((5+3*sec(c+d*x))^-3, x) == :(1//125*x+-8361//256000*d^-1*log(2*cos((1/2)*c+(1/2)*d*x)+sin((1/2)*c+(1/2)*d*x))+8361//256000*d^-1*log(-1*sin((1/2)*c+(1/2)*d*x)+2*cos((1/2)*c+(1/2)*d*x))+9//160*d^-1*(5+3*sec(c+d*x))^-2*tan(c+d*x)+963//12800*d^-1*(5+3*sec(c+d*x))^-1*tan(c+d*x))
@test integrate((5+3*sec(c+d*x))^-4, x) == :(1//625*x+-278151//20480000*d^-1*log(2*cos((1/2)*c+(1/2)*d*x)+sin((1/2)*c+(1/2)*d*x))+278151//20480000*d^-1*log(-1*sin((1/2)*c+(1/2)*d*x)+2*cos((1/2)*c+(1/2)*d*x))+3//80*d^-1*(5+3*sec(c+d*x))^-3*tan(c+d*x)+519//12800*d^-1*(5+3*sec(c+d*x))^-2*tan(c+d*x)+38733//1024000*d^-1*(5+3*sec(c+d*x))^-1*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^3, x) == :(2//5*b^-1*d^-1*(a+b*sec(c+d*x))^3//2*tan(c+d*x)+-4//15*a*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*tan(c+d*x)+1//15*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-9*b^2+2*a^2)*(-2b+2a)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//15*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(2a+9b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^2, x) == :(2//3*d^-1*(a+b*sec(c+d*x))^(1/2)*tan(c+d*x)+-1//3*b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+-2//3*a*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(a+-1b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^(1/2)*sec(c+d*x), x) == :(b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^3//2*sec(c+d*x)^4, x) == :(-8//63*a*b^-2*d^-1*(a+b*sec(c+d*x))^5//2*tan(c+d*x)+1//315*b^-2*d^-1*(a+b*sec(c+d*x))^3//2*(16*a^2+98*b^2)*tan(c+d*x)+2//9*b^-1*d^-1*(a+b*sec(c+d*x))^5//2*sec(c+d*x)*tan(c+d*x)+2//315*a*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(8*a^2+39*b^2)*tan(c+d*x)+-1//315*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-147*b^3+8*a^3+6*b*a^2+39*a*b^2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//315*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(8*a^4+147*b^4+33*a^2*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^3//2*sec(c+d*x)^3, x) == :(2//7*b^-1*d^-1*(a+b*sec(c+d*x))^5//2*tan(c+d*x)+-4//35*a*b^-1*d^-1*(a+b*sec(c+d*x))^3//2*tan(c+d*x)+-1//105*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*(-50*b^2+12*a^2)*tan(c+d*x)+1//105*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-25*b^2+6*a^2+57*a*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+4//105*a*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(a+-1b)*(-41*b^2+3*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^3//2*sec(c+d*x)^2, x) == :(2//5*d^-1*(a+b*sec(c+d*x))^3//2*tan(c+d*x)+2//5*a*d^-1*(a+b*sec(c+d*x))^(1/2)*tan(c+d*x)+-1//5*b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(a+-1b)*(-6b+2a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//5*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(a^2+3*b^2)*(-2a+2b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^3//2*sec(c+d*x), x) == :(2//3*b*d^-1*(a+b*sec(c+d*x))^(1/2)*tan(c+d*x)+-8//3*a*b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(a+-1b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//3*b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-1b+3a)*(-2b+2a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^5//2*sec(c+d*x)^4, x) == :(-8//99*a*b^-2*d^-1*(a+b*sec(c+d*x))^7//2*tan(c+d*x)+1//693*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(16*a^4+270*b^4+114*a^2*b^2)*tan(c+d*x)+1//693*b^-2*d^-1*(a+b*sec(c+d*x))^5//2*(16*a^2+162*b^2)*tan(c+d*x)+2//11*b^-1*d^-1*(a+b*sec(c+d*x))^7//2*sec(c+d*x)*tan(c+d*x)+2//693*a*b^-2*d^-1*(a+b*sec(c+d*x))^3//2*(8*a^2+67*b^2)*tan(c+d*x)+-1//693*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(8*a^4+135*b^4+-606*a*b^3+6*b*a^3+57*a^2*b^2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+-2//693*a*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(a+-1b)*(8*a^4+741*b^4+51*a^2*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^5//2*sec(c+d*x)^3, x) == :(2//9*b^-1*d^-1*(a+b*sec(c+d*x))^7//2*tan(c+d*x)+-4//63*a*b^-1*d^-1*(a+b*sec(c+d*x))^5//2*tan(c+d*x)+-1//315*b^-1*d^-1*(a+b*sec(c+d*x))^3//2*(-98*b^2+20*a^2)*tan(c+d*x)+-4//315*a*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*(-57*b^2+5*a^2)*tan(c+d*x)+1//315*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-147*b^4+10*a^4+-279*a^2*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//315*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(10*a^3+147*b^3+-114*a*b^2+165*b*a^2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^5//2*sec(c+d*x)^2, x) == :(2//7*d^-1*(a+b*sec(c+d*x))^5//2*tan(c+d*x)+1//21*d^-1*(a+b*sec(c+d*x))^(1/2)*(6*a^2+10*b^2)*tan(c+d*x)+2//7*a*d^-1*(a+b*sec(c+d*x))^3//2*tan(c+d*x)+-1//21*b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(3*a^2+5*b^2+-24*a*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+-2//21*a*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(a+-1b)*(3*a^2+29*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^5//2*sec(c+d*x), x) == :(2//5*b*d^-1*(a+b*sec(c+d*x))^3//2*tan(c+d*x)+16//15*a*b*d^-1*(a+b*sec(c+d*x))^(1/2)*tan(c+d*x)+1//15*b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(9*b^2+23*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//15*b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(9*b^2+15*a^2+-8*a*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-1//2*sec(c+d*x)^5, x) == :(1//105*b^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(48*a^2+50*b^2)*tan(c+d*x)+2//7*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^2*tan(c+d*x)+-12//35*a*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)*tan(c+d*x)+2//105*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(25*b^3+48*a^3+-12*b*a^2+44*a*b^2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+8//105*a*b^-5*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(a+-1b)*(11*b^2+12*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-1//2*sec(c+d*x)^4, x) == :(-8//15*a*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*tan(c+d*x)+2//5*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)*tan(c+d*x)+-2//15*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(8*a^2+9*b^2+-2*a*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//15*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(8*a^2+9*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-1//2*sec(c+d*x)^3, x) == :(2//3*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*tan(c+d*x)+2//3*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(b+2a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+4//3*a*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(a+-1b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-1//2*sec(c+d*x)^2, x) == :(-2*b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-1//2*sec(c+d*x), x) == :(2*b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3//2*sec(c+d*x)^5, x) == :(-2*a^2*b^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^2*tan(c+d*x)+-2//5*a*b^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*(-3*b^2+8*a^2)*tan(c+d*x)+1//5*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*(-2*b^2+12*a^2)*sec(c+d*x)*tan(c+d*x)+1//5*b^-5*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(-32*a^4+6*b^4+16*a^2*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+-1//5*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(b^2+4*a^2)*(6b+8a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3//2*sec(c+d*x)^4, x) == :(1//3*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*(-2*b^2+8*a^2)*tan(c+d*x)+-2*a^2*b^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)*tan(c+d*x)+1//3*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(b+4a)*(2b+4a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+2//3*a*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(-5*b^2+8*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3//2*sec(c+d*x)^3, x) == :(-2*a^2*b^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*tan(c+d*x)+b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(-4*a^2+2*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+-1*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(2b+4a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3//2*sec(c+d*x)^2, x) == :(2*a*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*tan(c+d*x)+2*b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+2*a*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3//2*sec(c+d*x), x) == :(-2*b*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*tan(c+d*x)+-2*b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+2*b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^5, x) == :(1//3*b^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*(-2*b^2+4*a^2)*tan(c+d*x)+-2//3*a^2*b^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*sec(c+d*x)^2*tan(c+d*x)+4//3*a^3*b^-3*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*(-5*b^2+3*a^2)*tan(c+d*x)+b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(-3b+3a)^-1*(-2*b^4+32*a^4+-32*a^2*b^2+-18*a*b^3+24*b*a^3)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+8*a*b^-5*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(-3b+3a)^-1*(2*b^4+4*a^4+-7*a^2*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^4, x) == :(-8//3*a^2*b^-2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*(a^2+-2*b^2)*tan(c+d*x)+-2//3*a^2*b^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*sec(c+d*x)*tan(c+d*x)+b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(-3b+3a)^-1*(-16*a^4+-6*b^4+30*a^2*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+-1*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(-3b+3a)^-1*(-6*b^3+16*a^3+-18*a*b^2+12*b*a^2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^3, x) == :(-2//3*a^2*b^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*tan(c+d*x)+4//3*a*b^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*(a^2+-3*b^2)*tan(c+d*x)+b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(-3b+3a)^-1*(-6*b^2+4*a^2+6*a*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+4*a*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(-3b+3a)^-1*(a^2+-3*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^2, x) == :(2*a*d^-1*(a+b*sec(c+d*x))^-3//2*(-3*b^2+3*a^2)^-1*tan(c+d*x)+1//3*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*(2*a^2+6*b^2)*tan(c+d*x)+b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(-3b+3a)^-1*(-6b+2a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(-3b+3a)^-1*(2*a^2+6*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x), x) == :(-2*b*d^-1*(a+b*sec(c+d*x))^-3//2*(-3*b^2+3*a^2)^-1*tan(c+d*x)+-8//3*a*b*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*tan(c+d*x)+b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(-3b+3a)^-1*(-2b+6a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+-8*a*b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(-3b+3a)^-1*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate(sec(c+d*x)^5//2*(a+b*sec(c+d*x)), x) == :(2//3*a*d^-1*sec(c+d*x)^3//2*sin(c+d*x)+2//5*b*d^-1*sec(c+d*x)^5//2*sin(c+d*x)+6//5*b*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+-6//5*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^3//2*(a+b*sec(c+d*x)), x) == :(2*a*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+2//3*b*d^-1*sec(c+d*x)^3//2*sin(c+d*x)+-2*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^(1/2)*(a+b*sec(c+d*x)), x) == :(2*b*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+-2*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^-1//2*(a+b*sec(c+d*x)), x) == :(2*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^-3//2*(a+b*sec(c+d*x)), x) == :(2//3*a*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+2*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^-5//2*(a+b*sec(c+d*x)), x) == :(2//3*b*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+2//5*a*d^-1*sec(c+d*x)^-3//2*sin(c+d*x)+2//3*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+6//5*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^-7//2*(a+b*sec(c+d*x)), x) == :(2//5*b*d^-1*sec(c+d*x)^-3//2*sin(c+d*x)+2//7*a*d^-1*sec(c+d*x)^-5//2*sin(c+d*x)+10//21*a*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+6//5*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+10//21*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^5//2, x) == :(1//21*d^-1*sec(c+d*x)^3//2*(10*b^2+14*a^2)*sin(c+d*x)+2//7*b^2*d^-1*sec(c+d*x)^7//2*sin(c+d*x)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(10*b^2+14*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+4//5*a*b*d^-1*sec(c+d*x)^5//2*sin(c+d*x)+12//5*a*b*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+-12//5*a*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^3//2, x) == :(1//5*d^-1*sec(c+d*x)^(1/2)*(6*b^2+10*a^2)*sin(c+d*x)+2//5*b^2*d^-1*sec(c+d*x)^5//2*sin(c+d*x)+-1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(6*b^2+10*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//3*a*b*d^-1*sec(c+d*x)^3//2*sin(c+d*x)+4//3*a*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^(1/2), x) == :(2//3*b^2*d^-1*sec(c+d*x)^3//2*sin(c+d*x)+4*a*b*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+1//3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*b^2+6*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-4*a*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^-1//2, x) == :(2*b^2*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-2*b^2+2*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4*a*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^-3//2, x) == :(2//3*a^2*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+1//3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*a^2+6*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+4*a*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^-5//2, x) == :(2//5*a^2*d^-1*sec(c+d*x)^-3//2*sin(c+d*x)+1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(6*a^2+10*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//3*a*b*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+4//3*a*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^-7//2, x) == :(1//21*d^-1*sec(c+d*x)^-1//2*(10*a^2+14*b^2)*sin(c+d*x)+2//7*a^2*d^-1*sec(c+d*x)^-5//2*sin(c+d*x)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(10*a^2+14*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+4//5*a*b*d^-1*sec(c+d*x)^-3//2*sin(c+d*x)+12//5*a*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^3//2, x) == :(2//5*a*d^-1*sec(c+d*x)^(1/2)*(5*a^2+9*b^2)*sin(c+d*x)+2//7*b^2*d^-1*sec(c+d*x)^5//2*(a+b*sec(c+d*x))*sin(c+d*x)+2//21*b*d^-1*sec(c+d*x)^3//2*(5*b^2+21*a^2)*sin(c+d*x)+32//35*a*b^2*d^-1*sec(c+d*x)^5//2*sin(c+d*x)+-2//5*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5*a^2+9*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//21*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5*b^2+21*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^(1/2), x) == :(2//5*b^2*d^-1*sec(c+d*x)^3//2*(a+b*sec(c+d*x))*sin(c+d*x)+6//5*b*d^-1*sec(c+d*x)^(1/2)*(b^2+5*a^2)*sin(c+d*x)+8//5*a*b^2*d^-1*sec(c+d*x)^3//2*sin(c+d*x)+2*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(a^2+b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-6//5*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(b^2+5*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^-1//2, x) == :(2//3*b^2*d^-1*sec(c+d*x)^(1/2)*(a+b*sec(c+d*x))*sin(c+d*x)+16//3*a*b^2*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+2*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(a^2+-3*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(b^2+9*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^-3//2, x) == :(-2//3*b*d^-1*sec(c+d*x)^(1/2)*(a^2+-3*b^2)*sin(c+d*x)+2//3*a^2*d^-1*sec(c+d*x)^-1//2*(a+b*sec(c+d*x))*sin(c+d*x)+2*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-1*b^2+3*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(a^2+9*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^-5//2, x) == :(2//5*a^2*d^-1*sec(c+d*x)^-3//2*(a+b*sec(c+d*x))*sin(c+d*x)+8//5*b*a^2*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+2*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(a^2+b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+6//5*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(a^2+5*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^-7//2, x) == :(2//7*a^2*d^-1*sec(c+d*x)^-5//2*(a+b*sec(c+d*x))*sin(c+d*x)+2//21*a*d^-1*sec(c+d*x)^-1//2*(5*a^2+21*b^2)*sin(c+d*x)+32//35*b*a^2*d^-1*sec(c+d*x)^-3//2*sin(c+d*x)+2//5*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5*b^2+9*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//21*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5*a^2+21*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^-9//2, x) == :(2//9*a^2*d^-1*sec(c+d*x)^-7//2*(a+b*sec(c+d*x))*sin(c+d*x)+2//21*b*d^-1*sec(c+d*x)^-1//2*(7*b^2+15*a^2)*sin(c+d*x)+2//45*a*d^-1*sec(c+d*x)^-3//2*(7*a^2+27*b^2)*sin(c+d*x)+40//63*b*a^2*d^-1*sec(c+d*x)^-5//2*sin(c+d*x)+2//15*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(7*a^2+27*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//21*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(7*b^2+15*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+b*sec(c+d*x))^4*sec(c+d*x)^3//2, x) == :(1//15*d^-1*sec(c+d*x)^(1/2)*(14*b^4+30*a^4+108*a^2*b^2)*sin(c+d*x)+-1//15*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(14*b^4+30*a^4+108*a^2*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//9*b^2*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^5//2*sin(c+d*x)+14//45*b^2*d^-1*sec(c+d*x)^5//2*(b^2+7*a^2)*sin(c+d*x)+44//63*a*b^3*d^-1*sec(c+d*x)^7//2*sin(c+d*x)+8//21*a*b*d^-1*sec(c+d*x)^3//2*(5*b^2+7*a^2)*sin(c+d*x)+8//21*a*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5*b^2+7*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+b*sec(c+d*x))^4*sec(c+d*x)^(1/2), x) == :(1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(10*b^4+42*a^4+84*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//7*b^2*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^3//2*sin(c+d*x)+2//21*b^2*d^-1*sec(c+d*x)^3//2*(5*b^2+39*a^2)*sin(c+d*x)+36//35*a*b^3*d^-1*sec(c+d*x)^5//2*sin(c+d*x)+8//5*a*b*d^-1*sec(c+d*x)^(1/2)*(3*b^2+5*a^2)*sin(c+d*x)+-8//5*a*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3*b^2+5*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+b*sec(c+d*x))^4*sec(c+d*x)^-1//2, x) == :(1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-6*b^4+10*a^4+-60*a^2*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//5*b^2*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^(1/2)*sin(c+d*x)+2//5*b^2*d^-1*sec(c+d*x)^(1/2)*(3*b^2+29*a^2)*sin(c+d*x)+28//15*a*b^3*d^-1*sec(c+d*x)^3//2*sin(c+d*x)+8//3*a*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(b^2+3*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+b*sec(c+d*x))^4*sec(c+d*x)^-3//2, x) == :(-2//3*b^2*d^-1*sec(c+d*x)^3//2*(a^2+-1*b^2)*sin(c+d*x)+1//3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*a^4+2*b^4+36*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*a^2*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^-1//2*sin(c+d*x)+-4//3*a*b*d^-1*sec(c+d*x)^(1/2)*(a^2+-6*b^2)*sin(c+d*x)+8*a*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(a^2+-1*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+b*sec(c+d*x))^4*sec(c+d*x)^-5//2, x) == :(-2//5*b^2*d^-1*sec(c+d*x)^(1/2)*(a^2+-5*b^2)*sin(c+d*x)+1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-10*b^4+6*a^4+60*a^2*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//5*a^2*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^-3//2*sin(c+d*x)+28//15*b*a^3*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+8//3*a*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(a^2+3*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+b*sec(c+d*x))^4*sec(c+d*x)^-7//2, x) == :(1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(10*a^4+42*b^4+84*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//7*a^2*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^-5//2*sin(c+d*x)+2//21*a^2*d^-1*sec(c+d*x)^-1//2*(5*a^2+39*b^2)*sin(c+d*x)+36//35*b*a^3*d^-1*sec(c+d*x)^-3//2*sin(c+d*x)+8//5*a*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3*a^2+5*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+b*sec(c+d*x))^4*sec(c+d*x)^-9//2, x) == :(1//15*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(14*a^4+30*b^4+108*a^2*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//9*a^2*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^-7//2*sin(c+d*x)+14//45*a^2*d^-1*sec(c+d*x)^-3//2*(a^2+7*b^2)*sin(c+d*x)+44//63*b*a^3*d^-1*sec(c+d*x)^-5//2*sin(c+d*x)+8//21*a*b*d^-1*sec(c+d*x)^-1//2*(5*a^2+7*b^2)*sin(c+d*x)+8//21*a*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5*a^2+7*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+b*sec(c+d*x))^4*sec(c+d*x)^-11//2, x) == :(1//231*d^-1*sec(c+d*x)^-1//2*(90*a^4+154*b^4+660*a^2*b^2)*sin(c+d*x)+1//231*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(90*a^4+154*b^4+660*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//11*a^2*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^-9//2*sin(c+d*x)+2//77*a^2*d^-1*sec(c+d*x)^-5//2*(9*a^2+59*b^2)*sin(c+d*x)+52//99*b*a^3*d^-1*sec(c+d*x)^-7//2*sin(c+d*x)+8//45*a*b*d^-1*sec(c+d*x)^-3//2*(7*a^2+9*b^2)*sin(c+d*x)+8//15*a*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(7*a^2+9*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2, x) == :(2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2, x) == :(2//3*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*sin(c+d*x)+1//3*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-2*b^2+2*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2//3*b*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2, x) == :(2//5*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*sin(c+d*x)+2//15*b*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*sin(c+d*x)+1//15*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(-4*b^2+18*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+-4//15*b*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(a^2+-1*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-7//2, x) == :(2//7*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*sin(c+d*x)+1//105*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(-8*b^2+50*a^2)*sin(c+d*x)+2//35*b*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*sin(c+d*x)+1//105*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-16*b^4+50*a^4+-34*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2//105*b*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(8*b^2+19*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^3//2*sec(c+d*x)^-3//2, x) == :(2//3*a*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*sin(c+d*x)+1//3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-2*b^2+2*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+8//3*b*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^3//2*sec(c+d*x)^-5//2, x) == :(2//5*a*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*sin(c+d*x)+4//5*b*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*sin(c+d*x)+1//5*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(2*b^2+6*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2//5*b*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(a^2+-1*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^3//2*sec(c+d*x)^-7//2, x) == :(2//7*a*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*sin(c+d*x)+16//35*b*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*sin(c+d*x)+1//105*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(6*b^2+50*a^2)*sin(c+d*x)+1//105*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(12*b^4+50*a^4+-62*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+4//105*b*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(-3*b^2+41*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^5//2*sec(c+d*x)^-5//2, x) == :(2//5*a^2*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*sin(c+d*x)+1//15*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(18*a^2+46*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+22//15*a*b*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*sin(c+d*x)+16//15*b*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(a^2+-1*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^5//2*sec(c+d*x)^-7//2, x) == :(1//21*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(10*a^2+18*b^2)*sin(c+d*x)+2//7*a^2*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*sin(c+d*x)+6//7*a*b*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*sin(c+d*x)+1//21*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-6*b^4+10*a^4+-4*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2//21*b*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(3*b^2+29*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^5//2*sec(c+d*x)^-9//2, x) == :(1//315*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*(98*a^2+150*b^2)*sin(c+d*x)+2//9*a^2*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-7//2*sin(c+d*x)+38//63*a*b*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*sin(c+d*x)+1//315*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(-20*b^4+294*a^4+558*a^2*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2//315*b*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(5*b^2+163*a^2)*sin(c+d*x)+4//315*b*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(5*b^4+57*a^4+-62*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2), x) == :(2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2, x) == :(2*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+-2*b*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2, x) == :(2//3*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*sin(c+d*x)+-4//3*b*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(2*a^2+4*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-1//2*sec(c+d*x)^-5//2, x) == :(2//5*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*sin(c+d*x)+-8//15*b*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*sin(c+d*x)+1//15*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(16*b^2+18*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+-2//15*b*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(7*a^2+8*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-3//2*sec(c+d*x)^3//2, x) == :(-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*sec(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2*a*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3//2*sec(c+d*x)^(1/2), x) == :(-2*b*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+2*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2*b*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*sec(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-3//2*sec(c+d*x)^-1//2, x) == :(-4*b*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2*a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*sec(c+d*x)^-1//2*(-4*b^2+2*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-3//2*sec(c+d*x)^-3//2, x) == :(2*a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^-1//2*sin(c+d*x)+1//3*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(2*a^2+16*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*sec(c+d*x)^-1//2*(-8*b^2+2*a^2)*sin(c+d*x)+-2//3*b*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*sec(c+d*x)^-1//2*(-8*b^2+5*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-3//2*sec(c+d*x)^-5//2, x) == :(2*a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^-3//2*sin(c+d*x)+1//5*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*sec(c+d*x)^-3//2*(-12*b^2+2*a^2)*sin(c+d*x)+-8//5*b*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(a^2+4*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+-2//5*b*a^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*sec(c+d*x)^-1//2*(-8*b^2+3*a^2)*sin(c+d*x)+1//5*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*sec(c+d*x)^-1//2*(-32*b^4+6*a^4+16*a^2*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^5//2, x) == :(2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(-3*b^2+3*a^2)^-1*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+-2//3*a^2*b^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+8//3*b*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*sec(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2//3*a*b^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*sec(c+d*x)^(1/2)*(a^2+-5*b^2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^3//2, x) == :(2*a*d^-1*(a+b*sec(c+d*x))^-3//2*(-3*b^2+3*a^2)^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+1//3*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*sec(c+d*x)^(1/2)*(4*a^2+4*b^2)*sin(c+d*x)+-2//3*b*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+-1//3*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*sec(c+d*x)^-1//2*(2*b^2+6*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^(1/2), x) == :(-2*b*d^-1*(a+b*sec(c+d*x))^-3//2*(-3*b^2+3*a^2)^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+-2//3*b*a^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*sec(c+d*x)^(1/2)*(-1*b^2+5*a^2)*sin(c+d*x)+1//3*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*(-4*b^2+6*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+4//3*b*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*sec(c+d*x)^-1//2*(-1*b^2+3*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^-1//2, x) == :(2//3*a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+1//3*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*sec(c+d*x)^-1//2*(6*a^4+16*b^4+-30*a^2*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+8//3*a^-2*b^2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*sec(c+d*x)^(1/2)*(-1*b^2+2*a^2)*sin(c+d*x)+-2//3*b*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*(-8*b^2+9*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^-3//2, x) == :(1//3*a^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*sec(c+d*x)^-1//2*(2*a^4+16*b^4+-26*a^2*b^2)*sin(c+d*x)+2//3*a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*sec(c+d*x)^-1//2*sin(c+d*x)+1//3*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*(-32*b^4+2*a^4+32*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+4//3*a^-2*b^2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*sec(c+d*x)^-1//2*(-3*b^2+5*a^2)*sin(c+d*x)+-8//3*b*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*sec(c+d*x)^-1//2*(2*a^4+4*b^4+-7*a^2*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^-5//2, x) == :(1//15*a^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*sec(c+d*x)^-3//2*(6*a^4+96*b^4+-142*a^2*b^2)*sin(c+d*x)+2//3*a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*sec(c+d*x)^-3//2*sin(c+d*x)+-4//15*b*a^-4*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*sec(c+d*x)^-1//2*(7*a^4+32*b^4+-49*a^2*b^2)*sin(c+d*x)+1//15*a^-5*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*sec(c+d*x)^-1//2*(18*a^6+256*b^6+-424*a^2*b^4+110*a^4*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+8//3*a^-2*b^2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*sec(c+d*x)^-3//2*(-2*b^2+3*a^2)*sin(c+d*x)+-2//15*b*a^-5*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*(-128*b^4+17*a^4+116*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((2+3*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2, x) == :(5^(1/2)*d^-1*(2+3*sec(c+d*x))^(1/2)*(3+2*cos(c+d*x))^-1//2*sec(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,4//5)+-3//5*5^(1/2)*d^-1*(2+3*sec(c+d*x))^-1//2*(3+2*cos(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,4//5))
@test integrate((-2+3*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2, x) == :(-1*d^-1*(-2+3*sec(c+d*x))^(1/2)*(3+-2*cos(c+d*x))^-1//2*sec(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,-4)+3*d^-1*(-2+3*sec(c+d*x))^-1//2*(3+-2*cos(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,-4))
@test integrate((2+-3*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2, x) == :(d^-1*(2+-3*sec(c+d*x))^(1/2)*(3+-2*cos(c+d*x))^-1//2*sec(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,-4)+3*d^-1*(2+-3*sec(c+d*x))^-1//2*(3+-2*cos(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,-4))
@test integrate((-2+-3*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2, x) == :(-1*5^(1/2)*d^-1*(-2+-3*sec(c+d*x))^(1/2)*(3+2*cos(c+d*x))^-1//2*sec(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,4//5)+-3//5*5^(1/2)*d^-1*(-2+-3*sec(c+d*x))^-1//2*(3+2*cos(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,4//5))
@test integrate((3+2*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2, x) == :(-4//15*5^(1/2)*d^-1*(2+3*cos(c+d*x))^(1/2)*(3+2*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,6//5)+2//3*5^(1/2)*d^-1*(2+3*cos(c+d*x))^-1//2*(3+2*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,6//5))
@test integrate((3+-2*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2, x) == :(2//3*d^-1*(-2+3*cos(c+d*x))^-1//2*(3+-2*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,6)+4//3*d^-1*(-2+3*cos(c+d*x))^(1/2)*(3+-2*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,6))
@test integrate((-3+2*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2, x) == :(-2//3*5^(1/2)*d^-1*(-3+2*sec(c+d*x))^(1/2)*(2+-3*cos(c+d*x))^-1//2*sec(c+d*x)^-1//2*Elliptic.E((1/2)*pi+(1/2)*c+(1/2)*d*x,6//5)+4//15*5^(1/2)*d^-1*(-3+2*sec(c+d*x))^-1//2*(2+-3*cos(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*pi+(1/2)*c+(1/2)*d*x,6//5))
@test integrate((-3+-2*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2, x) == :(-4//3*d^-1*(-3+-2*sec(c+d*x))^-1//2*(-2+-3*cos(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*pi+(1/2)*c+(1/2)*d*x,6)+-2//3*d^-1*(-3+-2*sec(c+d*x))^(1/2)*(-2+-3*cos(c+d*x))^-1//2*sec(c+d*x)^-1//2*Elliptic.E((1/2)*pi+(1/2)*c+(1/2)*d*x,6))
@test integrate((2+3*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2), x) == :(2//5*5^(1/2)*d^-1*(2+3*sec(c+d*x))^-1//2*(3+2*cos(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,4//5))
@test integrate((-2+3*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2), x) == :(2*d^-1*(-2+3*sec(c+d*x))^-1//2*(3+-2*cos(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,-4))
@test integrate((2+-3*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2), x) == :(2*d^-1*(2+-3*sec(c+d*x))^-1//2*(3+-2*cos(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,-4))
@test integrate((-2+-3*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2), x) == :(2//5*5^(1/2)*d^-1*(-2+-3*sec(c+d*x))^-1//2*(3+2*cos(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,4//5))
@test integrate((3+2*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2), x) == :(2//5*5^(1/2)*d^-1*(2+3*cos(c+d*x))^(1/2)*(3+2*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,6//5))
@test integrate((3+-2*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2), x) == :(2*d^-1*(-2+3*cos(c+d*x))^(1/2)*(3+-2*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,6))
@test integrate((-3+2*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2), x) == :(2//5*5^(1/2)*d^-1*(-3+2*sec(c+d*x))^-1//2*(2+-3*cos(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*pi+(1/2)*c+(1/2)*d*x,6//5))
@test integrate((-3+-2*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2), x) == :(2*d^-1*(-3+-2*sec(c+d*x))^-1//2*(-2+-3*cos(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*pi+(1/2)*c+(1/2)*d*x,6))
@test integrate(cos(c+d*x)^9//2*(a+b*sec(c+d*x)), x) == :(10//21*b*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+14//15*a*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//7*b*d^-1*cos(c+d*x)^5//2*sin(c+d*x)+2//9*a*d^-1*cos(c+d*x)^7//2*sin(c+d*x)+10//21*b*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+14//45*a*d^-1*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate(cos(c+d*x)^7//2*(a+b*sec(c+d*x)), x) == :(6//5*b*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+10//21*a*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*b*d^-1*cos(c+d*x)^3//2*sin(c+d*x)+2//7*a*d^-1*cos(c+d*x)^5//2*sin(c+d*x)+10//21*a*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate(cos(c+d*x)^5//2*(a+b*sec(c+d*x)), x) == :(2//3*b*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+6//5*a*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*b*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+2//5*a*d^-1*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate(cos(c+d*x)^3//2*(a+b*sec(c+d*x)), x) == :(2*b*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate(cos(c+d*x)^(1/2)*(a+b*sec(c+d*x)), x) == :(2*a*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*b*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(cos(c+d*x)^-1//2*(a+b*sec(c+d*x)), x) == :(-2*b*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*a*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*b*d^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate(cos(c+d*x)^-3//2*(a+b*sec(c+d*x)), x) == :(-2*a*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*b*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*a*d^-1*cos(c+d*x)^-1//2*sin(c+d*x)+2//3*b*d^-1*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate(cos(c+d*x)^-5//2*(a+b*sec(c+d*x)), x) == :(-6//5*b*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*cos(c+d*x)^-3//2*sin(c+d*x)+2//5*b*d^-1*cos(c+d*x)^-5//2*sin(c+d*x)+6//5*b*d^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^9//2, x) == :(1//15*d^-1*(14*a^2+18*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//45*d^-1*cos(c+d*x)^3//2*(14*a^2+18*b^2)*sin(c+d*x)+2//9*a^2*d^-1*cos(c+d*x)^7//2*sin(c+d*x)+20//21*a*b*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+4//7*a*b*d^-1*cos(c+d*x)^5//2*sin(c+d*x)+20//21*a*b*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^7//2, x) == :(1//21*d^-1*(10*a^2+14*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*(10*a^2+14*b^2)*sin(c+d*x)+2//7*a^2*d^-1*cos(c+d*x)^5//2*sin(c+d*x)+12//5*a*b*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//5*a*b*d^-1*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^5//2, x) == :(1//5*d^-1*(6*a^2+10*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//5*a^2*d^-1*cos(c+d*x)^3//2*sin(c+d*x)+4//3*a*b*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+4//3*a*b*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^3//2, x) == :(1//3*d^-1*(2*a^2+6*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+4*a*b*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a^2*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^(1/2), x) == :(d^-1*(-2*b^2+2*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*b^2*d^-1*cos(c+d*x)^-1//2*sin(c+d*x)+4*a*b*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^-1//2, x) == :(1//3*d^-1*(2*b^2+6*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-4*a*b*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*b^2*d^-1*cos(c+d*x)^-3//2*sin(c+d*x)+4*a*b*d^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^-3//2, x) == :(-1//5*d^-1*(6*b^2+10*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*cos(c+d*x)^-1//2*(6*b^2+10*a^2)*sin(c+d*x)+2//5*b^2*d^-1*cos(c+d*x)^-5//2*sin(c+d*x)+4//3*a*b*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+4//3*a*b*d^-1*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^-5//2, x) == :(1//21*d^-1*(10*b^2+14*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-12//5*a*b*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^-3//2*(10*b^2+14*a^2)*sin(c+d*x)+2//7*b^2*d^-1*cos(c+d*x)^-7//2*sin(c+d*x)+4//5*a*b*d^-1*cos(c+d*x)^-5//2*sin(c+d*x)+12//5*a*b*d^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^9//2, x) == :(2//15*a*d^-1*(7*a^2+27*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//21*b*d^-1*(7*b^2+15*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//9*a^2*d^-1*cos(c+d*x)^7//2*(a+b*sec(c+d*x))*sin(c+d*x)+2//21*b*d^-1*cos(c+d*x)^(1/2)*(7*b^2+15*a^2)*sin(c+d*x)+2//45*a*d^-1*cos(c+d*x)^3//2*(7*a^2+27*b^2)*sin(c+d*x)+40//63*b*a^2*d^-1*cos(c+d*x)^5//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^7//2, x) == :(2//5*b*d^-1*(5*b^2+9*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//21*a*d^-1*(5*a^2+21*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//7*a^2*d^-1*cos(c+d*x)^5//2*(a+b*sec(c+d*x))*sin(c+d*x)+2//21*a*d^-1*cos(c+d*x)^(1/2)*(5*a^2+21*b^2)*sin(c+d*x)+32//35*b*a^2*d^-1*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^5//2, x) == :(2*b*d^-1*(a^2+b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+6//5*a*d^-1*(a^2+5*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//5*a^2*d^-1*cos(c+d*x)^3//2*(a+b*sec(c+d*x))*sin(c+d*x)+8//5*b*a^2*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^3//2, x) == :(2*b*d^-1*(-1*b^2+3*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*(a^2+9*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-2//3*b*d^-1*cos(c+d*x)^-1//2*(a^2+-3*b^2)*sin(c+d*x)+2//3*a^2*d^-1*cos(c+d*x)^(1/2)*(a+b*sec(c+d*x))*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^(1/2), x) == :(2*a*d^-1*(a^2+-3*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*b*d^-1*(b^2+9*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*b^2*d^-1*cos(c+d*x)^-1//2*(a+b*sec(c+d*x))*sin(c+d*x)+16//3*a*b^2*d^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^-1//2, x) == :(2*a*d^-1*(a^2+b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-6//5*b*d^-1*(b^2+5*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//5*b^2*d^-1*cos(c+d*x)^-3//2*(a+b*sec(c+d*x))*sin(c+d*x)+6//5*b*d^-1*cos(c+d*x)^-1//2*(b^2+5*a^2)*sin(c+d*x)+8//5*a*b^2*d^-1*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^-3//2, x) == :(-2//5*a*d^-1*(5*a^2+9*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//21*b*d^-1*(5*b^2+21*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*a*d^-1*cos(c+d*x)^-1//2*(5*a^2+9*b^2)*sin(c+d*x)+2//7*b^2*d^-1*cos(c+d*x)^-5//2*(a+b*sec(c+d*x))*sin(c+d*x)+2//21*b*d^-1*cos(c+d*x)^-3//2*(5*b^2+21*a^2)*sin(c+d*x)+32//35*a*b^2*d^-1*cos(c+d*x)^-5//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2, x) == :(2//5*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*sin(c+d*x)+2//15*b*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x)+1//15*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(-4*b^2+18*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+-4//15*b*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(a^2+-1*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2, x) == :(2//3*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x)+1//3*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-2*b^2+2*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2//3*b*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2), x) == :(2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^3//2*cos(c+d*x)^7//2, x) == :(2//7*a*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*sin(c+d*x)+16//35*b*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*sin(c+d*x)+1//105*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(6*b^2+50*a^2)*sin(c+d*x)+1//105*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(12*b^4+50*a^4+-62*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+4//105*b*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(-3*b^2+41*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^3//2*cos(c+d*x)^5//2, x) == :(2//5*a*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*sin(c+d*x)+4//5*b*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x)+1//5*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(2*b^2+6*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2//5*b*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(a^2+-1*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^3//2*cos(c+d*x)^3//2, x) == :(2//3*a*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x)+1//3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-2*b^2+2*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+8//3*b*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^5//2*cos(c+d*x)^9//2, x) == :(1//315*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*(98*a^2+150*b^2)*sin(c+d*x)+2//9*a^2*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^7//2*sin(c+d*x)+38//63*a*b*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*sin(c+d*x)+1//315*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(-20*b^4+294*a^4+558*a^2*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2//315*b*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(5*b^2+163*a^2)*sin(c+d*x)+4//315*b*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(5*b^4+57*a^4+-62*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^5//2*cos(c+d*x)^7//2, x) == :(1//21*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(10*a^2+18*b^2)*sin(c+d*x)+2//7*a^2*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*sin(c+d*x)+6//7*a*b*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*sin(c+d*x)+1//21*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-6*b^4+10*a^4+-4*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2//21*b*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(3*b^2+29*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^5//2*cos(c+d*x)^5//2, x) == :(2//5*a^2*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*sin(c+d*x)+1//15*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(18*a^2+46*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+22//15*a*b*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x)+16//15*b*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(a^2+-1*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-1//2*cos(c+d*x)^5//2, x) == :(2//5*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*sin(c+d*x)+-8//15*b*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x)+1//15*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(16*b^2+18*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+-2//15*b*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(7*a^2+8*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-1//2*cos(c+d*x)^3//2, x) == :(2//3*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x)+-4//3*b*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(2*a^2+4*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2), x) == :(2*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+-2*b*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2, x) == :(2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-3//2*cos(c+d*x)^5//2, x) == :(2*a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^3//2*sin(c+d*x)+1//5*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*cos(c+d*x)^3//2*(-12*b^2+2*a^2)*sin(c+d*x)+-8//5*b*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(a^2+4*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+-2//5*b*a^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*cos(c+d*x)^(1/2)*(-8*b^2+3*a^2)*sin(c+d*x)+1//5*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*cos(c+d*x)^(1/2)*(-32*b^4+6*a^4+16*a^2*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-3//2*cos(c+d*x)^3//2, x) == :(2*a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+1//3*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(2*a^2+16*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*cos(c+d*x)^(1/2)*(-8*b^2+2*a^2)*sin(c+d*x)+-2//3*b*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*cos(c+d*x)^(1/2)*(-8*b^2+5*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-3//2*cos(c+d*x)^(1/2), x) == :(-4*b*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2*a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*sin(c+d*x)+a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*cos(c+d*x)^(1/2)*(-4*b^2+2*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-3//2*cos(c+d*x)^-1//2, x) == :(-2*b*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*sin(c+d*x)+2*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2*b*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*cos(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-3//2*cos(c+d*x)^-3//2, x) == :(-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*cos(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2*a*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*cos(c+d*x)^3//2, x) == :(1//3*a^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*cos(c+d*x)^(1/2)*(2*a^4+16*b^4+-26*a^2*b^2)*sin(c+d*x)+2//3*a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+1//3*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*(-32*b^4+2*a^4+32*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+4//3*a^-2*b^2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*cos(c+d*x)^(1/2)*(-3*b^2+5*a^2)*sin(c+d*x)+-8//3*b*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*cos(c+d*x)^(1/2)*(2*a^4+4*b^4+-7*a^2*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-5//2*cos(c+d*x)^(1/2), x) == :(2//3*a^-1*b^2*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*sin(c+d*x)+1//3*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*cos(c+d*x)^(1/2)*(6*a^4+16*b^4+-30*a^2*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+8//3*a^-2*b^2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*cos(c+d*x)^-1//2*(-1*b^2+2*a^2)*sin(c+d*x)+-2//3*b*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*(-8*b^2+9*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-5//2*cos(c+d*x)^-1//2, x) == :(-2*b*d^-1*(a+b*sec(c+d*x))^-3//2*(-3*b^2+3*a^2)^-1*cos(c+d*x)^-1//2*sin(c+d*x)+-2//3*b*a^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*cos(c+d*x)^-1//2*(-1*b^2+5*a^2)*sin(c+d*x)+1//3*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*(-4*b^2+6*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+4//3*b*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*cos(c+d*x)^(1/2)*(-1*b^2+3*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-5//2*cos(c+d*x)^-3//2, x) == :(2*a*d^-1*(a+b*sec(c+d*x))^-3//2*(-3*b^2+3*a^2)^-1*cos(c+d*x)^-1//2*sin(c+d*x)+1//3*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*cos(c+d*x)^-1//2*(4*a^2+4*b^2)*sin(c+d*x)+-2//3*b*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+-1//3*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*cos(c+d*x)^(1/2)*(2*b^2+6*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-5//2*cos(c+d*x)^-5//2, x) == :(2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(-3*b^2+3*a^2)^-1*cos(c+d*x)^-1//2*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+-2//3*a^2*b^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*sin(c+d*x)+8//3*b*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*cos(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2//3*a*b^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*cos(c+d*x)^-1//2*(a^2+-5*b^2)*sin(c+d*x))

max_stars_repo_path: test/4 Trig functions/4.5 Secant/4.5.1.2 (d sec)^n (a+b sec)^m.jl