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

@test integrate(cos(c+d*x)^5*(a+a*cos(c+d*x)), x) == :(5//16*a*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//6*a*d^-1*cos(c+d*x)^5*sin(c+d*x)+5//16*a*d^-1*cos(c+d*x)*sin(c+d*x)+5//24*a*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate(cos(c+d*x)^4*(a+a*cos(c+d*x)), x) == :(3//8*a*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*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)^3*(a+a*cos(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(cos(c+d*x)^2*(a+a*cos(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((a+a*cos(c+d*x))*cos(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(a+a*cos(c+d*x), x) == :(a*x+a*d^-1*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))*sec(c+d*x), x) == :(a*x+a*d^-1*arctanh(sin(c+d*x)))
@test integrate(sec(c+d*x)^2*(a+a*cos(c+d*x)), x) == :(a*d^-1*arctanh(sin(c+d*x))+a*d^-1*tan(c+d*x))
@test integrate(sec(c+d*x)^3*(a+a*cos(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(sec(c+d*x)^4*(a+a*cos(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)^5*(a+a*cos(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)^6*(a+a*cos(c+d*x)), x) == :(a*d^-1*tan(c+d*x)+1//5*a*d^-1*tan(c+d*x)^5+2//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((a+a*cos(c+d*x))^2*cos(c+d*x)^4, x) == :(11//16*x*a^2+2*a^2*d^-1*sin(c+d*x)+-4//3*a^2*d^-1*sin(c+d*x)^3+2//5*a^2*d^-1*sin(c+d*x)^5+1//6*a^2*d^-1*cos(c+d*x)^5*sin(c+d*x)+11//16*a^2*d^-1*cos(c+d*x)*sin(c+d*x)+11//24*a^2*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^2*cos(c+d*x)^3, 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*cos(c+d*x))^2*cos(c+d*x)^2, 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*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*cos(c+d*x))^2*sec(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*cos(c+d*x))^2*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*cos(c+d*x))^2*sec(c+d*x)^3, 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*cos(c+d*x))^2*sec(c+d*x)^4, x) == :(a^2*d^-1*arctanh(sin(c+d*x))+2*a^2*d^-1*tan(c+d*x)+1//3*a^2*d^-1*tan(c+d*x)^3+a^2*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*cos(c+d*x))^2*sec(c+d*x)^5, 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*cos(c+d*x))^3*cos(c+d*x)^3, 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*cos(c+d*x))^3*cos(c+d*x)^2, 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*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*cos(c+d*x))^3*sec(c+d*x), 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*cos(c+d*x))^3*sec(c+d*x)^2, 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*cos(c+d*x))^3*sec(c+d*x)^3, x) == :(x*a^3+3*a^3*d^-1*tan(c+d*x)+7//2*a^3*d^-1*arctanh(sin(c+d*x))+(1/2)*a^3*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*cos(c+d*x))^3*sec(c+d*x)^4, 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*cos(c+d*x))^3*sec(c+d*x)^5, 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*cos(c+d*x))^3*sec(c+d*x)^6, 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*cos(c+d*x))^4*cos(c+d*x)^2, 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*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*cos(c+d*x))^4*sec(c+d*x), 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*cos(c+d*x))^4*sec(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*cos(c+d*x))^4*sec(c+d*x)^3, 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*cos(c+d*x))^4*sec(c+d*x)^4, x) == :(x*a^4+6*a^4*d^-1*arctanh(sin(c+d*x))+7*a^4*d^-1*tan(c+d*x)+1//3*a^4*d^-1*tan(c+d*x)^3+2*a^4*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*cos(c+d*x))^4*sec(c+d*x)^5, 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*cos(c+d*x))^4*sec(c+d*x)^6, 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*cos(c+d*x))^4*sec(c+d*x)^7, 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*cos(c+d*x))^-1*cos(c+d*x)^5, 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*cos(c+d*x))^-1*cos(c+d*x)^4*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*cos(c+d*x))^-1*cos(c+d*x)^4, 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*cos(c+d*x))^-1*cos(c+d*x)^3*sin(c+d*x)+-3//2*a^-1*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-1*cos(c+d*x)^3, x) == :(3//2*x*a^-1+-2*a^-1*d^-1*sin(c+d*x)+-1*d^-1*(a+a*cos(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*cos(c+d*x))^-1*cos(c+d*x)^2, x) == :(-1*x*a^-1+a^-1*d^-1*sin(c+d*x)+a^-1*d^-1*(1+cos(c+d*x))^-1*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-1*cos(c+d*x), x) == :(x*a^-1+-1*d^-1*(a+a*cos(c+d*x))^-1*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-1, x) == :(d^-1*(a+a*cos(c+d*x))^-1*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-1*sec(c+d*x), x) == :(a^-1*d^-1*arctanh(sin(c+d*x))+-1*d^-1*(a+a*cos(c+d*x))^-1*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-1*sec(c+d*x)^2, x) == :(-1*a^-1*d^-1*arctanh(sin(c+d*x))+-1*d^-1*(a+a*cos(c+d*x))^-1*tan(c+d*x)+2*a^-1*d^-1*tan(c+d*x))
@test integrate((a+a*cos(c+d*x))^-1*sec(c+d*x)^3, 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*cos(c+d*x))^-1*sec(c+d*x)*tan(c+d*x)+3//2*a^-1*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*cos(c+d*x))^-1*sec(c+d*x)^4, 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*cos(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*cos(c+d*x))^-2*cos(c+d*x)^5, 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*cos(c+d*x))^-2*cos(c+d*x)^4*sin(c+d*x)+-10//3*a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-2*cos(c+d*x)^4, x) == :(7//2*x*a^-2+-16//3*a^-2*d^-1*sin(c+d*x)+-1//3*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^3*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+cos(c+d*x))^-1*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-2*cos(c+d*x)^3, x) == :(-2*x*a^-2+4//3*a^-2*d^-1*sin(c+d*x)+2*a^-2*d^-1*(1+cos(c+d*x))^-1*sin(c+d*x)+-1//3*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-2*cos(c+d*x)^2, x) == :(x*a^-2+1//3*d^-1*(a+a*cos(c+d*x))^-2*sin(c+d*x)+-5//3*a^-2*d^-1*(1+cos(c+d*x))^-1*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-2*cos(c+d*x), x) == :(-1//3*d^-1*(a+a*cos(c+d*x))^-2*sin(c+d*x)+2//3*d^-1*(a^2+a^2*cos(c+d*x))^-1*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-2, x) == :(1//3*d^-1*(a+a*cos(c+d*x))^-2*sin(c+d*x)+1//3*d^-1*(a^2+a^2*cos(c+d*x))^-1*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-2*sec(c+d*x), x) == :(a^-2*d^-1*arctanh(sin(c+d*x))+-1//3*d^-1*(a+a*cos(c+d*x))^-2*sin(c+d*x)+-4//3*a^-2*d^-1*(1+cos(c+d*x))^-1*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-2*sec(c+d*x)^2, x) == :(-2*a^-2*d^-1*arctanh(sin(c+d*x))+-1//3*d^-1*(a+a*cos(c+d*x))^-2*tan(c+d*x)+10//3*a^-2*d^-1*tan(c+d*x)+-2*a^-2*d^-1*(1+cos(c+d*x))^-1*tan(c+d*x))
@test integrate((a+a*cos(c+d*x))^-2*sec(c+d*x)^3, 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*cos(c+d*x))^-2*sec(c+d*x)*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+cos(c+d*x))^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*cos(c+d*x))^-2*sec(c+d*x)^4, x) == :(-5*a^-2*d^-1*arctanh(sin(c+d*x))+4*a^-2*d^-1*tan(c+d*x)^3+12*a^-2*d^-1*tan(c+d*x)+-5*a^-2*d^-1*sec(c+d*x)*tan(c+d*x)+-1//3*d^-1*(a+a*cos(c+d*x))^-2*sec(c+d*x)^2*tan(c+d*x)+-10//3*a^-2*d^-1*(1+cos(c+d*x))^-1*sec(c+d*x)^2*tan(c+d*x))
@test integrate((a+a*cos(c+d*x))^-3*cos(c+d*x)^5, x) == :(13//2*x*a^-3+-152//15*a^-3*d^-1*sin(c+d*x)+-76//15*d^-1*(a^3+a^3*cos(c+d*x))^-1*cos(c+d*x)^2*sin(c+d*x)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^4*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*cos(c+d*x))^-2*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-3*cos(c+d*x)^4, x) == :(-3*x*a^-3+3*d^-1*(a^3+a^3*cos(c+d*x))^-1*sin(c+d*x)+9//5*a^-3*d^-1*sin(c+d*x)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^3*sin(c+d*x)+-3//5*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-3*cos(c+d*x)^3, x) == :(x*a^-3+-29//15*d^-1*(a^3+a^3*cos(c+d*x))^-1*sin(c+d*x)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^2*sin(c+d*x)+7//15*a^-1*d^-1*(a+a*cos(c+d*x))^-2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-3*cos(c+d*x)^2, x) == :(1//5*d^-1*(a+a*cos(c+d*x))^-3*sin(c+d*x)+7//15*d^-1*(a^3+a^3*cos(c+d*x))^-1*sin(c+d*x)+-8//15*a^-1*d^-1*(a+a*cos(c+d*x))^-2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-3*cos(c+d*x), x) == :(-1//5*d^-1*(a+a*cos(c+d*x))^-3*sin(c+d*x)+1//5*d^-1*(a^3+a^3*cos(c+d*x))^-1*sin(c+d*x)+1//5*a^-1*d^-1*(a+a*cos(c+d*x))^-2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-3, x) == :(1//5*d^-1*(a+a*cos(c+d*x))^-3*sin(c+d*x)+2//15*d^-1*(a^3+a^3*cos(c+d*x))^-1*sin(c+d*x)+2//15*a^-1*d^-1*(a+a*cos(c+d*x))^-2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-3*sec(c+d*x), x) == :(a^-3*d^-1*arctanh(sin(c+d*x))+-22//15*d^-1*(a^3+a^3*cos(c+d*x))^-1*sin(c+d*x)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*sin(c+d*x)+-7//15*a^-1*d^-1*(a+a*cos(c+d*x))^-2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-3*sec(c+d*x)^2, x) == :(-3*a^-3*d^-1*arctanh(sin(c+d*x))+-3*d^-1*(a^3+a^3*cos(c+d*x))^-1*tan(c+d*x)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*tan(c+d*x)+24//5*a^-3*d^-1*tan(c+d*x)+-3//5*a^-1*d^-1*(a+a*cos(c+d*x))^-2*tan(c+d*x))
@test integrate((a+a*cos(c+d*x))^-3*sec(c+d*x)^3, 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*cos(c+d*x))^-1*sec(c+d*x)*tan(c+d*x)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*sec(c+d*x)*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*cos(c+d*x))^-2*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*cos(c+d*x))^-4*cos(c+d*x)^6, x) == :(21//2*x*a^-4+-576//35*a^-4*d^-1*sin(c+d*x)+-1//7*d^-1*(a+a*cos(c+d*x))^-4*cos(c+d*x)^5*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+cos(c+d*x))^-1*cos(c+d*x)^2*sin(c+d*x)+-43//35*a^-4*d^-1*(1+cos(c+d*x))^-2*cos(c+d*x)^3*sin(c+d*x)+-2//5*a^-1*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^4*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-4*cos(c+d*x)^5, x) == :(-4*x*a^-4+244//105*a^-4*d^-1*sin(c+d*x)+4*a^-4*d^-1*(1+cos(c+d*x))^-1*sin(c+d*x)+-1//7*d^-1*(a+a*cos(c+d*x))^-4*cos(c+d*x)^4*sin(c+d*x)+-88//105*a^-4*d^-1*(1+cos(c+d*x))^-2*cos(c+d*x)^2*sin(c+d*x)+-12//35*a^-1*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-4*cos(c+d*x)^4, x) == :(x*a^-4+-43//21*a^-4*d^-1*(1+cos(c+d*x))^-1*sin(c+d*x)+-1//7*d^-1*(a+a*cos(c+d*x))^-4*cos(c+d*x)^3*sin(c+d*x)+11//21*a^-4*d^-1*(1+cos(c+d*x))^-2*sin(c+d*x)+-2//7*a^-1*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-4*cos(c+d*x)^3, x) == :(-18//35*a^-4*d^-1*(1+cos(c+d*x))^-2*sin(c+d*x)+-1//7*d^-1*(a+a*cos(c+d*x))^-4*cos(c+d*x)^2*sin(c+d*x)+8//35*a^-1*d^-1*(a+a*cos(c+d*x))^-3*sin(c+d*x)+12//35*a^-4*d^-1*(1+cos(c+d*x))^-1*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-4*cos(c+d*x)^2, x) == :(1//7*d^-1*(a+a*cos(c+d*x))^-4*sin(c+d*x)+13//105*d^-1*(a^2+a^2*cos(c+d*x))^-2*sin(c+d*x)+13//105*d^-1*(a^4+a^4*cos(c+d*x))^-1*sin(c+d*x)+-11//35*a^-1*d^-1*(a+a*cos(c+d*x))^-3*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-4*cos(c+d*x), x) == :(-1//7*d^-1*(a+a*cos(c+d*x))^-4*sin(c+d*x)+8//105*d^-1*(a^2+a^2*cos(c+d*x))^-2*sin(c+d*x)+8//105*d^-1*(a^4+a^4*cos(c+d*x))^-1*sin(c+d*x)+4//35*a^-1*d^-1*(a+a*cos(c+d*x))^-3*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-4, x) == :(1//7*d^-1*(a+a*cos(c+d*x))^-4*sin(c+d*x)+2//35*d^-1*(a^2+a^2*cos(c+d*x))^-2*sin(c+d*x)+2//35*d^-1*(a^4+a^4*cos(c+d*x))^-1*sin(c+d*x)+3//35*a^-1*d^-1*(a+a*cos(c+d*x))^-3*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-4*sec(c+d*x), x) == :(a^-4*d^-1*arctanh(sin(c+d*x))+-1//7*d^-1*(a+a*cos(c+d*x))^-4*sin(c+d*x)+-32//21*a^-4*d^-1*(1+cos(c+d*x))^-1*sin(c+d*x)+-11//21*a^-4*d^-1*(1+cos(c+d*x))^-2*sin(c+d*x)+-2//7*a^-1*d^-1*(a+a*cos(c+d*x))^-3*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-4*sec(c+d*x)^2, x) == :(-4*a^-4*d^-1*arctanh(sin(c+d*x))+-1//7*d^-1*(a+a*cos(c+d*x))^-4*tan(c+d*x)+664//105*a^-4*d^-1*tan(c+d*x)+-4*a^-4*d^-1*(1+cos(c+d*x))^-1*tan(c+d*x)+-88//105*a^-4*d^-1*(1+cos(c+d*x))^-2*tan(c+d*x)+-12//35*a^-1*d^-1*(a+a*cos(c+d*x))^-3*tan(c+d*x))
@test integrate((a+a*cos(c+d*x))^-4*sec(c+d*x)^3, 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*cos(c+d*x))^-4*sec(c+d*x)*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+cos(c+d*x))^-1*sec(c+d*x)*tan(c+d*x)+-43//35*a^-4*d^-1*(1+cos(c+d*x))^-2*sec(c+d*x)*tan(c+d*x)+-2//5*a^-1*d^-1*(a+a*cos(c+d*x))^-3*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*cos(c+d*x))^-5*cos(c+d*x)^7, x) == :(31//2*x*a^-5+-7664//315*a^-5*d^-1*sin(c+d*x)+-3832//315*d^-1*(a^5+a^5*cos(c+d*x))^-1*cos(c+d*x)^2*sin(c+d*x)+-1//9*d^-1*(a+a*cos(c+d*x))^-5*cos(c+d*x)^6*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*cos(c+d*x))^-2*cos(c+d*x)^3*sin(c+d*x)+-28//45*a^-2*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^4*sin(c+d*x)+-17//63*a^-1*d^-1*(a+a*cos(c+d*x))^-4*cos(c+d*x)^5*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-5*cos(c+d*x)^6, x) == :(-5*x*a^-5+5*d^-1*(a^5+a^5*cos(c+d*x))^-1*sin(c+d*x)+181//63*a^-5*d^-1*sin(c+d*x)+-1//9*d^-1*(a+a*cos(c+d*x))^-5*cos(c+d*x)^5*sin(c+d*x)+-67//63*a^-3*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^2*sin(c+d*x)+-29//63*a^-2*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^3*sin(c+d*x)+-5//21*a^-1*d^-1*(a+a*cos(c+d*x))^-4*cos(c+d*x)^4*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-5*cos(c+d*x)^5, x) == :(x*a^-5+-661//315*d^-1*(a^5+a^5*cos(c+d*x))^-1*sin(c+d*x)+-1//9*d^-1*(a+a*cos(c+d*x))^-5*cos(c+d*x)^4*sin(c+d*x)+173//315*a^-3*d^-1*(a+a*cos(c+d*x))^-2*sin(c+d*x)+-34//105*a^-2*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^2*sin(c+d*x)+-13//63*a^-1*d^-1*(a+a*cos(c+d*x))^-4*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-5*cos(c+d*x)^4, x) == :(83//315*d^-1*(a^5+a^5*cos(c+d*x))^-1*sin(c+d*x)+-142//315*a^-3*d^-1*(a+a*cos(c+d*x))^-2*sin(c+d*x)+-1//9*d^-1*(a+a*cos(c+d*x))^-5*cos(c+d*x)^3*sin(c+d*x)+67//315*a^-2*d^-1*(a+a*cos(c+d*x))^-3*sin(c+d*x)+-11//63*a^-1*d^-1*(a+a*cos(c+d*x))^-4*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-5*cos(c+d*x)^3, x) == :(5//63*d^-1*(a^5+a^5*cos(c+d*x))^-1*sin(c+d*x)+-17//63*a^-2*d^-1*(a+a*cos(c+d*x))^-3*sin(c+d*x)+-1//9*d^-1*(a+a*cos(c+d*x))^-5*cos(c+d*x)^2*sin(c+d*x)+1//7*a^-1*d^-1*(a+a*cos(c+d*x))^-4*sin(c+d*x)+5//63*a^-3*d^-1*(a+a*cos(c+d*x))^-2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-5*cos(c+d*x)^2, x) == :(1//9*d^-1*(a+a*cos(c+d*x))^-5*sin(c+d*x)+2//45*d^-1*(a^5+a^5*cos(c+d*x))^-1*sin(c+d*x)+-2//9*a^-1*d^-1*(a+a*cos(c+d*x))^-4*sin(c+d*x)+1//15*a^-2*d^-1*(a+a*cos(c+d*x))^-3*sin(c+d*x)+2//45*a^-3*d^-1*(a+a*cos(c+d*x))^-2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-5*cos(c+d*x), x) == :(-1//9*d^-1*(a+a*cos(c+d*x))^-5*sin(c+d*x)+2//63*d^-1*(a^5+a^5*cos(c+d*x))^-1*sin(c+d*x)+1//21*a^-2*d^-1*(a+a*cos(c+d*x))^-3*sin(c+d*x)+2//63*a^-1*d^-1*(a^2+a^2*cos(c+d*x))^-2*sin(c+d*x)+5//63*a^-1*d^-1*(a+a*cos(c+d*x))^-4*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-5, x) == :(1//9*d^-1*(a+a*cos(c+d*x))^-5*sin(c+d*x)+8//315*d^-1*(a^5+a^5*cos(c+d*x))^-1*sin(c+d*x)+4//63*a^-1*d^-1*(a+a*cos(c+d*x))^-4*sin(c+d*x)+4//105*a^-2*d^-1*(a+a*cos(c+d*x))^-3*sin(c+d*x)+8//315*a^-1*d^-1*(a^2+a^2*cos(c+d*x))^-2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-5*sec(c+d*x), x) == :(a^-5*d^-1*arctanh(sin(c+d*x))+-488//315*d^-1*(a^5+a^5*cos(c+d*x))^-1*sin(c+d*x)+-1//9*d^-1*(a+a*cos(c+d*x))^-5*sin(c+d*x)+-173//315*a^-3*d^-1*(a+a*cos(c+d*x))^-2*sin(c+d*x)+-34//105*a^-2*d^-1*(a+a*cos(c+d*x))^-3*sin(c+d*x)+-13//63*a^-1*d^-1*(a+a*cos(c+d*x))^-4*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-5*sec(c+d*x)^2, x) == :(-5*a^-5*d^-1*arctanh(sin(c+d*x))+-5*d^-1*(a^5+a^5*cos(c+d*x))^-1*tan(c+d*x)+-1//9*d^-1*(a+a*cos(c+d*x))^-5*tan(c+d*x)+496//63*a^-5*d^-1*tan(c+d*x)+-67//63*a^-3*d^-1*(a+a*cos(c+d*x))^-2*tan(c+d*x)+-29//63*a^-2*d^-1*(a+a*cos(c+d*x))^-3*tan(c+d*x)+-5//21*a^-1*d^-1*(a+a*cos(c+d*x))^-4*tan(c+d*x))
@test integrate((a+a*cos(c+d*x))^-5*sec(c+d*x)^3, x) == :(-7664//315*a^-5*d^-1*tan(c+d*x)+31//2*a^-5*d^-1*arctanh(sin(c+d*x))+-3832//315*d^-1*(a^5+a^5*cos(c+d*x))^-1*sec(c+d*x)*tan(c+d*x)+-1//9*d^-1*(a+a*cos(c+d*x))^-5*sec(c+d*x)*tan(c+d*x)+31//2*a^-5*d^-1*sec(c+d*x)*tan(c+d*x)+-577//315*a^-3*d^-1*(a+a*cos(c+d*x))^-2*sec(c+d*x)*tan(c+d*x)+-28//45*a^-2*d^-1*(a+a*cos(c+d*x))^-3*sec(c+d*x)*tan(c+d*x)+-17//63*a^-1*d^-1*(a+a*cos(c+d*x))^-4*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*cos(c+d*x))^-6*cos(c+d*x)^5, x) == :(-268//693*a^-6*d^-1*(1+cos(c+d*x))^-2*sin(c+d*x)+-1//11*d^-1*(a+a*cos(c+d*x))^-6*cos(c+d*x)^4*sin(c+d*x)+130//693*a^-6*d^-1*(1+cos(c+d*x))^-3*sin(c+d*x)+146//693*a^-6*d^-1*(1+cos(c+d*x))^-1*sin(c+d*x)+-118//693*a^-2*d^-1*(a+a*cos(c+d*x))^-4*cos(c+d*x)^2*sin(c+d*x)+-14//99*a^-1*d^-1*(a+a*cos(c+d*x))^-5*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-6*cos(c+d*x)^4, x) == :(-241//1155*a^-6*d^-1*(1+cos(c+d*x))^-3*sin(c+d*x)+-1//11*d^-1*(a+a*cos(c+d*x))^-6*cos(c+d*x)^3*sin(c+d*x)+9//77*a^-2*d^-1*(a+a*cos(c+d*x))^-4*sin(c+d*x)+61//1155*a^-6*d^-1*(1+cos(c+d*x))^-1*sin(c+d*x)+61//1155*a^-6*d^-1*(1+cos(c+d*x))^-2*sin(c+d*x)+-4//33*a^-1*d^-1*(a+a*cos(c+d*x))^-5*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^(1/2)*cos(c+d*x)^4, x) == :(-64//315*d^-1*(a+a*cos(c+d*x))^(1/2)*sin(c+d*x)+32//45*a*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)+32//105*a^-1*d^-1*(a+a*cos(c+d*x))^3//2*sin(c+d*x)+2//9*a*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^4*sin(c+d*x)+16//63*a*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^(1/2)*cos(c+d*x)^3, x) == :(-8//35*d^-1*(a+a*cos(c+d*x))^(1/2)*sin(c+d*x)+4//5*a*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)+12//35*a^-1*d^-1*(a+a*cos(c+d*x))^3//2*sin(c+d*x)+2//7*a*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^(1/2)*cos(c+d*x)^2, x) == :(-4//15*d^-1*(a+a*cos(c+d*x))^(1/2)*sin(c+d*x)+2//5*a^-1*d^-1*(a+a*cos(c+d*x))^3//2*sin(c+d*x)+14//15*a*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^(1/2)*cos(c+d*x), x) == :(2//3*d^-1*(a+a*cos(c+d*x))^(1/2)*sin(c+d*x)+2//3*a*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^(1/2), x) == :(2*a*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^(1/2)*sec(c+d*x), x) == :(2*a^(1/2)*d^-1*arctanh(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^(1/2)*sec(c+d*x)^2, x) == :(a^(1/2)*d^-1*arctanh(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+a*d^-1*(a+a*cos(c+d*x))^-1//2*tan(c+d*x))
@test integrate((a+a*cos(c+d*x))^(1/2)*sec(c+d*x)^3, x) == :(3//4*a^(1/2)*d^-1*arctanh(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+3//4*a*d^-1*(a+a*cos(c+d*x))^-1//2*tan(c+d*x)+(1/2)*a*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*cos(c+d*x))^(1/2)*sec(c+d*x)^4, x) == :(5//8*a^(1/2)*d^-1*arctanh(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+5//8*a*d^-1*(a+a*cos(c+d*x))^-1//2*tan(c+d*x)+1//3*a*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^2*tan(c+d*x)+5//12*a*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*cos(c+d*x))^3//2*cos(c+d*x)^3, x) == :(68//105*d^-1*(a+a*cos(c+d*x))^3//2*sin(c+d*x)+-136//315*a*d^-1*(a+a*cos(c+d*x))^(1/2)*sin(c+d*x)+68//45*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)+2//9*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^4*sin(c+d*x)+34//63*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^3//2*cos(c+d*x)^2, x) == :(-4//35*d^-1*(a+a*cos(c+d*x))^3//2*sin(c+d*x)+2//7*a^-1*d^-1*(a+a*cos(c+d*x))^5//2*sin(c+d*x)+38//105*a*d^-1*(a+a*cos(c+d*x))^(1/2)*sin(c+d*x)+152//105*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^3//2*cos(c+d*x), x) == :(2//5*d^-1*(a+a*cos(c+d*x))^3//2*sin(c+d*x)+2//5*a*d^-1*(a+a*cos(c+d*x))^(1/2)*sin(c+d*x)+8//5*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^3//2, x) == :(2//3*a*d^-1*(a+a*cos(c+d*x))^(1/2)*sin(c+d*x)+8//3*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^3//2*sec(c+d*x), x) == :(2*a^3//2*d^-1*arctanh(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+2*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^3//2*sec(c+d*x)^2, x) == :(3*a^3//2*d^-1*arctanh(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+a^2*d^-1*(a+a*cos(c+d*x))^-1//2*tan(c+d*x))
@test integrate((a+a*cos(c+d*x))^3//2*sec(c+d*x)^3, x) == :(7//4*a^3//2*d^-1*arctanh(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+7//4*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*tan(c+d*x)+(1/2)*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*cos(c+d*x))^3//2*sec(c+d*x)^4, x) == :(11//8*a^3//2*d^-1*arctanh(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+11//8*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*tan(c+d*x)+1//3*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^2*tan(c+d*x)+11//12*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*cos(c+d*x))^5//2*cos(c+d*x)^3, x) == :(-568//693*a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*sin(c+d*x)+284//99*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)+284//231*a*d^-1*(a+a*cos(c+d*x))^3//2*sin(c+d*x)+2//11*a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*cos(c+d*x)^4*sin(c+d*x)+46//99*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^4*sin(c+d*x)+710//693*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^5//2*cos(c+d*x)^2, x) == :(-4//63*d^-1*(a+a*cos(c+d*x))^5//2*sin(c+d*x)+2//9*a^-1*d^-1*(a+a*cos(c+d*x))^7//2*sin(c+d*x)+26//105*a*d^-1*(a+a*cos(c+d*x))^3//2*sin(c+d*x)+208//315*a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*sin(c+d*x)+832//315*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^5//2*cos(c+d*x), x) == :(2//7*d^-1*(a+a*cos(c+d*x))^5//2*sin(c+d*x)+2//7*a*d^-1*(a+a*cos(c+d*x))^3//2*sin(c+d*x)+16//21*a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*sin(c+d*x)+64//21*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^5//2, x) == :(2//5*a*d^-1*(a+a*cos(c+d*x))^3//2*sin(c+d*x)+16//15*a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*sin(c+d*x)+64//15*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^5//2*sec(c+d*x), x) == :(2*a^5//2*d^-1*arctanh(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+2//3*a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*sin(c+d*x)+14//3*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^5//2*sec(c+d*x)^2, x) == :(5*a^5//2*d^-1*arctanh(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*tan(c+d*x)+a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^5//2*sec(c+d*x)^3, x) == :(19//4*a^5//2*d^-1*arctanh(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+9//4*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*tan(c+d*x)+(1/2)*a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*cos(c+d*x))^5//2*sec(c+d*x)^4, x) == :(25//8*a^5//2*d^-1*arctanh(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+25//8*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*tan(c+d*x)+1//3*a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*sec(c+d*x)^2*tan(c+d*x)+13//12*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*cos(c+d*x))^5//2*sec(c+d*x)^5, x) == :(163//64*a^5//2*d^-1*arctanh(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+163//64*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*tan(c+d*x)+1//4*a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*sec(c+d*x)^3*tan(c+d*x)+17//24*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^2*tan(c+d*x)+163//96*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*cos(c+d*x))^7//2, x) == :(2//7*a*d^-1*(a+a*cos(c+d*x))^5//2*sin(c+d*x)+24//35*a^2*d^-1*(a+a*cos(c+d*x))^3//2*sin(c+d*x)+64//35*a^3*d^-1*(a+a*cos(c+d*x))^(1/2)*sin(c+d*x)+256//35*a^4*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-1//2*cos(c+d*x)^4, x) == :(-148//105*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)+2^(1/2)*a^-1//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+-2//35*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^2*sin(c+d*x)+2//7*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^3*sin(c+d*x)+62//105*a^-1*d^-1*(a+a*cos(c+d*x))^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-1//2*cos(c+d*x)^3, x) == :(28//15*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+-2//15*a^-1*d^-1*(a+a*cos(c+d*x))^(1/2)*sin(c+d*x)+2//5*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-1//2*cos(c+d*x)^2, x) == :(-4//3*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)+2^(1/2)*a^-1//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+2//3*a^-1*d^-1*(a+a*cos(c+d*x))^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-1//2*cos(c+d*x), x) == :(2*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(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*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-1//2*sec(c+d*x), x) == :(2*a^-1//2*d^-1*arctanh(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+-1*2^(1/2)*a^-1//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-1//2*sec(c+d*x)^2, x) == :(d^-1*(a+a*cos(c+d*x))^-1//2*tan(c+d*x)+-1*a^-1//2*d^-1*arctanh(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+2^(1/2)*a^-1//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-1//2*sec(c+d*x)^3, x) == :(-1//4*d^-1*(a+a*cos(c+d*x))^-1//2*tan(c+d*x)+7//4*a^-1//2*d^-1*arctanh(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+(1/2)*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)*tan(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-1//2*sec(c+d*x)^4, x) == :(-9//8*a^-1//2*d^-1*arctanh(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+7//8*d^-1*(a+a*cos(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*cos(c+d*x))^-1//2*sin(c+d*x))+-1//12*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)*tan(c+d*x)+1//3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^2*tan(c+d*x))
@test integrate((a+a*cos(c+d*x))^-3//2*cos(c+d*x)^4, x) == :(-15//4*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+-13//10*a^-2*d^-1*(a+a*cos(c+d*x))^(1/2)*sin(c+d*x)+-1//2*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^3*sin(c+d*x)+31//5*a^-1*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)+9//10*a^-1*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-3//2*cos(c+d*x)^3, x) == :(-13//3*a^-1*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)+-1//2*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^2*sin(c+d*x)+7//6*a^-2*d^-1*(a+a*cos(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*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-3//2*cos(c+d*x)^2, x) == :((1/2)*d^-1*(a+a*cos(c+d*x))^-3//2*sin(c+d*x)+2*a^-1*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)+-7//4*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-3//2*cos(c+d*x), x) == :(-1//2*d^-1*(a+a*cos(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*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-3//2, x) == :((1/2)*d^-1*(a+a*cos(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*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-3//2*sec(c+d*x), x) == :(2*a^-3//2*d^-1*arctanh(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+-1//2*d^-1*(a+a*cos(c+d*x))^-3//2*sin(c+d*x)+-5//4*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-3//2*sec(c+d*x)^2, x) == :(-3*a^-3//2*d^-1*arctanh(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+-1//2*d^-1*(a+a*cos(c+d*x))^-3//2*tan(c+d*x)+3//2*a^-1*d^-1*(a+a*cos(c+d*x))^-1//2*tan(c+d*x)+9//4*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-3//2*sec(c+d*x)^3, x) == :(19//4*a^-3//2*d^-1*arctanh(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+-13//4*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+-7//4*a^-1*d^-1*(a+a*cos(c+d*x))^-1//2*tan(c+d*x)+-1//2*d^-1*(a+a*cos(c+d*x))^-3//2*sec(c+d*x)*tan(c+d*x)+a^-1*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*cos(c+d*x))^-5//2*cos(c+d*x)^4, x) == :(-197//24*a^-2*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)+-1//4*d^-1*(a+a*cos(c+d*x))^-5//2*cos(c+d*x)^3*sin(c+d*x)+95//48*a^-3*d^-1*(a+a*cos(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*cos(c+d*x))^-1//2*sin(c+d*x))+-17//16*a^-1*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-5//2*cos(c+d*x)^3, x) == :(-75//32*2^(1/2)*a^-5//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+-1//4*d^-1*(a+a*cos(c+d*x))^-5//2*cos(c+d*x)^2*sin(c+d*x)+9//4*a^-2*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)+13//16*a^-1*d^-1*(a+a*cos(c+d*x))^-3//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-5//2*cos(c+d*x)^2, x) == :(1//4*d^-1*(a+a*cos(c+d*x))^-5//2*sin(c+d*x)+-13//16*a^-1*d^-1*(a+a*cos(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*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-5//2*cos(c+d*x), x) == :(-1//4*d^-1*(a+a*cos(c+d*x))^-5//2*sin(c+d*x)+5//16*a^-1*d^-1*(a+a*cos(c+d*x))^-3//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*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-5//2, x) == :(1//4*d^-1*(a+a*cos(c+d*x))^-5//2*sin(c+d*x)+3//16*a^-1*d^-1*(a+a*cos(c+d*x))^-3//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*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-5//2*sec(c+d*x), x) == :(2*a^-5//2*d^-1*arctanh(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+-1//4*d^-1*(a+a*cos(c+d*x))^-5//2*sin(c+d*x)+-43//32*2^(1/2)*a^-5//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+-11//16*a^-1*d^-1*(a+a*cos(c+d*x))^-3//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-5//2*sec(c+d*x)^2, x) == :(-5*a^-5//2*d^-1*arctanh(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+-1//4*d^-1*(a+a*cos(c+d*x))^-5//2*tan(c+d*x)+-15//16*a^-1*d^-1*(a+a*cos(c+d*x))^-3//2*tan(c+d*x)+35//16*a^-2*d^-1*(a+a*cos(c+d*x))^-1//2*tan(c+d*x)+115//32*2^(1/2)*a^-5//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate(cos(c+d*x)^5//2*(a+a*cos(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)^3//2*(a+a*cos(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)^(1/2)*(a+a*cos(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*cos(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)^-3//2*(a+a*cos(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)^-5//2*(a+a*cos(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)^-7//2*(a+a*cos(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((a+a*cos(c+d*x))^2*cos(c+d*x)^5//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*cos(c+d*x))^2*cos(c+d*x)^3//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*cos(c+d*x))^2*cos(c+d*x)^(1/2), 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*cos(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)+2//3*a^2*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^2*cos(c+d*x)^-3//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*cos(c+d*x))^2*cos(c+d*x)^-5//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*cos(c+d*x))^2*cos(c+d*x)^-7//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*cos(c+d*x))^3*cos(c+d*x)^3//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*cos(c+d*x))^3*cos(c+d*x)^(1/2), 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*cos(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)^(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*cos(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*cos(c+d*x))^3*cos(c+d*x)^-5//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*cos(c+d*x))^3*cos(c+d*x)^-7//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*cos(c+d*x))^3*cos(c+d*x)^-9//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*cos(c+d*x))^4*cos(c+d*x)^3//2, x) == :(128//15*a^4*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+904//231*a^4*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//11*a^4*d^-1*cos(c+d*x)^9//2*sin(c+d*x)+8//9*a^4*d^-1*cos(c+d*x)^7//2*sin(c+d*x)+128//45*a^4*d^-1*cos(c+d*x)^3//2*sin(c+d*x)+150//77*a^4*d^-1*cos(c+d*x)^5//2*sin(c+d*x)+904//231*a^4*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^4*cos(c+d*x)^(1/2), x) == :(32//7*a^4*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+152//15*a^4*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//9*a^4*d^-1*cos(c+d*x)^7//2*sin(c+d*x)+8//7*a^4*d^-1*cos(c+d*x)^5//2*sin(c+d*x)+32//7*a^4*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+122//45*a^4*d^-1*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^4*cos(c+d*x)^-1//2, x) == :(64//5*a^4*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+136//21*a^4*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//7*a^4*d^-1*cos(c+d*x)^5//2*sin(c+d*x)+8//5*a^4*d^-1*cos(c+d*x)^3//2*sin(c+d*x)+94//21*a^4*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^4*cos(c+d*x)^-3//2, x) == :(32//3*a^4*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+56//5*a^4*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*a^4*d^-1*cos(c+d*x)^-1//2*sin(c+d*x)+2//5*a^4*d^-1*cos(c+d*x)^3//2*sin(c+d*x)+8//3*a^4*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^4*cos(c+d*x)^-5//2, x) == :(40//3*a^4*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+8*a^4*d^-1*cos(c+d*x)^-1//2*sin(c+d*x)+2//3*a^4*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+2//3*a^4*d^-1*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^4*cos(c+d*x)^-7//2, x) == :(-56//5*a^4*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+32//3*a^4*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*a^4*d^-1*cos(c+d*x)^-5//2*sin(c+d*x)+8//3*a^4*d^-1*cos(c+d*x)^-3//2*sin(c+d*x)+66//5*a^4*d^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^4*cos(c+d*x)^-9//2, x) == :(-64//5*a^4*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+136//21*a^4*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//7*a^4*d^-1*cos(c+d*x)^-7//2*sin(c+d*x)+8//5*a^4*d^-1*cos(c+d*x)^-5//2*sin(c+d*x)+64//5*a^4*d^-1*cos(c+d*x)^-1//2*sin(c+d*x)+94//21*a^4*d^-1*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-1*cos(c+d*x)^7//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*cos(c+d*x))^-1*cos(c+d*x)^5//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*cos(c+d*x))^-1*cos(c+d*x)^5//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*cos(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))
@test integrate((a+a*cos(c+d*x))^-1*cos(c+d*x)^3//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*cos(c+d*x))^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(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*cos(c+d*x))^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-1*cos(c+d*x)^-1//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*cos(c+d*x))^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-1*cos(c+d*x)^-3//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*cos(c+d*x))^-1*cos(c+d*x)^-1//2*sin(c+d*x)+3*a^-1*d^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-1*cos(c+d*x)^-5//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*cos(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)+5//3*a^-1*d^-1*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-2*cos(c+d*x)^9//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*cos(c+d*x))^-2*cos(c+d*x)^7//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+cos(c+d*x))^-1*cos(c+d*x)^5//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-2*cos(c+d*x)^7//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*cos(c+d*x))^-2*cos(c+d*x)^5//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+cos(c+d*x))^-1*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-2*cos(c+d*x)^5//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*cos(c+d*x))^-2*cos(c+d*x)^3//2*sin(c+d*x)+-5//3*a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-2*cos(c+d*x)^3//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*cos(c+d*x))^-2*cos(c+d*x)^(1/2)*sin(c+d*x)+a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-2*cos(c+d*x)^(1/2), x) == :(1//3*a^-2*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-2*cos(c+d*x)^-1//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*cos(c+d*x))^-2*cos(c+d*x)^(1/2)*sin(c+d*x)+-1*a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(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)+-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*cos(c+d*x))^-2*cos(c+d*x)^-1//2*sin(c+d*x)+-5//3*a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-2*cos(c+d*x)^-5//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*cos(c+d*x))^-2*cos(c+d*x)^-3//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+cos(c+d*x))^-1*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-3*cos(c+d*x)^11//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*cos(c+d*x))^-1*cos(c+d*x)^5//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*cos(c+d*x))^-3*cos(c+d*x)^9//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*cos(c+d*x))^-2*cos(c+d*x)^7//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-3*cos(c+d*x)^9//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*cos(c+d*x))^-1*cos(c+d*x)^3//2*sin(c+d*x)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^7//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*cos(c+d*x))^-2*cos(c+d*x)^5//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-3*cos(c+d*x)^7//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*cos(c+d*x))^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^5//2*sin(c+d*x)+-8//15*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-3*cos(c+d*x)^5//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//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^3//2*sin(c+d*x)+9//10*d^-1*(a^3+a^3*cos(c+d*x))^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+-2//5*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(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*cos(c+d*x))^-3*cos(c+d*x)^(1/2)*sin(c+d*x)+1//10*d^-1*(a^3+a^3*cos(c+d*x))^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+4//15*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-3*cos(c+d*x)^(1/2), 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//10*d^-1*(a^3+a^3*cos(c+d*x))^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^(1/2)*sin(c+d*x)+1//15*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(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)+-9//10*d^-1*(a^3+a^3*cos(c+d*x))^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^(1/2)*sin(c+d*x)+-2//5*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-3*cos(c+d*x)^-3//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*cos(c+d*x))^-1*cos(c+d*x)^-1//2*sin(c+d*x)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^-1//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*cos(c+d*x))^-2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-3*cos(c+d*x)^-5//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*cos(c+d*x))^-1*cos(c+d*x)^-3//2*sin(c+d*x)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^-3//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*cos(c+d*x))^-2*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^(1/2)*cos(c+d*x)^5//2, x) == :(5//8*a^(1/2)*d^-1*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+1//3*a*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^5//2*sin(c+d*x)+5//8*a*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)+5//12*a*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^(1/2)*cos(c+d*x)^3//2, x) == :(3//4*a^(1/2)*d^-1*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+(1/2)*a*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x)+3//4*a*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^(1/2)*cos(c+d*x)^(1/2), x) == :(a^(1/2)*d^-1*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+a*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2, x) == :(2*a^(1/2)*d^-1*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2, x) == :(2*a*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^(1/2)*cos(c+d*x)^-5//2, x) == :(2//3*a*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+4//3*a*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^(1/2)*cos(c+d*x)^-7//2, x) == :(2//5*a*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x)+8//15*a*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+16//15*a*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^(1/2)*cos(c+d*x)^-9//2, x) == :(2//7*a*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-7//2*sin(c+d*x)+12//35*a*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x)+16//35*a*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+32//35*a*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^3//2*cos(c+d*x)^3//2, x) == :(11//8*a^3//2*d^-1*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+1//3*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^5//2*sin(c+d*x)+11//8*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)+11//12*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^3//2*cos(c+d*x)^(1/2), x) == :(7//4*a^3//2*d^-1*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+(1/2)*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x)+7//4*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^3//2*cos(c+d*x)^-1//2, x) == :(3*a^3//2*d^-1*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+a^2*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^3//2*cos(c+d*x)^-3//2, x) == :(2*a^3//2*d^-1*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+2*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^3//2*cos(c+d*x)^-5//2, x) == :(2//3*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+10//3*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^3//2*cos(c+d*x)^-7//2, x) == :(2//5*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x)+6//5*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+12//5*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^3//2*cos(c+d*x)^-9//2, x) == :(2//7*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-7//2*sin(c+d*x)+26//35*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x)+104//105*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+208//105*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^5//2*cos(c+d*x)^3//2, x) == :(163//64*a^5//2*d^-1*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+1//4*a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*cos(c+d*x)^5//2*sin(c+d*x)+17//24*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^5//2*sin(c+d*x)+163//64*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)+163//96*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^5//2*cos(c+d*x)^(1/2), x) == :(25//8*a^5//2*d^-1*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+1//3*a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*cos(c+d*x)^3//2*sin(c+d*x)+13//12*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x)+25//8*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^5//2*cos(c+d*x)^-1//2, x) == :(19//4*a^5//2*d^-1*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+(1/2)*a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x)+9//4*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^5//2*cos(c+d*x)^-3//2, x) == :(5*a^5//2*d^-1*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+-1*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)+2*a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^5//2*cos(c+d*x)^-5//2, x) == :(2*a^5//2*d^-1*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+2//3*a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2*sin(c+d*x)+14//3*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^5//2*cos(c+d*x)^-7//2, x) == :(2//5*a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*cos(c+d*x)^-5//2*sin(c+d*x)+22//15*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+86//15*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^5//2*cos(c+d*x)^-9//2, x) == :(2//7*a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*cos(c+d*x)^-7//2*sin(c+d*x)+6//7*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x)+46//21*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+92//21*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^5//2*cos(c+d*x)^-11//2, x) == :(2//9*a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*cos(c+d*x)^-9//2*sin(c+d*x)+38//63*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-7//2*sin(c+d*x)+146//105*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x)+584//315*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+1168//315*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^3//2*cos(c+d*x)^-5//4, x) == :(4*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//4*sin(c+d*x))
@test integrate((a+a*cos(e+f*x))^(1/2)*cos(e+f*x)^-1//2, x) == :(2*a^(1/2)*f^-1*arcsin(a^(1/2)*(a+a*cos(e+f*x))^-1//2*sin(e+f*x)))
@test integrate((-1*cos(e+f*x))^-1//2*(a+-1*a*cos(e+f*x))^(1/2), x) == :(-2*a^(1/2)*f^-1*arcsin(a^(1/2)*(a+-1*a*cos(e+f*x))^-1//2*sin(e+f*x)))
@test integrate((a+a*cos(c+d*x))^-1//2*cos(c+d*x)^5//2, x) == :(7//4*a^-1//2*d^-1*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+(1/2)*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-1//4*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-1//2*cos(c+d*x)^3//2, x) == :(-1*a^-1//2*d^-1*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+2^(1/2)*a^-1//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2), x) == :(2*a^-1//2*d^-1*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+-1*2^(1/2)*a^-1//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2, x) == :(2^(1/2)*a^-1//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2, x) == :(-1*2^(1/2)*a^-1//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+2*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-5//2, x) == :(2^(1/2)*a^-1//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-2//3*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+2//3*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-7//2, x) == :(-1*2^(1/2)*a^-1//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-2//15*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+2//5*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x)+26//15*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((1+cos(c+d*x))^-1//2*cos(c+d*x)^5//2, x) == :(7//4*d^-1*arcsin((1+cos(c+d*x))^-1//2*sin(c+d*x))+-1*2^(1/2)*d^-1*arcsin((1+cos(c+d*x))^-1*sin(c+d*x))+(1/2)*d^-1*(1+cos(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x)+-1//4*d^-1*(1+cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((1+cos(c+d*x))^-1//2*cos(c+d*x)^3//2, x) == :(-1*d^-1*arcsin((1+cos(c+d*x))^-1//2*sin(c+d*x))+2^(1/2)*d^-1*arcsin((1+cos(c+d*x))^-1*sin(c+d*x))+d^-1*(1+cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((1+cos(c+d*x))^-1//2*cos(c+d*x)^(1/2), x) == :(2*d^-1*arcsin((1+cos(c+d*x))^-1//2*sin(c+d*x))+-1*2^(1/2)*d^-1*arcsin((1+cos(c+d*x))^-1*sin(c+d*x)))
@test integrate((1+cos(c+d*x))^-1//2*cos(c+d*x)^-1//2, x) == :(2^(1/2)*d^-1*arcsin((1+cos(c+d*x))^-1*sin(c+d*x)))
@test integrate((1+cos(c+d*x))^-1//2*cos(c+d*x)^-3//2, x) == :(-1*2^(1/2)*d^-1*arcsin((1+cos(c+d*x))^-1*sin(c+d*x))+2*d^-1*(1+cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((1+cos(c+d*x))^-1//2*cos(c+d*x)^-5//2, x) == :(2^(1/2)*d^-1*arcsin((1+cos(c+d*x))^-1*sin(c+d*x))+-2//3*d^-1*(1+cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+2//3*d^-1*(1+cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((1+cos(c+d*x))^-1//2*cos(c+d*x)^-7//2, x) == :(-1*2^(1/2)*d^-1*arcsin((1+cos(c+d*x))^-1*sin(c+d*x))+-2//15*d^-1*(1+cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+2//5*d^-1*(1+cos(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x)+26//15*d^-1*(1+cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-3//2*cos(c+d*x)^5//2, x) == :(-3*a^-3//2*d^-1*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+-1//2*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^3//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*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+3//2*a^-1*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-3//2*cos(c+d*x)^3//2, x) == :(2*a^-3//2*d^-1*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+-5//4*2^(1/2)*a^-3//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-1//2*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-3//2*cos(c+d*x)^(1/2), x) == :((1/2)*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^(1/2)*sin(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-3//2*cos(c+d*x)^-1//2, x) == :(-1//2*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^(1/2)*sin(c+d*x)+3//4*2^(1/2)*a^-3//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-3//2*cos(c+d*x)^-3//2, x) == :(-7//4*2^(1/2)*a^-3//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-1//2*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^-1//2*sin(c+d*x)+5//2*a^-1*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-3//2*cos(c+d*x)^-5//2, x) == :(-1//2*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^-3//2*sin(c+d*x)+11//4*2^(1/2)*a^-3//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-19//6*a^-1*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+7//6*a^-1*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-5//2*cos(c+d*x)^7//2, x) == :(-5*a^-5//2*d^-1*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+-1//4*d^-1*(a+a*cos(c+d*x))^-5//2*cos(c+d*x)^5//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*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-15//16*a^-1*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^3//2*sin(c+d*x)+35//16*a^-2*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-5//2*cos(c+d*x)^5//2, x) == :(2*a^-5//2*d^-1*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+-43//32*2^(1/2)*a^-5//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-1//4*d^-1*(a+a*cos(c+d*x))^-5//2*cos(c+d*x)^3//2*sin(c+d*x)+-11//16*a^-1*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-5//2*cos(c+d*x)^3//2, x) == :(-1//4*d^-1*(a+a*cos(c+d*x))^-5//2*cos(c+d*x)^(1/2)*sin(c+d*x)+3//32*2^(1/2)*a^-5//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+7//16*a^-1*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-5//2*cos(c+d*x)^(1/2), x) == :(1//4*d^-1*(a+a*cos(c+d*x))^-5//2*cos(c+d*x)^(1/2)*sin(c+d*x)+5//32*2^(1/2)*a^-5//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+1//16*a^-1*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-5//2*cos(c+d*x)^-1//2, x) == :(-1//4*d^-1*(a+a*cos(c+d*x))^-5//2*cos(c+d*x)^(1/2)*sin(c+d*x)+19//32*2^(1/2)*a^-5//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-9//16*a^-1*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-5//2*cos(c+d*x)^-3//2, x) == :(-75//32*2^(1/2)*a^-5//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-1//4*d^-1*(a+a*cos(c+d*x))^-5//2*cos(c+d*x)^-1//2*sin(c+d*x)+-13//16*a^-1*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^-1//2*sin(c+d*x)+49//16*a^-2*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-5//2*cos(c+d*x)^-5//2, x) == :(-1//4*d^-1*(a+a*cos(c+d*x))^-5//2*cos(c+d*x)^-3//2*sin(c+d*x)+163//32*2^(1/2)*a^-5//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-299//48*a^-2*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+-17//16*a^-1*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^-3//2*sin(c+d*x)+95//48*a^-2*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-7//2*cos(c+d*x)^9//2, x) == :(-7*a^-7//2*d^-1*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+-1//6*d^-1*(a+a*cos(c+d*x))^-7//2*cos(c+d*x)^7//2*sin(c+d*x)+637//128*2^(1/2)*a^-7//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-259//192*a^-2*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^3//2*sin(c+d*x)+-7//16*a^-1*d^-1*(a+a*cos(c+d*x))^-5//2*cos(c+d*x)^5//2*sin(c+d*x)+189//64*a^-3*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-7//2*cos(c+d*x)^7//2, x) == :(2*a^-7//2*d^-1*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+-177//128*2^(1/2)*a^-7//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-1//6*d^-1*(a+a*cos(c+d*x))^-7//2*cos(c+d*x)^5//2*sin(c+d*x)+-49//64*a^-2*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^(1/2)*sin(c+d*x)+-17//48*a^-1*d^-1*(a+a*cos(c+d*x))^-5//2*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-7//2*cos(c+d*x)^5//2, x) == :(-1//6*d^-1*(a+a*cos(c+d*x))^-7//2*cos(c+d*x)^3//2*sin(c+d*x)+5//128*2^(1/2)*a^-7//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-13//48*a^-1*d^-1*(a+a*cos(c+d*x))^-5//2*cos(c+d*x)^(1/2)*sin(c+d*x)+67//192*a^-2*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-7//2*cos(c+d*x)^3//2, x) == :(-1//6*d^-1*(a+a*cos(c+d*x))^-7//2*cos(c+d*x)^(1/2)*sin(c+d*x)+7//128*2^(1/2)*a^-7//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+3//16*a^-1*d^-1*(a+a*cos(c+d*x))^-5//2*cos(c+d*x)^(1/2)*sin(c+d*x)+17//192*a^-2*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-7//2*cos(c+d*x)^(1/2), x) == :(1//6*d^-1*(a+a*cos(c+d*x))^-7//2*cos(c+d*x)^(1/2)*sin(c+d*x)+13//128*2^(1/2)*a^-7//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-5//192*a^-2*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^(1/2)*sin(c+d*x)+1//16*a^-1*d^-1*(a+a*cos(c+d*x))^-5//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-7//2*cos(c+d*x)^-1//2, x) == :(-1//6*d^-1*(a+a*cos(c+d*x))^-7//2*cos(c+d*x)^(1/2)*sin(c+d*x)+63//128*2^(1/2)*a^-7//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-103//192*a^-2*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^(1/2)*sin(c+d*x)+-5//16*a^-1*d^-1*(a+a*cos(c+d*x))^-5//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-7//2*cos(c+d*x)^-3//2, x) == :(-363//128*2^(1/2)*a^-7//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-1//6*d^-1*(a+a*cos(c+d*x))^-7//2*cos(c+d*x)^-1//2*sin(c+d*x)+-199//192*a^-2*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^-1//2*sin(c+d*x)+-19//48*a^-1*d^-1*(a+a*cos(c+d*x))^-5//2*cos(c+d*x)^-1//2*sin(c+d*x)+691//192*a^-3*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-7//2*cos(c+d*x)^-5//2, x) == :(-1//6*d^-1*(a+a*cos(c+d*x))^-7//2*cos(c+d*x)^-3//2*sin(c+d*x)+1015//128*2^(1/2)*a^-7//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-629//64*a^-3*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+-109//64*a^-2*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^-3//2*sin(c+d*x)+-23//48*a^-1*d^-1*(a+a*cos(c+d*x))^-5//2*cos(c+d*x)^-3//2*sin(c+d*x)+193//64*a^-3*d^-1*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-9//2*cos(c+d*x)^7//2, x) == :(-1//8*d^-1*(a+a*cos(c+d*x))^-9//2*cos(c+d*x)^5//2*sin(c+d*x)+35//2048*2^(1/2)*a^-9//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-187//768*a^-2*d^-1*(a+a*cos(c+d*x))^-5//2*cos(c+d*x)^(1/2)*sin(c+d*x)+-19//96*a^-1*d^-1*(a+a*cos(c+d*x))^-7//2*cos(c+d*x)^3//2*sin(c+d*x)+853//3072*a^-3*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-9//2*cos(c+d*x)^5//2, x) == :(-1//8*d^-1*(a+a*cos(c+d*x))^-9//2*cos(c+d*x)^3//2*sin(c+d*x)+45//2048*2^(1/2)*a^-9//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-5//32*a^-1*d^-1*(a+a*cos(c+d*x))^-7//2*cos(c+d*x)^(1/2)*sin(c+d*x)+33//256*a^-2*d^-1*(a+a*cos(c+d*x))^-5//2*cos(c+d*x)^(1/2)*sin(c+d*x)+73//1024*a^-3*d^-1*(a+a*cos(c+d*x))^-3//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((1+cos(x))^-1//2*cos(x)^-1//2, x) == :(2^(1/2)*arcsin((1+cos(x))^-1*sin(x)))
@test integrate((a+a*cos(x))^-1//2*cos(x)^-1//2, x) == :(2^(1/2)*a^-1//2*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(x))^-1//2*cos(x)^-1//2*sin(x)))
@test integrate((a+-1*a*cos(c+d*x))^(1/2)*cos(c+d*x)^3//2, x) == :(-3//4*a^(1/2)*d^-1*arctanh(a^(1/2)*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-1//2*a*d^-1*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x)+3//4*a*d^-1*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+-1*a*cos(c+d*x))^(1/2)*cos(c+d*x)^(1/2), x) == :(a^(1/2)*d^-1*arctanh(a^(1/2)*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-1*a*d^-1*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+-1*a*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2, x) == :(-2*a^(1/2)*d^-1*arctanh(a^(1/2)*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+-1*a*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2, x) == :(2*a*d^-1*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+-1*a*cos(c+d*x))^(1/2)*cos(c+d*x)^-5//2, x) == :(-4//3*a*d^-1*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+2//3*a*d^-1*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+-1*a*cos(c+d*x))^(1/2)*cos(c+d*x)^-7//2, x) == :(-8//15*a*d^-1*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+2//5*a*d^-1*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x)+16//15*a*d^-1*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((1+-1*cos(c+d*x))^(1/2)*cos(c+d*x)^3//2, x) == :(-3//4*d^-1*arctanh((1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-1//2*d^-1*(1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x)+3//4*d^-1*(1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((1+-1*cos(c+d*x))^(1/2)*cos(c+d*x)^(1/2), x) == :(d^-1*arctanh((1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-1*d^-1*(1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((1+-1*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2, x) == :(-2*d^-1*arctanh((1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((1+-1*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2, x) == :(2*d^-1*(1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((1+-1*cos(c+d*x))^(1/2)*cos(c+d*x)^-5//2, x) == :(-4//3*d^-1*(1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+2//3*d^-1*(1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((1+-1*cos(c+d*x))^(1/2)*cos(c+d*x)^-7//2, x) == :(-8//15*d^-1*(1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+2//5*d^-1*(1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x)+16//15*d^-1*(1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^5//2, x) == :(7//4*a^-1//2*d^-1*arctanh(a^(1/2)*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+(1/2)*d^-1*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+1//4*d^-1*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^3//2, x) == :(a^-1//2*d^-1*arctanh(a^(1/2)*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+d^-1*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2), x) == :(2*a^-1//2*d^-1*arctanh(a^(1/2)*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-1*2^(1/2)*a^-1//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+-1*a*cos(c+d*x))^-1//2*cos(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+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2, x) == :(-1*2^(1/2)*a^-1//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+2*d^-1*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+-1*a*cos(c+d*x))^-1//2*cos(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+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+2//3*d^-1*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+2//3*d^-1*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-7//2, x) == :(-1*2^(1/2)*a^-1//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+2//5*d^-1*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x)+2//15*d^-1*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+26//15*d^-1*(a+-1*a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^5//2, x) == :(7//4*d^-1*arctanh((1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-1*2^(1/2)*d^-1*arctanh((1/2)*2^(1/2)*(1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+(1/2)*d^-1*(1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x)+1//4*d^-1*(1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^3//2, x) == :(d^-1*arctanh((1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-1*2^(1/2)*d^-1*arctanh((1/2)*2^(1/2)*(1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+d^-1*(1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2), x) == :(2*d^-1*arctanh((1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+-1*2^(1/2)*d^-1*arctanh((1/2)*2^(1/2)*(1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2, x) == :(-1*2^(1/2)*d^-1*arctanh((1/2)*2^(1/2)*(1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2, x) == :(-1*2^(1/2)*d^-1*arctanh((1/2)*2^(1/2)*(1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+2*d^-1*(1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^-5//2, x) == :(-1*2^(1/2)*d^-1*arctanh((1/2)*2^(1/2)*(1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))+2//3*d^-1*(1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+2//3*d^-1*(1+-1*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate(sec(c+d*x)^7//2*(a+a*cos(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)^5//2*(a+a*cos(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)^3//2*(a+a*cos(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*cos(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)^-1//2*(a+a*cos(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)^-3//2*(a+a*cos(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)^-5//2*(a+a*cos(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*cos(c+d*x))^2*sec(c+d*x)^7//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*cos(c+d*x))^2*sec(c+d*x)^5//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*cos(c+d*x))^2*sec(c+d*x)^3//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*cos(c+d*x))^2*sec(c+d*x)^(1/2), 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*cos(c+d*x))^2*sec(c+d*x)^-1//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*cos(c+d*x))^2*sec(c+d*x)^-3//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*cos(c+d*x))^3*sec(c+d*x)^9//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*cos(c+d*x))^3*sec(c+d*x)^7//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*cos(c+d*x))^3*sec(c+d*x)^5//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*cos(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*cos(c+d*x))^3*sec(c+d*x)^(1/2), 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*cos(c+d*x))^3*sec(c+d*x)^-1//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*cos(c+d*x))^3*sec(c+d*x)^-3//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*cos(c+d*x))^4*sec(c+d*x)^9//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*cos(c+d*x))^4*sec(c+d*x)^7//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*cos(c+d*x))^4*sec(c+d*x)^5//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*cos(c+d*x))^4*sec(c+d*x)^3//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*cos(c+d*x))^4*sec(c+d*x)^(1/2), 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*cos(c+d*x))^4*sec(c+d*x)^-1//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*cos(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)^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*cos(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)^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*cos(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)+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*cos(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*cos(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)+-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*cos(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)^-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*cos(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)^-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*cos(c+d*x))^-2*sec(c+d*x)^5//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*cos(c+d*x))^-2*sec(c+d*x)^3//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*cos(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*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*cos(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)+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*cos(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)+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*cos(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)^(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*cos(c+d*x))^-2*sec(c+d*x)^-7//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*cos(c+d*x))^-2*sec(c+d*x)^-9//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*cos(c+d*x))^-3*sec(c+d*x)^3//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*cos(c+d*x))^-3*sec(c+d*x)^(1/2), 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*cos(c+d*x))^-3*sec(c+d*x)^-1//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*cos(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*cos(c+d*x))^-3*sec(c+d*x)^-5//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*cos(c+d*x))^-3*sec(c+d*x)^-7//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*cos(c+d*x))^-3*sec(c+d*x)^-9//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*cos(c+d*x))^(1/2)*sec(c+d*x)^9//2, x) == :(2//7*a*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^7//2*sin(c+d*x)+12//35*a*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^5//2*sin(c+d*x)+16//35*a*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x)+32//35*a*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^(1/2)*sec(c+d*x)^7//2, x) == :(2//5*a*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^5//2*sin(c+d*x)+8//15*a*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x)+16//15*a*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^(1/2)*sec(c+d*x)^5//2, x) == :(2//3*a*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x)+4//3*a*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^(1/2)*sec(c+d*x)^3//2, x) == :(2*a*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^(1/2)*sec(c+d*x)^(1/2), x) == :(2*a^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^(1/2)*sec(c+d*x)^-1//2, x) == :(a*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x)+a^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^(1/2)*sec(c+d*x)^-3//2, x) == :((1/2)*a*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^-3//2*sin(c+d*x)+3//4*a*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x)+3//4*a^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^3//2*sec(c+d*x)^9//2, x) == :(2//7*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^7//2*sin(c+d*x)+26//35*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^5//2*sin(c+d*x)+104//105*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x)+208//105*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^3//2*sec(c+d*x)^7//2, x) == :(2//5*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^5//2*sin(c+d*x)+6//5*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x)+12//5*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^3//2*sec(c+d*x)^5//2, x) == :(2//3*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x)+10//3*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^3//2*sec(c+d*x)^3//2, x) == :(2*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*sec(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)*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^3//2*sec(c+d*x)^(1/2), x) == :(a^2*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x)+3*a^3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^3//2*sec(c+d*x)^-1//2, x) == :((1/2)*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^-3//2*sin(c+d*x)+7//4*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x)+7//4*a^3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^3//2*sec(c+d*x)^-3//2, x) == :(1//3*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^-5//2*sin(c+d*x)+11//8*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x)+11//8*a^3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+11//12*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^5//2*sec(c+d*x)^11//2, x) == :(2//9*a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*sec(c+d*x)^9//2*sin(c+d*x)+38//63*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^7//2*sin(c+d*x)+146//105*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^5//2*sin(c+d*x)+584//315*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x)+1168//315*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^5//2*sec(c+d*x)^9//2, x) == :(2//7*a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*sec(c+d*x)^7//2*sin(c+d*x)+6//7*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^5//2*sin(c+d*x)+46//21*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x)+92//21*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^5//2*sec(c+d*x)^7//2, x) == :(2//5*a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*sec(c+d*x)^5//2*sin(c+d*x)+22//15*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x)+86//15*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^5//2*sec(c+d*x)^5//2, x) == :(2*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+2//3*a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*sec(c+d*x)^3//2*sin(c+d*x)+14//3*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^5//2*sec(c+d*x)^3//2, x) == :(-1*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x)+2*a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*sec(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)*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^5//2*sec(c+d*x)^(1/2), x) == :((1/2)*a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*sec(c+d*x)^-1//2*sin(c+d*x)+9//4*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x)+19//4*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^5//2*sec(c+d*x)^-1//2, x) == :(1//3*a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*sec(c+d*x)^-3//2*sin(c+d*x)+13//12*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^-3//2*sin(c+d*x)+25//8*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x)+25//8*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^5//2*sec(c+d*x)^-3//2, x) == :(1//4*a^2*d^-1*(a+a*cos(c+d*x))^(1/2)*sec(c+d*x)^-5//2*sin(c+d*x)+17//24*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^-5//2*sin(c+d*x)+163//64*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x)+163//64*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+163//96*a^3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^-3//2*sin(c+d*x))
@test integrate((1+cos(c+d*x))^-1//2*sec(c+d*x)^7//2, x) == :(-2//15*d^-1*(1+cos(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x)+2//5*d^-1*(1+cos(c+d*x))^-1//2*sec(c+d*x)^5//2*sin(c+d*x)+26//15*d^-1*(1+cos(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)+-1*2^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsin((1+cos(c+d*x))^-1*sin(c+d*x)))
@test integrate((1+cos(c+d*x))^-1//2*sec(c+d*x)^5//2, x) == :(-2//3*d^-1*(1+cos(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)+2//3*d^-1*(1+cos(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x)+2^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsin((1+cos(c+d*x))^-1*sin(c+d*x)))
@test integrate((1+cos(c+d*x))^-1//2*sec(c+d*x)^3//2, x) == :(2*d^-1*(1+cos(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)+-1*2^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsin((1+cos(c+d*x))^-1*sin(c+d*x)))
@test integrate((1+cos(c+d*x))^-1//2*sec(c+d*x)^(1/2), x) == :(2^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsin((1+cos(c+d*x))^-1*sin(c+d*x)))
@test integrate((1+cos(c+d*x))^-1//2*sec(c+d*x)^-1//2, x) == :(2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsin((1+cos(c+d*x))^-1//2*sin(c+d*x))+-1*2^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsin((1+cos(c+d*x))^-1*sin(c+d*x)))
@test integrate((1+cos(c+d*x))^-1//2*sec(c+d*x)^-3//2, x) == :(d^-1*(1+cos(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x)+-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsin((1+cos(c+d*x))^-1//2*sin(c+d*x))+2^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsin((1+cos(c+d*x))^-1*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-1//2*sec(c+d*x)^7//2, x) == :(-2//15*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x)+2//5*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^5//2*sin(c+d*x)+26//15*d^-1*(a+a*cos(c+d*x))^-1//2*sec(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)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-1//2*sec(c+d*x)^5//2, x) == :(-2//3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)+2//3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^3//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)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-1//2*sec(c+d*x)^3//2, x) == :(2*d^-1*(a+a*cos(c+d*x))^-1//2*sec(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)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-1//2*sec(c+d*x)^-3//2, x) == :(d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x)+-1*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsin(a^(1/2)*(a+a*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)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-3//2*sec(c+d*x)^5//2, x) == :(-1//2*d^-1*(a+a*cos(c+d*x))^-3//2*sec(c+d*x)^3//2*sin(c+d*x)+-19//6*a^-1*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)+7//6*a^-1*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^3//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)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-3//2*sec(c+d*x)^3//2, x) == :(-1//2*d^-1*(a+a*cos(c+d*x))^-3//2*sec(c+d*x)^(1/2)*sin(c+d*x)+5//2*a^-1*d^-1*(a+a*cos(c+d*x))^-1//2*sec(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)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-3//2*sec(c+d*x)^(1/2), x) == :(-1//2*d^-1*(a+a*cos(c+d*x))^-3//2*sec(c+d*x)^-1//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)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-3//2*sec(c+d*x)^-1//2, x) == :((1/2)*d^-1*(a+a*cos(c+d*x))^-3//2*sec(c+d*x)^-1//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)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-3//2*sec(c+d*x)^-3//2, x) == :(-1//2*d^-1*(a+a*cos(c+d*x))^-3//2*sec(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)*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(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)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-3//2*sec(c+d*x)^-5//2, x) == :(-1//2*d^-1*(a+a*cos(c+d*x))^-3//2*sec(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)*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+3//2*a^-1*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^-1//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)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-5//2*sec(c+d*x)^5//2, x) == :(-1//4*d^-1*(a+a*cos(c+d*x))^-5//2*sec(c+d*x)^3//2*sin(c+d*x)+-299//48*a^-2*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)+-17//16*a^-1*d^-1*(a+a*cos(c+d*x))^-3//2*sec(c+d*x)^3//2*sin(c+d*x)+95//48*a^-2*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^3//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)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-5//2*sec(c+d*x)^3//2, x) == :(-1//4*d^-1*(a+a*cos(c+d*x))^-5//2*sec(c+d*x)^(1/2)*sin(c+d*x)+-13//16*a^-1*d^-1*(a+a*cos(c+d*x))^-3//2*sec(c+d*x)^(1/2)*sin(c+d*x)+49//16*a^-2*d^-1*(a+a*cos(c+d*x))^-1//2*sec(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)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-5//2*sec(c+d*x)^(1/2), x) == :(-1//4*d^-1*(a+a*cos(c+d*x))^-5//2*sec(c+d*x)^-1//2*sin(c+d*x)+-9//16*a^-1*d^-1*(a+a*cos(c+d*x))^-3//2*sec(c+d*x)^-1//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)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-5//2*sec(c+d*x)^-1//2, x) == :(1//4*d^-1*(a+a*cos(c+d*x))^-5//2*sec(c+d*x)^-1//2*sin(c+d*x)+1//16*a^-1*d^-1*(a+a*cos(c+d*x))^-3//2*sec(c+d*x)^-1//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)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-5//2*sec(c+d*x)^-3//2, x) == :(-1//4*d^-1*(a+a*cos(c+d*x))^-5//2*sec(c+d*x)^-1//2*sin(c+d*x)+7//16*a^-1*d^-1*(a+a*cos(c+d*x))^-3//2*sec(c+d*x)^-1//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)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-5//2*sec(c+d*x)^-5//2, x) == :(-1//4*d^-1*(a+a*cos(c+d*x))^-5//2*sec(c+d*x)^-3//2*sin(c+d*x)+2*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+-11//16*a^-1*d^-1*(a+a*cos(c+d*x))^-3//2*sec(c+d*x)^-1//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)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-5//2*sec(c+d*x)^-7//2, x) == :(-1//4*d^-1*(a+a*cos(c+d*x))^-5//2*sec(c+d*x)^-5//2*sin(c+d*x)+-5*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+-15//16*a^-1*d^-1*(a+a*cos(c+d*x))^-3//2*sec(c+d*x)^-3//2*sin(c+d*x)+35//16*a^-2*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^-1//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)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-7//2*sec(c+d*x)^5//2, x) == :(-1//6*d^-1*(a+a*cos(c+d*x))^-7//2*sec(c+d*x)^3//2*sin(c+d*x)+-629//64*a^-3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)+-109//64*a^-2*d^-1*(a+a*cos(c+d*x))^-3//2*sec(c+d*x)^3//2*sin(c+d*x)+-23//48*a^-1*d^-1*(a+a*cos(c+d*x))^-5//2*sec(c+d*x)^3//2*sin(c+d*x)+193//64*a^-3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x)+1015//128*2^(1/2)*a^-7//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-7//2*sec(c+d*x)^3//2, x) == :(-1//6*d^-1*(a+a*cos(c+d*x))^-7//2*sec(c+d*x)^(1/2)*sin(c+d*x)+-199//192*a^-2*d^-1*(a+a*cos(c+d*x))^-3//2*sec(c+d*x)^(1/2)*sin(c+d*x)+-19//48*a^-1*d^-1*(a+a*cos(c+d*x))^-5//2*sec(c+d*x)^(1/2)*sin(c+d*x)+691//192*a^-3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)+-363//128*2^(1/2)*a^-7//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-7//2*sec(c+d*x)^(1/2), x) == :(-1//6*d^-1*(a+a*cos(c+d*x))^-7//2*sec(c+d*x)^-1//2*sin(c+d*x)+-103//192*a^-2*d^-1*(a+a*cos(c+d*x))^-3//2*sec(c+d*x)^-1//2*sin(c+d*x)+-5//16*a^-1*d^-1*(a+a*cos(c+d*x))^-5//2*sec(c+d*x)^-1//2*sin(c+d*x)+63//128*2^(1/2)*a^-7//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-7//2*sec(c+d*x)^-1//2, x) == :(1//6*d^-1*(a+a*cos(c+d*x))^-7//2*sec(c+d*x)^-1//2*sin(c+d*x)+-5//192*a^-2*d^-1*(a+a*cos(c+d*x))^-3//2*sec(c+d*x)^-1//2*sin(c+d*x)+1//16*a^-1*d^-1*(a+a*cos(c+d*x))^-5//2*sec(c+d*x)^-1//2*sin(c+d*x)+13//128*2^(1/2)*a^-7//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-7//2*sec(c+d*x)^-3//2, x) == :(-1//6*d^-1*(a+a*cos(c+d*x))^-7//2*sec(c+d*x)^-1//2*sin(c+d*x)+3//16*a^-1*d^-1*(a+a*cos(c+d*x))^-5//2*sec(c+d*x)^-1//2*sin(c+d*x)+17//192*a^-2*d^-1*(a+a*cos(c+d*x))^-3//2*sec(c+d*x)^-1//2*sin(c+d*x)+7//128*2^(1/2)*a^-7//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-7//2*sec(c+d*x)^-5//2, x) == :(-1//6*d^-1*(a+a*cos(c+d*x))^-7//2*sec(c+d*x)^-3//2*sin(c+d*x)+-13//48*a^-1*d^-1*(a+a*cos(c+d*x))^-5//2*sec(c+d*x)^-1//2*sin(c+d*x)+67//192*a^-2*d^-1*(a+a*cos(c+d*x))^-3//2*sec(c+d*x)^-1//2*sin(c+d*x)+5//128*2^(1/2)*a^-7//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-7//2*sec(c+d*x)^-7//2, x) == :(-1//6*d^-1*(a+a*cos(c+d*x))^-7//2*sec(c+d*x)^-5//2*sin(c+d*x)+2*a^-7//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+-49//64*a^-2*d^-1*(a+a*cos(c+d*x))^-3//2*sec(c+d*x)^-1//2*sin(c+d*x)+-17//48*a^-1*d^-1*(a+a*cos(c+d*x))^-5//2*sec(c+d*x)^-3//2*sin(c+d*x)+-177//128*2^(1/2)*a^-7//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-7//2*sec(c+d*x)^-9//2, x) == :(-1//6*d^-1*(a+a*cos(c+d*x))^-7//2*sec(c+d*x)^-7//2*sin(c+d*x)+-7*a^-7//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsin(a^(1/2)*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))+-259//192*a^-2*d^-1*(a+a*cos(c+d*x))^-3//2*sec(c+d*x)^-3//2*sin(c+d*x)+-7//16*a^-1*d^-1*(a+a*cos(c+d*x))^-5//2*sec(c+d*x)^-5//2*sin(c+d*x)+189//64*a^-3*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x)+637//128*2^(1/2)*a^-7//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-9//2*sec(c+d*x)^-5//2, x) == :(-1//8*d^-1*(a+a*cos(c+d*x))^-9//2*sec(c+d*x)^-3//2*sin(c+d*x)+-5//32*a^-1*d^-1*(a+a*cos(c+d*x))^-7//2*sec(c+d*x)^-1//2*sin(c+d*x)+33//256*a^-2*d^-1*(a+a*cos(c+d*x))^-5//2*sec(c+d*x)^-1//2*sin(c+d*x)+73//1024*a^-3*d^-1*(a+a*cos(c+d*x))^-3//2*sec(c+d*x)^-1//2*sin(c+d*x)+45//2048*2^(1/2)*a^-9//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^-9//2*sec(c+d*x)^-7//2, x) == :(-1//8*d^-1*(a+a*cos(c+d*x))^-9//2*sec(c+d*x)^-5//2*sin(c+d*x)+-187//768*a^-2*d^-1*(a+a*cos(c+d*x))^-5//2*sec(c+d*x)^-1//2*sin(c+d*x)+-19//96*a^-1*d^-1*(a+a*cos(c+d*x))^-7//2*sec(c+d*x)^-3//2*sin(c+d*x)+853//3072*a^-3*d^-1*(a+a*cos(c+d*x))^-3//2*sec(c+d*x)^-1//2*sin(c+d*x)+35//2048*2^(1/2)*a^-9//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)))
@test integrate((a+a*cos(c+d*x))^3//2*sec(c+d*x)^5//4, x) == :(4*a^2*d^-1*(a+a*cos(c+d*x))^-1//2*sec(c+d*x)^1//4*sin(c+d*x))
@test integrate(cos(c+d*x)^7*(a+b*cos(c+d*x)), x) == :(35//128*b*x+a*d^-1*sin(c+d*x)+-1*a*d^-1*sin(c+d*x)^3+-1//7*a*d^-1*sin(c+d*x)^7+3//5*a*d^-1*sin(c+d*x)^5+1//8*b*d^-1*cos(c+d*x)^7*sin(c+d*x)+7//48*b*d^-1*cos(c+d*x)^5*sin(c+d*x)+35//128*b*d^-1*cos(c+d*x)*sin(c+d*x)+35//192*b*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate(cos(c+d*x)^6*(a+b*cos(c+d*x)), x) == :(5//16*a*x+b*d^-1*sin(c+d*x)+-1*b*d^-1*sin(c+d*x)^3+-1//7*b*d^-1*sin(c+d*x)^7+3//5*b*d^-1*sin(c+d*x)^5+1//6*a*d^-1*cos(c+d*x)^5*sin(c+d*x)+5//16*a*d^-1*cos(c+d*x)*sin(c+d*x)+5//24*a*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate(cos(c+d*x)^5*(a+b*cos(c+d*x)), x) == :(5//16*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//6*b*d^-1*cos(c+d*x)^5*sin(c+d*x)+5//16*b*d^-1*cos(c+d*x)*sin(c+d*x)+5//24*b*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate(cos(c+d*x)^4*(a+b*cos(c+d*x)), x) == :(3//8*a*x+b*d^-1*sin(c+d*x)+-2//3*b*d^-1*sin(c+d*x)^3+1//5*b*d^-1*sin(c+d*x)^5+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)^3*(a+b*cos(c+d*x)), x) == :(3//8*b*x+a*d^-1*sin(c+d*x)+-1//3*a*d^-1*sin(c+d*x)^3+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(cos(c+d*x)^2*(a+b*cos(c+d*x)), x) == :((1/2)*a*x+b*d^-1*sin(c+d*x)+-1//3*b*d^-1*sin(c+d*x)^3+(1/2)*a*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))*cos(c+d*x), x) == :((1/2)*b*x+a*d^-1*sin(c+d*x)+(1/2)*b*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(a+b*cos(c+d*x), x) == :(a*x+b*d^-1*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))*sec(c+d*x), x) == :(b*x+a*d^-1*arctanh(sin(c+d*x)))
@test integrate(sec(c+d*x)^2*(a+b*cos(c+d*x)), x) == :(a*d^-1*tan(c+d*x)+b*d^-1*arctanh(sin(c+d*x)))
@test integrate(sec(c+d*x)^3*(a+b*cos(c+d*x)), x) == :(b*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(sec(c+d*x)^4*(a+b*cos(c+d*x)), x) == :(a*d^-1*tan(c+d*x)+(1/2)*b*d^-1*arctanh(sin(c+d*x))+1//3*a*d^-1*tan(c+d*x)^3+(1/2)*b*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate(sec(c+d*x)^5*(a+b*cos(c+d*x)), x) == :(b*d^-1*tan(c+d*x)+1//3*b*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)^6*(a+b*cos(c+d*x)), x) == :(a*d^-1*tan(c+d*x)+1//5*a*d^-1*tan(c+d*x)^5+2//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((a+b*cos(c+d*x))^2*cos(c+d*x)^4, x) == :(x*(3//8*a^2+5//16*b^2)+2*a*b*d^-1*sin(c+d*x)+-4//3*a*b*d^-1*sin(c+d*x)^3+1//6*b^2*d^-1*cos(c+d*x)^5*sin(c+d*x)+1//16*d^-1*(5*b^2+6*a^2)*cos(c+d*x)*sin(c+d*x)+1//24*d^-1*cos(c+d*x)^3*(5*b^2+6*a^2)*sin(c+d*x)+2//5*a*b*d^-1*sin(c+d*x)^5)
@test integrate((a+b*cos(c+d*x))^2*cos(c+d*x)^3, x) == :(d^-1*(a^2+b^2)*sin(c+d*x)+-1//3*d^-1*sin(c+d*x)^3*(a^2+2*b^2)+1//5*b^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*cos(c+d*x))^2*cos(c+d*x)^2, x) == :(x*((1/2)*a^2+3//8*b^2)+2*a*b*d^-1*sin(c+d*x)+-2//3*a*b*d^-1*sin(c+d*x)^3+1//4*b^2*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//8*d^-1*(3*b^2+4*a^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^2*cos(c+d*x), x) == :(a*b*x+1//3*d^-1*(a+b*cos(c+d*x))^2*sin(c+d*x)+1//3*d^-1*(2*a^2+2*b^2)*sin(c+d*x)+1//3*a*b*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^2, x) == :(x*(a^2+(1/2)*b^2)+(1/2)*b^2*d^-1*cos(c+d*x)*sin(c+d*x)+2*a*b*d^-1*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^2*sec(c+d*x), x) == :(a^2*d^-1*arctanh(sin(c+d*x))+b^2*d^-1*sin(c+d*x)+2*a*b*x)
@test integrate((a+b*cos(c+d*x))^2*sec(c+d*x)^2, x) == :(x*b^2+a^2*d^-1*tan(c+d*x)+2*a*b*d^-1*arctanh(sin(c+d*x)))
@test integrate((a+b*cos(c+d*x))^2*sec(c+d*x)^3, x) == :((1/2)*d^-1*(a^2+2*b^2)*arctanh(sin(c+d*x))+(1/2)*a^2*d^-1*sec(c+d*x)*tan(c+d*x)+2*a*b*d^-1*tan(c+d*x))
@test integrate((a+b*cos(c+d*x))^2*sec(c+d*x)^4, x) == :(1//3*d^-1*(2*a^2+3*b^2)*tan(c+d*x)+a*b*d^-1*arctanh(sin(c+d*x))+1//3*a^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*cos(c+d*x))^2*sec(c+d*x)^5, x) == :(1//8*d^-1*(3*a^2+4*b^2)*arctanh(sin(c+d*x))+2*a*b*d^-1*tan(c+d*x)+1//4*a^2*d^-1*sec(c+d*x)^3*tan(c+d*x)+1//8*d^-1*(3*a^2+4*b^2)*sec(c+d*x)*tan(c+d*x)+2//3*a*b*d^-1*tan(c+d*x)^3)
@test integrate((a+b*cos(c+d*x))^2*sec(c+d*x)^6, x) == :(1//5*d^-1*(4*a^2+5*b^2)*tan(c+d*x)+1//15*d^-1*tan(c+d*x)^3*(4*a^2+5*b^2)+1//5*a^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*cos(c+d*x))^3*cos(c+d*x)^2, x) == :(1//8*a*x*(4*a^2+9*b^2)+-1//30*b^-1*d^-1*(-16*b^4+3*a^4+-52*a^2*b^2)*sin(c+d*x)+1//5*b^-1*d^-1*(a+b*cos(c+d*x))^4*sin(c+d*x)+-1//20*a*b^-1*d^-1*(a+b*cos(c+d*x))^3*sin(c+d*x)+-1//60*b^-1*d^-1*(a+b*cos(c+d*x))^2*(-16*b^2+3*a^2)*sin(c+d*x)+-1//120*a*d^-1*(-71*b^2+6*a^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^3*cos(c+d*x), x) == :(1//4*d^-1*(a+b*cos(c+d*x))^3*sin(c+d*x)+3//8*b*x*(b^2+4*a^2)+(1/2)*a*d^-1*(a^2+4*b^2)*sin(c+d*x)+1//4*a*d^-1*(a+b*cos(c+d*x))^2*sin(c+d*x)+1//8*b*d^-1*(2*a^2+3*b^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^3*sec(c+d*x), x) == :(a^3*d^-1*arctanh(sin(c+d*x))+(1/2)*b*x*(b^2+6*a^2)+(1/2)*b^2*d^-1*(a+b*cos(c+d*x))*sin(c+d*x)+5//2*a*b^2*d^-1*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^3*sec(c+d*x)^2, x) == :(3*a*x*b^2+a^2*d^-1*(a+b*cos(c+d*x))*tan(c+d*x)+-1*b*d^-1*(a^2+-1*b^2)*sin(c+d*x)+3*b*a^2*d^-1*arctanh(sin(c+d*x)))
@test integrate((a+b*cos(c+d*x))^3*sec(c+d*x)^3, x) == :(x*b^3+(1/2)*a*d^-1*(a^2+6*b^2)*arctanh(sin(c+d*x))+5//2*b*a^2*d^-1*tan(c+d*x)+(1/2)*a^2*d^-1*(a+b*cos(c+d*x))*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*cos(c+d*x))^3*sec(c+d*x)^4, x) == :((1/2)*b*d^-1*(2*b^2+3*a^2)*arctanh(sin(c+d*x))+1//3*a*d^-1*(2*a^2+9*b^2)*tan(c+d*x)+1//3*a^2*d^-1*sec(c+d*x)^2*(a+b*cos(c+d*x))*tan(c+d*x)+7//6*b*a^2*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*cos(c+d*x))^3*sec(c+d*x)^5, x) == :(b*d^-1*(b^2+2*a^2)*tan(c+d*x)+3//8*a*d^-1*(a^2+4*b^2)*arctanh(sin(c+d*x))+1//4*a^2*d^-1*sec(c+d*x)^3*(a+b*cos(c+d*x))*tan(c+d*x)+3//4*b*a^2*d^-1*sec(c+d*x)^2*tan(c+d*x)+3//8*a*d^-1*(a^2+4*b^2)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*cos(c+d*x))^3*sec(c+d*x)^6, x) == :(1//5*a*d^-1*(4*a^2+15*b^2)*tan(c+d*x)+1//8*b*d^-1*(4*b^2+9*a^2)*arctanh(sin(c+d*x))+1//15*a*d^-1*tan(c+d*x)^3*(4*a^2+15*b^2)+1//5*a^2*d^-1*sec(c+d*x)^4*(a+b*cos(c+d*x))*tan(c+d*x)+1//8*b*d^-1*(4*b^2+9*a^2)*sec(c+d*x)*tan(c+d*x)+11//20*b*a^2*d^-1*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+b*cos(c+d*x))^4*cos(c+d*x)^3, x) == :(-1//105*d^-1*sin(c+d*x)^3*(24*b^4+35*a^4+168*a^2*b^2)+1//35*d^-1*(24*b^4+35*a^4+168*a^2*b^2)*sin(c+d*x)+1//4*a*b*x*(5*b^2+6*a^2)+1//7*b^2*d^-1*(a+b*cos(c+d*x))^2*cos(c+d*x)^4*sin(c+d*x)+1//35*b^2*d^-1*cos(c+d*x)^4*(6*b^2+37*a^2)*sin(c+d*x)+8//21*a*b^3*d^-1*cos(c+d*x)^5*sin(c+d*x)+1//4*a*b*d^-1*(5*b^2+6*a^2)*cos(c+d*x)*sin(c+d*x)+1//6*a*b*d^-1*cos(c+d*x)^3*(5*b^2+6*a^2)*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^4*cos(c+d*x)^2, x) == :(x*((1/2)*a^4+5//16*b^4+9//4*a^2*b^2)+-1//240*d^-1*(-75*b^4+8*a^4+-178*a^2*b^2)*cos(c+d*x)*sin(c+d*x)+1//6*b^-1*d^-1*(a+b*cos(c+d*x))^5*sin(c+d*x)+-1//30*a*b^-1*d^-1*(a+b*cos(c+d*x))^4*sin(c+d*x)+-1//60*a*b^-1*d^-1*(-128*b^4+4*a^4+-121*a^2*b^2)*sin(c+d*x)+-1//120*b^-1*d^-1*(a+b*cos(c+d*x))^3*(-25*b^2+4*a^2)*sin(c+d*x)+-1//120*a*b^-1*d^-1*(a+b*cos(c+d*x))^2*(-53*b^2+4*a^2)*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^4*cos(c+d*x), x) == :(1//5*d^-1*(a+b*cos(c+d*x))^4*sin(c+d*x)+1//15*d^-1*(6*a^4+8*b^4+56*a^2*b^2)*sin(c+d*x)+(1/2)*a*b*x*(3*b^2+4*a^2)+1//5*a*d^-1*(a+b*cos(c+d*x))^3*sin(c+d*x)+1//15*d^-1*(a+b*cos(c+d*x))^2*(3*a^2+4*b^2)*sin(c+d*x)+1//30*a*b*d^-1*(6*a^2+29*b^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^4, x) == :(x*(a^4+3//8*b^4+3*a^2*b^2)+1//4*b*d^-1*(a+b*cos(c+d*x))^3*sin(c+d*x)+1//6*a*b*d^-1*(16*b^2+19*a^2)*sin(c+d*x)+1//24*b^2*d^-1*(9*b^2+26*a^2)*cos(c+d*x)*sin(c+d*x)+7//12*a*b*d^-1*(a+b*cos(c+d*x))^2*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^4*sec(c+d*x), x) == :(a^4*d^-1*arctanh(sin(c+d*x))+2*a*b*x*(b^2+2*a^2)+1//3*b^2*d^-1*(a+b*cos(c+d*x))^2*sin(c+d*x)+1//3*b^2*d^-1*(2*b^2+17*a^2)*sin(c+d*x)+4//3*a*b^3*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^4*sec(c+d*x)^2, x) == :((1/2)*x*b^2*(b^2+12*a^2)+a^2*d^-1*(a+b*cos(c+d*x))^2*tan(c+d*x)+4*b*a^3*d^-1*arctanh(sin(c+d*x))+-2*a*b*d^-1*(a^2+-2*b^2)*sin(c+d*x)+-1//2*b^2*d^-1*(-1*b^2+2*a^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^4*sec(c+d*x)^3, x) == :(4*a*x*b^3+(1/2)*a^2*d^-1*(a^2+12*b^2)*arctanh(sin(c+d*x))+3*b*a^3*d^-1*tan(c+d*x)+-1//2*b^2*d^-1*(a^2+-2*b^2)*sin(c+d*x)+(1/2)*a^2*d^-1*(a+b*cos(c+d*x))^2*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*cos(c+d*x))^4*sec(c+d*x)^4, x) == :(x*b^4+1//3*a^2*d^-1*(2*a^2+17*b^2)*tan(c+d*x)+2*a*b*d^-1*(a^2+2*b^2)*arctanh(sin(c+d*x))+1//3*a^2*d^-1*(a+b*cos(c+d*x))^2*sec(c+d*x)^2*tan(c+d*x)+4//3*b*a^3*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*cos(c+d*x))^4*sec(c+d*x)^5, x) == :(1//8*d^-1*(3*a^4+8*b^4+24*a^2*b^2)*arctanh(sin(c+d*x))+1//4*a^2*d^-1*(a+b*cos(c+d*x))^2*sec(c+d*x)^3*tan(c+d*x)+1//8*a^2*d^-1*(3*a^2+22*b^2)*sec(c+d*x)*tan(c+d*x)+4//3*a*b*d^-1*(2*a^2+3*b^2)*tan(c+d*x)+5//6*b*a^3*d^-1*sec(c+d*x)^2*tan(c+d*x))
@test integrate((a+b*cos(c+d*x))^4*sec(c+d*x)^6, x) == :(1//15*d^-1*(8*a^4+15*b^4+60*a^2*b^2)*tan(c+d*x)+(1/2)*a*b*d^-1*(3*a^2+4*b^2)*arctanh(sin(c+d*x))+1//5*a^2*d^-1*(a+b*cos(c+d*x))^2*sec(c+d*x)^4*tan(c+d*x)+1//15*a^2*d^-1*sec(c+d*x)^2*(4*a^2+27*b^2)*tan(c+d*x)+3//5*b*a^3*d^-1*sec(c+d*x)^3*tan(c+d*x)+(1/2)*a*b*d^-1*(3*a^2+4*b^2)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*cos(c+d*x))^4*sec(c+d*x)^7, x) == :(1//16*d^-1*(5*a^4+8*b^4+36*a^2*b^2)*arctanh(sin(c+d*x))+1//16*d^-1*(5*a^4+8*b^4+36*a^2*b^2)*sec(c+d*x)*tan(c+d*x)+1//6*a^2*d^-1*(a+b*cos(c+d*x))^2*sec(c+d*x)^5*tan(c+d*x)+1//24*a^2*d^-1*sec(c+d*x)^3*(5*a^2+32*b^2)*tan(c+d*x)+4//5*a*b*d^-1*(4*a^2+5*b^2)*tan(c+d*x)+4//15*a*b*d^-1*tan(c+d*x)^3*(4*a^2+5*b^2)+7//15*b*a^3*d^-1*sec(c+d*x)^4*tan(c+d*x))
@test integrate((a+b*cos(c+d*x))^-1*cos(c+d*x)^5, x) == :(1//8*x*b^-5*(3*b^4+8*a^4+4*a^2*b^2)+1//4*b^-1*d^-1*cos(c+d*x)^3*sin(c+d*x)+-1//3*a*b^-4*d^-1*(2*b^2+3*a^2)*sin(c+d*x)+-1//3*a*b^-2*d^-1*cos(c+d*x)^2*sin(c+d*x)+1//8*b^-3*d^-1*(3*b^2+4*a^2)*cos(c+d*x)*sin(c+d*x)+-2*a^5*b^-5*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*cos(c+d*x))^-1*cos(c+d*x)^4, x) == :(-1//2*a*x*b^-4*(b^2+2*a^2)+1//3*b^-1*d^-1*cos(c+d*x)^2*sin(c+d*x)+1//3*b^-3*d^-1*(2*b^2+3*a^2)*sin(c+d*x)+-1//2*a*b^-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*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*cos(c+d*x))^-1*cos(c+d*x)^3, x) == :((1/2)*x*b^-3*(b^2+2*a^2)+(1/2)*b^-1*d^-1*cos(c+d*x)*sin(c+d*x)+-1*a*b^-2*d^-1*sin(c+d*x)+-2*a^3*b^-3*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*cos(c+d*x))^-1*cos(c+d*x)^2, x) == :(b^-1*d^-1*sin(c+d*x)+-1*a*x*b^-2+2*a^2*b^-2*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*cos(c+d*x))^-1*cos(c+d*x), x) == :(x*b^-1+-2*a*b^-1*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*cos(c+d*x))^-1, x) == :(2*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*cos(c+d*x))^-1*sec(c+d*x), x) == :(a^-1*d^-1*arctanh(sin(c+d*x))+-2*b*a^-1*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*cos(c+d*x))^-1*sec(c+d*x)^2, x) == :(a^-1*d^-1*tan(c+d*x)+-1*b*a^-2*d^-1*arctanh(sin(c+d*x))+2*a^-2*b^2*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*cos(c+d*x))^-1*sec(c+d*x)^3, x) == :((1/2)*a^-1*d^-1*sec(c+d*x)*tan(c+d*x)+(1/2)*a^-3*d^-1*(a^2+2*b^2)*arctanh(sin(c+d*x))+-1*b*a^-2*d^-1*tan(c+d*x)+-2*a^-3*b^3*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*cos(c+d*x))^-1*sec(c+d*x)^4, x) == :(1//3*a^-1*d^-1*sec(c+d*x)^2*tan(c+d*x)+1//3*a^-3*d^-1*(2*a^2+3*b^2)*tan(c+d*x)+-1//2*b*a^-4*d^-1*(a^2+2*b^2)*arctanh(sin(c+d*x))+-1//2*b*a^-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*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*cos(c+d*x))^-2*cos(c+d*x)^5, x) == :(-1*a*x*b^-5*(b^2+4*a^2)+1//3*b^-4*d^-1*(a^2+-1*b^2)^-1*(-2*b^4+12*a^4+-7*a^2*b^2)*sin(c+d*x)+1//3*b^-2*d^-1*(a^2+-1*b^2)^-1*cos(c+d*x)^2*(-1*b^2+4*a^2)*sin(c+d*x)+-1*a*b^-3*d^-1*(a^2+-1*b^2)^-1*(-1*b^2+2*a^2)*cos(c+d*x)*sin(c+d*x)+-1*a^2*b^-1*d^-1*(a+b*cos(c+d*x))^-1*(a^2+-1*b^2)^-1*cos(c+d*x)^3*sin(c+d*x)+2*a^4*b^-5*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-5*b^2+4*a^2)*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*cos(c+d*x))^-2*cos(c+d*x)^3, x) == :(-2*a*x*b^-3+b^-2*d^-1*(a^2+-1*b^2)^-1*(-1*b^2+2*a^2)*sin(c+d*x)+-1*a^2*b^-1*d^-1*(a+b*cos(c+d*x))^-1*(a^2+-1*b^2)^-1*cos(c+d*x)*sin(c+d*x)+2*a^2*b^-3*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-3*b^2+2*a^2)*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*cos(c+d*x))^-2*cos(c+d*x)^2, x) == :(x*b^-2+-1*a^2*b^-1*d^-1*(a+b*cos(c+d*x))^-1*(a^2+-1*b^2)^-1*sin(c+d*x)+-2*a*b^-2*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(a^2+-2*b^2)*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*cos(c+d*x))^-2*cos(c+d*x), x) == :(a*d^-1*(a+b*cos(c+d*x))^-1*(a^2+-1*b^2)^-1*sin(c+d*x)+-2*b*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*cos(c+d*x))^-2, x) == :(-1*b*d^-1*(a+b*cos(c+d*x))^-1*(a^2+-1*b^2)^-1*sin(c+d*x)+2*a*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*cos(c+d*x))^-2*sec(c+d*x), x) == :(a^-2*d^-1*arctanh(sin(c+d*x))+a^-1*b^2*d^-1*(a+b*cos(c+d*x))^-1*(a^2+-1*b^2)^-1*sin(c+d*x)+-2*b*a^-2*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-1*b^2+2*a^2)*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*cos(c+d*x))^-2*sec(c+d*x)^2, x) == :(-2*b*a^-3*d^-1*arctanh(sin(c+d*x))+a^-2*d^-1*(a^2+-1*b^2)^-1*(a^2+-2*b^2)*tan(c+d*x)+a^-1*b^2*d^-1*(a+b*cos(c+d*x))^-1*(a^2+-1*b^2)^-1*tan(c+d*x)+2*a^-3*b^2*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-2*b^2+3*a^2)*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*cos(c+d*x))^-2*sec(c+d*x)^3, x) == :((1/2)*a^-4*d^-1*(a^2+6*b^2)*arctanh(sin(c+d*x))+(1/2)*a^-2*d^-1*(a^2+-1*b^2)^-1*(a^2+-3*b^2)*sec(c+d*x)*tan(c+d*x)+-1*b*a^-3*d^-1*(a^2+-1*b^2)^-1*(-3*b^2+2*a^2)*tan(c+d*x)+a^-1*b^2*d^-1*(a+b*cos(c+d*x))^-1*(a^2+-1*b^2)^-1*sec(c+d*x)*tan(c+d*x)+-2*a^-4*b^3*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-3*b^2+4*a^2)*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*cos(c+d*x))^-2*sec(c+d*x)^4, x) == :(-1*b*a^-5*d^-1*(a^2+4*b^2)*arctanh(sin(c+d*x))+1//3*a^-4*d^-1*(a^2+-1*b^2)^-1*(-12*b^4+2*a^4+7*a^2*b^2)*tan(c+d*x)+1//3*a^-2*d^-1*(a^2+-1*b^2)^-1*sec(c+d*x)^2*(a^2+-4*b^2)*tan(c+d*x)+a^-1*b^2*d^-1*(a+b*cos(c+d*x))^-1*(a^2+-1*b^2)^-1*sec(c+d*x)^2*tan(c+d*x)+-1*b*a^-3*d^-1*(a^2+-1*b^2)^-1*(a^2+-2*b^2)*sec(c+d*x)*tan(c+d*x)+2*a^-5*b^4*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-4*b^2+5*a^2)*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*cos(c+d*x))^-3*cos(c+d*x)^5, x) == :((1/2)*x*b^-5*(b^2+12*a^2)+(1/2)*b^-3*d^-1*(a^2+-1*b^2)^-2*(b^4+6*a^4+-10*a^2*b^2)*cos(c+d*x)*sin(c+d*x)+-3//2*a*b^-4*d^-1*(a^2+-1*b^2)^-2*(2*b^4+4*a^4+-7*a^2*b^2)*sin(c+d*x)+-1*a^3*b^-5*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(12*a^4+20*b^4+-29*a^2*b^2)*arctan((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*cos(c+d*x))^-2*(a^2+-1*b^2)^-1*cos(c+d*x)^3*sin(c+d*x)+-1//2*a^2*b^-2*d^-1*(a+b*cos(c+d*x))^-1*(a^2+-1*b^2)^-2*cos(c+d*x)^2*(-7*b^2+4*a^2)*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^-3*cos(c+d*x)^4, x) == :(-3*a*x*b^-4+(1/2)*b^-3*d^-1*(a^2+-1*b^2)^-1*(-2*b^2+3*a^2)*sin(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)*arctan((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*cos(c+d*x))^-2*(a^2+-1*b^2)^-1*cos(c+d*x)^2*sin(c+d*x)+3//2*a^3*b^-3*d^-1*(a+b*cos(c+d*x))^-1*(a^2+-1*b^2)^-2*(a^2+-2*b^2)*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^-3*cos(c+d*x)^3, x) == :(x*b^-3+-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)*arctan((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*cos(c+d*x))^-2*(a^2+-1*b^2)^-1*cos(c+d*x)*sin(c+d*x)+-1//2*a^2*b^-2*d^-1*(a+b*cos(c+d*x))^-1*(a^2+-1*b^2)^-2*(-5*b^2+2*a^2)*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^-3*cos(c+d*x)^2, x) == :(d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(a^2+2*b^2)*arctan((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*cos(c+d*x))^-2*(a^2+-1*b^2)^-1*sin(c+d*x)+(1/2)*a*b^-1*d^-1*(a+b*cos(c+d*x))^-1*(a^2+-1*b^2)^-2*(a^2+-4*b^2)*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^-3*cos(c+d*x), x) == :(a*d^-1*(a+b*cos(c+d*x))^-2*(-2*b^2+2*a^2)^-1*sin(c+d*x)+(1/2)*d^-1*(a+b*cos(c+d*x))^-1*(a^2+-1*b^2)^-2*(a^2+2*b^2)*sin(c+d*x)+-3*a*b*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*cos(c+d*x))^-3, x) == :(d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(b^2+2*a^2)*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1*b*d^-1*(a+b*cos(c+d*x))^-2*(-2*b^2+2*a^2)^-1*sin(c+d*x)+-3//2*a*b*d^-1*(a+b*cos(c+d*x))^-1*(a^2+-1*b^2)^-2*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^-3*sec(c+d*x), x) == :(a^-3*d^-1*arctanh(sin(c+d*x))+(1/2)*a^-1*b^2*d^-1*(a+b*cos(c+d*x))^-2*(a^2+-1*b^2)^-1*sin(c+d*x)+(1/2)*a^-2*b^2*d^-1*(a+b*cos(c+d*x))^-1*(a^2+-1*b^2)^-2*(-2*b^2+5*a^2)*sin(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)*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*cos(c+d*x))^-3*sec(c+d*x)^2, x) == :(-3*b*a^-4*d^-1*arctanh(sin(c+d*x))+(1/2)*a^-3*d^-1*(a^2+-1*b^2)^-2*(2*a^4+6*b^4+-11*a^2*b^2)*tan(c+d*x)+(1/2)*a^-1*b^2*d^-1*(a+b*cos(c+d*x))^-2*(a^2+-1*b^2)^-1*tan(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)*arctan((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*cos(c+d*x))^-1*(a^2+-1*b^2)^-2*(-1*b^2+2*a^2)*tan(c+d*x))
@test integrate((a+b*cos(c+d*x))^-3*sec(c+d*x)^3, x) == :((1/2)*a^-5*d^-1*(a^2+12*b^2)*arctanh(sin(c+d*x))+(1/2)*a^-3*d^-1*(a^2+-1*b^2)^-2*(a^4+6*b^4+-10*a^2*b^2)*sec(c+d*x)*tan(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)*tan(c+d*x)+(1/2)*a^-1*b^2*d^-1*(a+b*cos(c+d*x))^-2*(a^2+-1*b^2)^-1*sec(c+d*x)*tan(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)*arctan((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*cos(c+d*x))^-1*(a^2+-1*b^2)^-2*(-4*b^2+7*a^2)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*cos(c+d*x))^-4*cos(c+d*x)^5, x) == :(-4*a*x*b^-5+1//6*b^-4*d^-1*(a^2+-1*b^2)^-2*(6*b^4+12*a^4+-23*a^2*b^2)*sin(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)*arctan((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*cos(c+d*x))^-1*(a^2+-1*b^2)^-3*(4*a^4+12*b^4+-11*a^2*b^2)*sin(c+d*x)+-1//3*a^2*b^-1*d^-1*(a+b*cos(c+d*x))^-3*(a^2+-1*b^2)^-1*cos(c+d*x)^3*sin(c+d*x)+-1//6*a^2*b^-2*d^-1*(a+b*cos(c+d*x))^-2*(a^2+-1*b^2)^-2*cos(c+d*x)^2*(-9*b^2+4*a^2)*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^-4*cos(c+d*x)^4, x) == :(x*b^-4+-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)*arctan((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*cos(c+d*x))^-3*(a^2+-1*b^2)^-1*cos(c+d*x)^2*sin(c+d*x)+-1//6*a^2*b^-3*d^-1*(a+b*cos(c+d*x))^-1*(a^2+-1*b^2)^-3*(9*a^4+34*b^4+-28*a^2*b^2)*sin(c+d*x)+1//6*a^3*b^-3*d^-1*(a+b*cos(c+d*x))^-2*(a^2+-1*b^2)^-2*(-8*b^2+3*a^2)*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^-4*cos(c+d*x)^3, x) == :(-1*b*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(2*b^2+3*a^2)*arctan((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*cos(c+d*x))^-3*(a^2+-1*b^2)^-1*cos(c+d*x)*sin(c+d*x)+-1//6*a^2*b^-2*d^-1*(a+b*cos(c+d*x))^-2*(a^2+-1*b^2)^-2*(-7*b^2+2*a^2)*sin(c+d*x)+1//6*a*b^-2*d^-1*(a+b*cos(c+d*x))^-1*(a^2+-1*b^2)^-3*(2*a^4+18*b^4+-5*a^2*b^2)*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^-4*cos(c+d*x)^2, x) == :(a*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(a^2+4*b^2)*arctan((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*cos(c+d*x))^-3*(a^2+-1*b^2)^-1*sin(c+d*x)+1//6*b^-1*d^-1*(a+b*cos(c+d*x))^-1*(a^2+-1*b^2)^-3*(a^4+-6*b^4+-10*a^2*b^2)*sin(c+d*x)+1//6*a*b^-1*d^-1*(a+b*cos(c+d*x))^-2*(a^2+-1*b^2)^-2*(a^2+-6*b^2)*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^-4*cos(c+d*x), x) == :(a*d^-1*(a+b*cos(c+d*x))^-3*(-3*b^2+3*a^2)^-1*sin(c+d*x)+1//6*d^-1*(a+b*cos(c+d*x))^-2*(a^2+-1*b^2)^-2*(2*a^2+3*b^2)*sin(c+d*x)+-1*b*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(b^2+4*a^2)*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+1//6*a*d^-1*(a+b*cos(c+d*x))^-1*(a^2+-1*b^2)^-3*(2*a^2+13*b^2)*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^-4, x) == :(-1*b*d^-1*(a+b*cos(c+d*x))^-3*(-3*b^2+3*a^2)^-1*sin(c+d*x)+a*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(2*a^2+3*b^2)*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-5//6*a*b*d^-1*(a+b*cos(c+d*x))^-2*(a^2+-1*b^2)^-2*sin(c+d*x)+-1//6*b*d^-1*(a+b*cos(c+d*x))^-1*(a^2+-1*b^2)^-3*(4*b^2+11*a^2)*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^-4*sec(c+d*x), x) == :(a^-4*d^-1*arctanh(sin(c+d*x))+1//3*a^-1*b^2*d^-1*(a+b*cos(c+d*x))^-3*(a^2+-1*b^2)^-1*sin(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)*arctan((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*cos(c+d*x))^-1*(a^2+-1*b^2)^-3*(6*b^4+26*a^4+-17*a^2*b^2)*sin(c+d*x)+1//6*a^-2*b^2*d^-1*(a+b*cos(c+d*x))^-2*(a^2+-1*b^2)^-2*(-3*b^2+8*a^2)*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^-4*sec(c+d*x)^2, x) == :(-4*b*a^-5*d^-1*arctanh(sin(c+d*x))+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)*tan(c+d*x)+1//3*a^-1*b^2*d^-1*(a+b*cos(c+d*x))^-3*(a^2+-1*b^2)^-1*tan(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)*arctan((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*cos(c+d*x))^-1*(a^2+-1*b^2)^-3*(4*b^4+12*a^4+-11*a^2*b^2)*tan(c+d*x)+1//6*a^-2*b^2*d^-1*(a+b*cos(c+d*x))^-2*(a^2+-1*b^2)^-2*(-4*b^2+9*a^2)*tan(c+d*x))
@test integrate((a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^3, x) == :(-8//35*a*b^-2*d^-1*(a+b*cos(c+d*x))^3//2*sin(c+d*x)+1//105*b^-2*d^-1*(a+b*cos(c+d*x))^(1/2)*(16*a^2+50*b^2)*sin(c+d*x)+2//7*b^-1*d^-1*(a+b*cos(c+d*x))^3//2*cos(c+d*x)*sin(c+d*x)+-1//105*b^-3*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*(-50*b^4+16*a^4+34*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+2//105*a*b^-3*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*(8*a^2+19*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^2, x) == :(2//5*b^-1*d^-1*(a+b*cos(c+d*x))^3//2*sin(c+d*x)+-4//15*a*b^-1*d^-1*(a+b*cos(c+d*x))^(1/2)*sin(c+d*x)+-1//15*b^-2*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*(-18*b^2+4*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+4//15*a*b^-2*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^(1/2)*cos(c+d*x), x) == :(2//3*d^-1*(a+b*cos(c+d*x))^(1/2)*sin(c+d*x)+-1//3*b^-1*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*(-2*b^2+2*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+2//3*a*b^-1*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^(1/2), x) == :(2*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^3//2*cos(c+d*x)^3, x) == :(-8//63*a*b^-2*d^-1*(a+b*cos(c+d*x))^5//2*sin(c+d*x)+1//315*b^-2*d^-1*(a+b*cos(c+d*x))^3//2*(16*a^2+98*b^2)*sin(c+d*x)+2//9*b^-1*d^-1*(a+b*cos(c+d*x))^5//2*cos(c+d*x)*sin(c+d*x)+1//315*b^-3*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*(16*a^4+294*b^4+66*a^2*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+2//315*a*b^-2*d^-1*(a+b*cos(c+d*x))^(1/2)*(8*a^2+39*b^2)*sin(c+d*x)+-2//315*a*b^-3*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*(-39*b^4+8*a^4+31*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^3//2*cos(c+d*x)^2, x) == :(2//7*b^-1*d^-1*(a+b*cos(c+d*x))^5//2*sin(c+d*x)+-4//35*a*b^-1*d^-1*(a+b*cos(c+d*x))^3//2*sin(c+d*x)+-1//105*b^-1*d^-1*(a+b*cos(c+d*x))^(1/2)*(-50*b^2+12*a^2)*sin(c+d*x)+1//105*b^-2*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*(12*a^4+50*b^4+-62*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+-4//105*a*b^-2*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*(-41*b^2+3*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^3//2*cos(c+d*x), x) == :(2//5*d^-1*(a+b*cos(c+d*x))^3//2*sin(c+d*x)+2//5*a*d^-1*(a+b*cos(c+d*x))^(1/2)*sin(c+d*x)+1//5*b^-1*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*(2*a^2+6*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+-2//5*a*b^-1*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^3//2, x) == :(2//3*b*d^-1*(a+b*cos(c+d*x))^(1/2)*sin(c+d*x)+-1//3*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*(-2*b^2+2*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+8//3*a*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^5//2*cos(c+d*x)^3, x) == :(-8//99*a*b^-2*d^-1*(a+b*cos(c+d*x))^7//2*sin(c+d*x)+1//693*b^-2*d^-1*(a+b*cos(c+d*x))^(1/2)*(16*a^4+270*b^4+114*a^2*b^2)*sin(c+d*x)+1//693*b^-2*d^-1*(a+b*cos(c+d*x))^5//2*(16*a^2+162*b^2)*sin(c+d*x)+2//11*b^-1*d^-1*(a+b*cos(c+d*x))^7//2*cos(c+d*x)*sin(c+d*x)+-1//693*b^-3*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*(-270*b^6+16*a^6+98*a^4*b^2+156*a^2*b^4)*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+2//693*a*b^-2*d^-1*(a+b*cos(c+d*x))^3//2*(8*a^2+67*b^2)*sin(c+d*x)+2//693*a*b^-3*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*(8*a^4+741*b^4+51*a^2*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^5//2*cos(c+d*x)^2, x) == :(2//9*b^-1*d^-1*(a+b*cos(c+d*x))^7//2*sin(c+d*x)+-4//63*a*b^-1*d^-1*(a+b*cos(c+d*x))^5//2*sin(c+d*x)+-1//315*b^-1*d^-1*(a+b*cos(c+d*x))^3//2*(-98*b^2+20*a^2)*sin(c+d*x)+-4//315*a*b^-1*d^-1*(a+b*cos(c+d*x))^(1/2)*(-57*b^2+5*a^2)*sin(c+d*x)+-1//315*b^-2*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*(-294*b^4+20*a^4+-558*a^2*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+4//315*a*b^-2*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*(5*a^4+57*b^4+-62*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^5//2*cos(c+d*x), x) == :(2//7*d^-1*(a+b*cos(c+d*x))^5//2*sin(c+d*x)+1//21*d^-1*(a+b*cos(c+d*x))^(1/2)*(6*a^2+10*b^2)*sin(c+d*x)+2//7*a*d^-1*(a+b*cos(c+d*x))^3//2*sin(c+d*x)+-1//21*b^-1*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*(-10*b^4+6*a^4+4*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+2//21*a*b^-1*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*(3*a^2+29*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^5//2, x) == :(2//5*b*d^-1*(a+b*cos(c+d*x))^3//2*sin(c+d*x)+1//15*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*(18*b^2+46*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+16//15*a*b*d^-1*(a+b*cos(c+d*x))^(1/2)*sin(c+d*x)+-16//15*a*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^7//2, x) == :(2//7*b*d^-1*(a+b*cos(c+d*x))^5//2*sin(c+d*x)+-1//105*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*(-50*b^4+142*a^4+-92*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+2//105*b*d^-1*(a+b*cos(c+d*x))^(1/2)*(25*b^2+71*a^2)*sin(c+d*x)+24//35*a*b*d^-1*(a+b*cos(c+d*x))^3//2*sin(c+d*x)+32//105*a*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*(11*a^2+13*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((3+4*cos(c+d*x))^(1/2)*cos(c+d*x)^3, x) == :(-3//70*d^-1*(3+4*cos(c+d*x))^3//2*sin(c+d*x)+47//140*7^(1/2)*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,8//7)+59//105*d^-1*(3+4*cos(c+d*x))^(1/2)*sin(c+d*x)+59//420*7^(1/2)*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,8//7)+1//14*d^-1*(3+4*cos(c+d*x))^3//2*cos(c+d*x)*sin(c+d*x))
@test integrate((3+4*cos(c+d*x))^(1/2)*cos(c+d*x)^2, x) == :(-1//5*d^-1*(3+4*cos(c+d*x))^(1/2)*sin(c+d*x)+-1//20*7^(1/2)*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,8//7)+1//10*d^-1*(3+4*cos(c+d*x))^3//2*sin(c+d*x)+21//20*7^(1/2)*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,8//7))
@test integrate((3+4*cos(c+d*x))^(1/2)*cos(c+d*x), x) == :((1/2)*7^(1/2)*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,8//7)+1//6*7^(1/2)*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,8//7)+2//3*d^-1*(3+4*cos(c+d*x))^(1/2)*sin(c+d*x))
@test integrate((3+4*cos(c+d*x))^(1/2), x) == :(2*7^(1/2)*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,8//7))
@test integrate((3+-4*cos(c+d*x))^(1/2)*cos(c+d*x)^3, x) == :(-59//420*7^(1/2)*d^-1*Elliptic.F((1/2)*pi+(1/2)*c+(1/2)*d*x,8//7)+-47//140*7^(1/2)*d^-1*Elliptic.E((1/2)*pi+(1/2)*c+(1/2)*d*x,8//7)+-3//70*d^-1*(3+-4*cos(c+d*x))^3//2*sin(c+d*x)+59//105*d^-1*(3+-4*cos(c+d*x))^(1/2)*sin(c+d*x)+-1//14*d^-1*(3+-4*cos(c+d*x))^3//2*cos(c+d*x)*sin(c+d*x))
@test integrate((3+-4*cos(c+d*x))^(1/2)*cos(c+d*x)^2, x) == :(-1//10*d^-1*(3+-4*cos(c+d*x))^3//2*sin(c+d*x)+-1//20*7^(1/2)*d^-1*Elliptic.F((1/2)*pi+(1/2)*c+(1/2)*d*x,8//7)+1//5*d^-1*(3+-4*cos(c+d*x))^(1/2)*sin(c+d*x)+21//20*7^(1/2)*d^-1*Elliptic.E((1/2)*pi+(1/2)*c+(1/2)*d*x,8//7))
@test integrate((3+-4*cos(c+d*x))^(1/2)*cos(c+d*x), x) == :(-1//2*7^(1/2)*d^-1*Elliptic.E((1/2)*pi+(1/2)*c+(1/2)*d*x,8//7)+-1//6*7^(1/2)*d^-1*Elliptic.F((1/2)*pi+(1/2)*c+(1/2)*d*x,8//7)+2//3*d^-1*(3+-4*cos(c+d*x))^(1/2)*sin(c+d*x))
@test integrate((3+-4*cos(c+d*x))^(1/2), x) == :(2*7^(1/2)*d^-1*Elliptic.E((1/2)*pi+(1/2)*c+(1/2)*d*x,8//7))
@test integrate((a+b*cos(c+d*x))^-1//2*cos(c+d*x)^3, x) == :(-8//15*a*b^-2*d^-1*(a+b*cos(c+d*x))^(1/2)*sin(c+d*x)+2//5*b^-1*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)*sin(c+d*x)+1//15*b^-3*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*(16*a^2+18*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+-2//15*a*b^-3*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*(7*b^2+8*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^-1//2*cos(c+d*x)^2, x) == :(2//3*b^-1*d^-1*(a+b*cos(c+d*x))^(1/2)*sin(c+d*x)+-4//3*a*b^-2*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+1//3*b^-2*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*(2*b^2+4*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^-1//2*cos(c+d*x), x) == :(2*b^-1*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+-2*a*b^-1*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^-1//2, x) == :(2*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^-3//2*cos(c+d*x)^4, x) == :(-2*a^2*b^-1*d^-1*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^2*sin(c+d*x)+-8//5*a*b^-4*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*(b^2+4*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+-2//5*a*b^-3*d^-1*(a+b*cos(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*(-3*b^2+8*a^2)*sin(c+d*x)+1//5*b^-4*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*(-6*b^4+32*a^4+-16*a^2*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+1//5*b^-2*d^-1*(a+b*cos(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*(-2*b^2+12*a^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^-3//2*cos(c+d*x)^3, x) == :(1//3*b^-3*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*(2*b^2+16*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+1//3*b^-2*d^-1*(a+b*cos(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*(-2*b^2+8*a^2)*sin(c+d*x)+-2*a^2*b^-1*d^-1*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)*sin(c+d*x)+-2//3*a*b^-3*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*(-5*b^2+8*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^-3//2*cos(c+d*x)^2, x) == :(-4*a*b^-2*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+-2*a^2*b^-1*d^-1*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sin(c+d*x)+b^-2*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*(-2*b^2+4*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^-3//2*cos(c+d*x), x) == :(2*a*d^-1*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sin(c+d*x)+2*b^-1*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+-2*a*b^-1*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^-3//2, x) == :(-2*b*d^-1*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sin(c+d*x)+2*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^-5//2*cos(c+d*x)^5, x) == :(-4//15*a*b^-4*d^-1*(a+b*cos(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*(7*b^4+32*a^4+-49*a^2*b^2)*sin(c+d*x)+-2//3*a^2*b^-1*d^-1*(a+b*cos(c+d*x))^-3//2*(a^2+-1*b^2)^-1*cos(c+d*x)^3*sin(c+d*x)+1//15*b^-5*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*(18*b^6+256*a^6+-424*a^4*b^2+110*a^2*b^4)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+1//15*b^-3*d^-1*(a+b*cos(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*(6*b^4+96*a^4+-142*a^2*b^2)*cos(c+d*x)*sin(c+d*x)+-8//3*a^2*b^-2*d^-1*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-2*cos(c+d*x)^2*(-3*b^2+2*a^2)*sin(c+d*x)+-2//15*a*b^-5*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-1*(-17*b^4+128*a^4+-116*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^-5//2*cos(c+d*x)^4, x) == :(1//3*b^-3*d^-1*(a+b*cos(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*(-2*b^2+4*a^2)*sin(c+d*x)+-2//3*a^2*b^-1*d^-1*(a+b*cos(c+d*x))^-3//2*(a^2+-1*b^2)^-1*cos(c+d*x)^2*sin(c+d*x)+1//3*b^-4*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-1*(-2*b^4+32*a^4+-32*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+4//3*a^3*b^-3*d^-1*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-2*(-5*b^2+3*a^2)*sin(c+d*x)+-8//3*a*b^-4*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*(2*b^4+4*a^4+-7*a^2*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^-5//2*cos(c+d*x)^3, x) == :(-8//3*a^2*b^-2*d^-1*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-2*(a^2+-2*b^2)*sin(c+d*x)+-2//3*a^2*b^-1*d^-1*(a+b*cos(c+d*x))^-3//2*(a^2+-1*b^2)^-1*cos(c+d*x)*sin(c+d*x)+1//3*b^-3*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*(6*b^4+16*a^4+-30*a^2*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+-2//3*a*b^-3*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-1*(-9*b^2+8*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^-5//2*cos(c+d*x)^2, x) == :(-2//3*a^2*b^-1*d^-1*(a+b*cos(c+d*x))^-3//2*(a^2+-1*b^2)^-1*sin(c+d*x)+1//3*b^-2*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-1*(-6*b^2+4*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+4//3*a*b^-1*d^-1*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-2*(a^2+-3*b^2)*sin(c+d*x)+-4//3*a*b^-2*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*(a^2+-3*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^-5//2*cos(c+d*x), x) == :(2*a*d^-1*(a+b*cos(c+d*x))^-3//2*(-3*b^2+3*a^2)^-1*sin(c+d*x)+1//3*d^-1*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-2*(2*a^2+6*b^2)*sin(c+d*x)+1//3*b^-1*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*(-6*b^2+-2*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+2//3*a*b^-1*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^-5//2, x) == :(-2*b*d^-1*(a+b*cos(c+d*x))^-3//2*(-3*b^2+3*a^2)^-1*sin(c+d*x)+-2*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*(-3*b^2+3*a^2)^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+-8//3*a*b*d^-1*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-2*sin(c+d*x)+8//3*a*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*cos(c+d*x))^-7//2, x) == :(-2*b*d^-1*(a+b*cos(c+d*x))^-5//2*(-5*b^2+5*a^2)^-1*sin(c+d*x)+-16//15*a*b*d^-1*(a+b*cos(c+d*x))^-3//2*(a^2+-1*b^2)^-2*sin(c+d*x)+-16//15*a*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^(1/2)*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-2*Elliptic.F((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1)+-2//15*b*d^-1*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-3*(9*b^2+23*a^2)*sin(c+d*x)+1//15*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*(a^2+-1*b^2)^-3*(18*b^2+46*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((3+4*cos(c+d*x))^-1//2*cos(c+d*x)^3, x) == :(-23//140*7^(1/2)*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,8//7)+-1//10*d^-1*(3+4*cos(c+d*x))^(1/2)*sin(c+d*x)+9//20*7^(1/2)*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,8//7)+1//10*d^-1*(3+4*cos(c+d*x))^(1/2)*cos(c+d*x)*sin(c+d*x))
@test integrate((3+4*cos(c+d*x))^-1//2*cos(c+d*x)^2, x) == :(-1//4*7^(1/2)*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,8//7)+1//6*d^-1*(3+4*cos(c+d*x))^(1/2)*sin(c+d*x)+17//84*7^(1/2)*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,8//7))
@test integrate((3+4*cos(c+d*x))^-1//2*cos(c+d*x), x) == :((1/2)*7^(1/2)*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,8//7)+-3//14*7^(1/2)*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,8//7))
@test integrate((3+4*cos(c+d*x))^-1//2, x) == :(2//7*7^(1/2)*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,8//7))
@test integrate((3+-4*cos(c+d*x))^-1//2*cos(c+d*x)^3, x) == :(-9//20*7^(1/2)*d^-1*Elliptic.E((1/2)*pi+(1/2)*c+(1/2)*d*x,8//7)+-1//10*d^-1*(3+-4*cos(c+d*x))^(1/2)*sin(c+d*x)+23//140*7^(1/2)*d^-1*Elliptic.F((1/2)*pi+(1/2)*c+(1/2)*d*x,8//7)+-1//10*d^-1*(3+-4*cos(c+d*x))^(1/2)*cos(c+d*x)*sin(c+d*x))
@test integrate((3+-4*cos(c+d*x))^-1//2*cos(c+d*x)^2, x) == :(-1//4*7^(1/2)*d^-1*Elliptic.E((1/2)*pi+(1/2)*c+(1/2)*d*x,8//7)+-1//6*d^-1*(3+-4*cos(c+d*x))^(1/2)*sin(c+d*x)+17//84*7^(1/2)*d^-1*Elliptic.F((1/2)*pi+(1/2)*c+(1/2)*d*x,8//7))
@test integrate((3+-4*cos(c+d*x))^-1//2*cos(c+d*x), x) == :(-1//2*7^(1/2)*d^-1*Elliptic.E((1/2)*pi+(1/2)*c+(1/2)*d*x,8//7)+3//14*7^(1/2)*d^-1*Elliptic.F((1/2)*pi+(1/2)*c+(1/2)*d*x,8//7))
@test integrate((3+-4*cos(c+d*x))^-1//2, x) == :(2//7*7^(1/2)*d^-1*Elliptic.F((1/2)*pi+(1/2)*c+(1/2)*d*x,8//7))
@test integrate(cos(c+d*x)^5//2*(A+B*cos(c+d*x)), x) == :(6//5*A*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+10//21*B*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*A*d^-1*cos(c+d*x)^3//2*sin(c+d*x)+2//7*B*d^-1*cos(c+d*x)^5//2*sin(c+d*x)+10//21*B*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate(cos(c+d*x)^3//2*(A+B*cos(c+d*x)), x) == :(2//3*A*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+6//5*B*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*A*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+2//5*B*d^-1*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate(cos(c+d*x)^(1/2)*(A+B*cos(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//3*B*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate(cos(c+d*x)^-1//2*(A+B*cos(c+d*x)), x) == :(2*A*d^-1*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*B*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate(cos(c+d*x)^-3//2*(A+B*cos(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)+2*A*d^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate(cos(c+d*x)^-5//2*(A+B*cos(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*B*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)^-7//2*(A+B*cos(c+d*x)), x) == :(-6//5*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//3*B*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((a+b*cos(c+d*x))^2*cos(c+d*x)^5//2, x) == :(1//15*d^-1*(14*b^2+18*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//45*d^-1*cos(c+d*x)^3//2*(14*b^2+18*a^2)*sin(c+d*x)+2//9*b^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*cos(c+d*x))^2*cos(c+d*x)^3//2, x) == :(1//21*d^-1*(10*b^2+14*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*(10*b^2+14*a^2)*sin(c+d*x)+2//7*b^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*cos(c+d*x))^2*cos(c+d*x)^(1/2), x) == :(1//5*d^-1*(6*b^2+10*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//5*b^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*cos(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)^(1/2)*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^2*cos(c+d*x)^-3//2, x) == :(-1*d^-1*(-2*b^2+2*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*a^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*cos(c+d*x))^2*cos(c+d*x)^-5//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)^-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*cos(c+d*x))^2*cos(c+d*x)^-7//2, x) == :(-1//5*d^-1*(6*a^2+10*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*cos(c+d*x)^-1//2*(6*a^2+10*b^2)*sin(c+d*x)+2//5*a^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*cos(c+d*x))^3*cos(c+d*x)^3//2, x) == :(2//15*b*d^-1*(7*b^2+27*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//21*a*d^-1*(7*a^2+15*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//9*b^2*d^-1*cos(c+d*x)^5//2*(a+b*cos(c+d*x))*sin(c+d*x)+2//21*a*d^-1*cos(c+d*x)^(1/2)*(7*a^2+15*b^2)*sin(c+d*x)+2//45*b*d^-1*cos(c+d*x)^3//2*(7*b^2+27*a^2)*sin(c+d*x)+40//63*a*b^2*d^-1*cos(c+d*x)^5//2*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^3*cos(c+d*x)^(1/2), 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//7*b^2*d^-1*cos(c+d*x)^3//2*(a+b*cos(c+d*x))*sin(c+d*x)+2//21*b*d^-1*cos(c+d*x)^(1/2)*(5*b^2+21*a^2)*sin(c+d*x)+32//35*a*b^2*d^-1*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+b*cos(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)^(1/2)*(a+b*cos(c+d*x))*sin(c+d*x)+8//5*a*b^2*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^3*cos(c+d*x)^-3//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*a^2*d^-1*cos(c+d*x)^-1//2*(a+b*cos(c+d*x))*sin(c+d*x)+-2//3*b*d^-1*cos(c+d*x)^(1/2)*(-1*b^2+3*a^2)*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^3*cos(c+d*x)^-5//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*a^2*d^-1*cos(c+d*x)^-3//2*(a+b*cos(c+d*x))*sin(c+d*x)+16//3*b*a^2*d^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^3*cos(c+d*x)^-7//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)^-5//2*(a+b*cos(c+d*x))*sin(c+d*x)+6//5*a*d^-1*cos(c+d*x)^-1//2*(a^2+5*b^2)*sin(c+d*x)+8//5*b*a^2*d^-1*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^3*cos(c+d*x)^-9//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//5*b*d^-1*cos(c+d*x)^-1//2*(5*b^2+9*a^2)*sin(c+d*x)+2//7*a^2*d^-1*cos(c+d*x)^-7//2*(a+b*cos(c+d*x))*sin(c+d*x)+2//21*a*d^-1*cos(c+d*x)^-3//2*(5*a^2+21*b^2)*sin(c+d*x)+32//35*b*a^2*d^-1*cos(c+d*x)^-5//2*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2, x) == :(a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x)+-1*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(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*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-5//2, x) == :(2//3*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2*sin(c+d*x)+1//3*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(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*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x)+1//3*b*a^-2*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-7//2, x) == :(2//5*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-5//2*sin(c+d*x)+2//15*b*a^-1*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2*sin(c+d*x)+-1//15*a^-2*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(2b+9a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x)+1//15*a^-3*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-2*b^2+9*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-9//2, x) == :(2//7*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-7//2*sin(c+d*x)+1//105*a^-2*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2*(-8*b^2+50*a^2)*sin(c+d*x)+2//35*b*a^-1*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-5//2*sin(c+d*x)+1//105*a^-3*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(8*b^2+25*a^2+6*a*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x)+1//105*b*a^-4*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(8*b^2+19*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*cos(c+d*x))^3//2*cos(c+d*x)^-5//2, x) == :(2//3*a*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2*sin(c+d*x)+1//3*b*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-8b+8a)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x)+1//3*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(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*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*cos(c+d*x))^3//2*cos(c+d*x)^-7//2, x) == :(2//5*a*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-5//2*sin(c+d*x)+4//5*b*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2*sin(c+d*x)+-1//5*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(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*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x)+1//5*a^-2*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(b^2+3*a^2)*(-2b+2a)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*cos(c+d*x))^3//2*cos(c+d*x)^-9//2, x) == :(2//7*a*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-7//2*sin(c+d*x)+16//35*b*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-5//2*sin(c+d*x)+1//105*a^-1*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2*(6*b^2+50*a^2)*sin(c+d*x)+1//105*a^-2*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-6*b^2+25*a^2+-57*a*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x)+1//105*b*a^-3*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-4b+4a)*(-3*b^2+41*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*cos(c+d*x))^3//2*cos(c+d*x)^-11//2, x) == :(2//9*a*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-9//2*sin(c+d*x)+20//63*b*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-7//2*sin(c+d*x)+1//315*a^-1*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-5//2*(6*b^2+98*a^2)*sin(c+d*x)+8//315*b*a^-2*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2*(-1*b^2+22*a^2)*sin(c+d*x)+-1//315*a^-3*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-8*b^3+147*a^3+-39*b*a^2+-6*a*b^2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x)+1//315*a^-4*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(8*b^4+147*a^4+33*a^2*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*cos(c+d*x))^5//2*cos(c+d*x)^-7//2, x) == :(2//5*a^2*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-5//2*sin(c+d*x)+22//15*a*b*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2*sin(c+d*x)+-1//15*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(9*a^2+15*b^2+-8*a*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x)+1//15*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(9*a^2+23*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*cos(c+d*x))^5//2*cos(c+d*x)^-9//2, x) == :(1//21*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2*(10*a^2+18*b^2)*sin(c+d*x)+2//7*a^2*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-7//2*sin(c+d*x)+6//7*a*b*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-5//2*sin(c+d*x)+1//21*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(3*b^2+5*a^2+-24*a*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x)+1//21*b*a^-2*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(3*b^2+29*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*cos(c+d*x))^5//2*cos(c+d*x)^-11//2, x) == :(1//315*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-5//2*(98*a^2+150*b^2)*sin(c+d*x)+2//9*a^2*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-9//2*sin(c+d*x)+38//63*a*b*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-7//2*sin(c+d*x)+2//315*b*a^-1*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2*(5*b^2+163*a^2)*sin(c+d*x)+-1//315*a^-2*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(10*b^3+147*a^3+-114*b*a^2+165*a*b^2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x)+1//315*a^-3*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-10*b^4+147*a^4+279*a^2*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*cos(c+d*x))^5//2*cos(c+d*x)^-13//2, x) == :(1//693*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-7//2*(162*a^2+226*b^2)*sin(c+d*x)+2//11*a^2*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-11//2*sin(c+d*x)+1//693*a^-2*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2*(-8*b^4+270*a^4+410*a^2*b^2)*sin(c+d*x)+46//99*a*b*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-9//2*sin(c+d*x)+2//693*b*a^-1*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-5//2*(3*b^2+229*a^2)*sin(c+d*x)+1//693*a^-3*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(8*b^4+135*a^4+-606*b*a^3+6*a*b^3+57*a^2*b^2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x)+1//693*b*a^-4*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(8*b^4+741*a^4+51*a^2*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2, x) == :(2*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2, x) == :(-2*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x)+a^-2*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*cos(c+d*x))^-1//2*cos(c+d*x)^-5//2, x) == :(2//3*a^-1*d^-1*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2*sin(c+d*x)+2//3*a^-2*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(a+2b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x)+-1//3*b*a^-3*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-4b+4a)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*cos(c+d*x))^-3//2*cos(c+d*x)^(1/2), x) == :(2*a*d^-1*(a+b*cos(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*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x)+2*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*cos(c+d*x))^-3//2*cos(c+d*x)^-1//2, x) == :(-2*b*d^-1*(a+b*cos(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*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x)+2*b*a^-2*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*cos(c+d*x))^-3//2*cos(c+d*x)^-3//2, x) == :(2*a^-1*b^2*d^-1*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*sin(c+d*x)+a^-3*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(-4*b^2+2*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x)+-1*a^-2*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(2a+4b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*cos(c+d*x))^-3//2*cos(c+d*x)^-5//2, x) == :(2*a^-1*b^2*d^-1*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-3//2*sin(c+d*x)+1//3*a^-2*d^-1*(a+b*cos(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*cos(c+d*x)^-3//2*(-8*b^2+2*a^2)*sin(c+d*x)+-2//3*b*a^-4*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(-8*b^2+5*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x)+1//3*a^-3*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(a+4b)*(2a+4b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*cos(c+d*x))^-3//2*cos(c+d*x)^-7//2, x) == :(2*a^-1*b^2*d^-1*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-5//2*sin(c+d*x)+1//5*a^-2*d^-1*(a+b*cos(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*cos(c+d*x)^-5//2*(-12*b^2+2*a^2)*sin(c+d*x)+-2//5*b*a^-3*d^-1*(a+b*cos(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*cos(c+d*x)^-3//2*(-8*b^2+3*a^2)*sin(c+d*x)+1//5*a^-5*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(-32*b^4+6*a^4+16*a^2*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x)+-1//5*a^-4*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(a^2+4*b^2)*(6a+8b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*cos(c+d*x))^-5//2*cos(c+d*x)^3//2, x) == :(2*a*d^-1*(a+b*cos(c+d*x))^-3//2*(-3*b^2+3*a^2)^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+-8//3*a*b*d^-1*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-2*cos(c+d*x)^-1//2*sin(c+d*x)+1//3*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(a+-1b)^-1*(-6b+2a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x)+8//3*b*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(a+-1b)^-1*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*cos(c+d*x))^-5//2*cos(c+d*x)^(1/2), x) == :(-2*b*d^-1*(a+b*cos(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*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-2*cos(c+d*x)^-1//2*(2*b^2+6*a^2)*sin(c+d*x)+-1//3*a^-2*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(a+-1b)^-1*(2*b^2+6*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x)+1//3*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(a+-1b)^-1*(-2b+6a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*cos(c+d*x))^-5//2*cos(c+d*x)^-1//2, x) == :(2//3*a^-1*b^2*d^-1*(a+b*cos(c+d*x))^-3//2*(a^2+-1*b^2)^-1*cos(c+d*x)^(1/2)*sin(c+d*x)+-4//3*b*a^-1*d^-1*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-2*cos(c+d*x)^-1//2*(-1*b^2+3*a^2)*sin(c+d*x)+1//3*a^-2*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(a+-1b)^-1*(-4*b^2+6*a^2+-6*a*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x)+4//3*b*a^-3*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(a+-1b)^-1*(-1*b^2+3*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*cos(c+d*x))^-5//2*cos(c+d*x)^-3//2, x) == :(2//3*a^-1*b^2*d^-1*(a+b*cos(c+d*x))^-3//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*sin(c+d*x)+8//3*a^-2*b^2*d^-1*(a+b*cos(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)+-1//3*a^-3*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(a+-1b)^-1*(-16*b^3+6*a^3+-12*a*b^2+18*b*a^2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x)+1//3*a^-4*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(a+-1b)^-1*(6*a^4+16*b^4+-30*a^2*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*cos(c+d*x))^-5//2*cos(c+d*x)^-5//2, x) == :(1//3*a^-3*d^-1*(a+b*cos(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*cos(c+d*x)^-3//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*cos(c+d*x))^-3//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-3//2*sin(c+d*x)+4//3*a^-2*b^2*d^-1*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-2*cos(c+d*x)^-3//2*(-3*b^2+5*a^2)*sin(c+d*x)+1//3*a^-4*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(a+-1b)^-1*(-32*b^4+2*a^4+-24*a*b^3+18*b*a^3+32*a^2*b^2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x)+-8//3*b*a^-5*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(a+-1b)^-1*(2*a^4+4*b^4+-7*a^2*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((2+3*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2, x) == :(2//5*5^(1/2)*d^-1*Elliptic.F(arcsin((1+cos(c+d*x))^-1*sin(c+d*x)),1//5))
@test integrate((-2+3*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2, x) == :(2*d^-1*Elliptic.F(arcsin((1+cos(c+d*x))^-1*sin(c+d*x)),5))
@test integrate((2+-3*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2, x) == :(-2//5*5^(1/2)*d^-1*(-1*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.F(arcsin((1+-1*cos(c+d*x))^-1*sin(c+d*x)),1//5))
@test integrate((-2+-3*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2, x) == :(-2*d^-1*(-1*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.F(arcsin((1+-1*cos(c+d*x))^-1*sin(c+d*x)),5))
@test integrate((3+2*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2, x) == :(2*d^-1*(-1*tan(c+d*x)^2)^(1/2)*Elliptic.F(arcsin(1//5*5^(1/2)*(3+2*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-5)*cot(c+d*x))
@test integrate((3+-2*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2, x) == :(2//5*5^(1/2)*d^-1*(-1*tan(c+d*x)^2)^(1/2)*Elliptic.F(arcsin((3+-2*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1//5)*cot(c+d*x))
@test integrate((-3+2*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2, x) == :(-2//5*5^(1/2)*d^-1*(-1*tan(c+d*x)^2)^(1/2)*(-1*cos(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*Elliptic.F(arcsin((-1*cos(c+d*x))^-1//2*(-3+2*cos(c+d*x))^(1/2)),-1//5)*csc(c+d*x))
@test integrate((-3+-2*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2, x) == :(-2*d^-1*(-1*tan(c+d*x)^2)^(1/2)*(-1*cos(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*Elliptic.F(arcsin(1//5*5^(1/2)*(-1*cos(c+d*x))^-1//2*(-3+-2*cos(c+d*x))^(1/2)),-5)*csc(c+d*x))
@test integrate((-1*cos(c+d*x))^-1//2*(2+3*cos(c+d*x))^-1//2, x) == :(2//5*5^(1/2)*d^-1*(-1*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F(arcsin((1+cos(c+d*x))^-1*sin(c+d*x)),1//5))
@test integrate((-1*cos(c+d*x))^-1//2*(-2+3*cos(c+d*x))^-1//2, x) == :(2*d^-1*(-1*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F(arcsin((1+cos(c+d*x))^-1*sin(c+d*x)),5))
@test integrate((-1*cos(c+d*x))^-1//2*(2+-3*cos(c+d*x))^-1//2, x) == :(-2//5*5^(1/2)*d^-1*Elliptic.F(arcsin((1+-1*cos(c+d*x))^-1*sin(c+d*x)),1//5))
@test integrate((-1*cos(c+d*x))^-1//2*(-2+-3*cos(c+d*x))^-1//2, x) == :(-2*d^-1*Elliptic.F(arcsin((1+-1*cos(c+d*x))^-1*sin(c+d*x)),5))
@test integrate((-1*cos(c+d*x))^-1//2*(3+2*cos(c+d*x))^-1//2, x) == :(2*d^-1*(-1*tan(c+d*x)^2)^(1/2)*(-1*cos(c+d*x))^-1//2*cos(c+d*x)^3//2*Elliptic.F(arcsin(1//5*5^(1/2)*(3+2*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-5)*csc(c+d*x))
@test integrate((-1*cos(c+d*x))^-1//2*(3+-2*cos(c+d*x))^-1//2, x) == :(2//5*5^(1/2)*d^-1*(-1*tan(c+d*x)^2)^(1/2)*(-1*cos(c+d*x))^-1//2*cos(c+d*x)^3//2*Elliptic.F(arcsin((3+-2*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1//5)*csc(c+d*x))
@test integrate((-1*cos(c+d*x))^-1//2*(-3+2*cos(c+d*x))^-1//2, x) == :(-2//5*5^(1/2)*d^-1*(-1*tan(c+d*x)^2)^(1/2)*Elliptic.F(arcsin((-1*cos(c+d*x))^-1//2*(-3+2*cos(c+d*x))^(1/2)),-1//5)*cot(c+d*x))
@test integrate((-1*cos(c+d*x))^-1//2*(-3+-2*cos(c+d*x))^-1//2, x) == :(-2*d^-1*(-1*tan(c+d*x)^2)^(1/2)*Elliptic.F(arcsin(1//5*5^(1/2)*(-1*cos(c+d*x))^-1//2*(-3+-2*cos(c+d*x))^(1/2)),-5)*cot(c+d*x))
@test integrate(sec(c+d*x)^7//2*(A+B*cos(c+d*x)), x) == :(2//3*B*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*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)^5//2*(A+B*cos(c+d*x)), x) == :(2*B*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*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*cos(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*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*cos(c+d*x)), x) == :(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)+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))
@test integrate(sec(c+d*x)^-1//2*(A+B*cos(c+d*x)), x) == :(2//3*B*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*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*cos(c+d*x)), x) == :(2//3*A*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+2//5*B*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*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(sec(c+d*x)^-5//2*(A+B*cos(c+d*x)), x) == :(2//5*A*d^-1*sec(c+d*x)^-3//2*sin(c+d*x)+2//7*B*d^-1*sec(c+d*x)^-5//2*sin(c+d*x)+10//21*B*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*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*cos(c+d*x))^2*sec(c+d*x)^9//2, x) == :(1//21*d^-1*sec(c+d*x)^3//2*(10*a^2+14*b^2)*sin(c+d*x)+2//7*a^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*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)^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*cos(c+d*x))^2*sec(c+d*x)^7//2, x) == :(1//5*d^-1*sec(c+d*x)^(1/2)*(6*a^2+10*b^2)*sin(c+d*x)+2//5*a^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*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)^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*cos(c+d*x))^2*sec(c+d*x)^5//2, x) == :(2//3*a^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*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*cos(c+d*x))^2*sec(c+d*x)^3//2, x) == :(2*a^2*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+-1*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*cos(c+d*x))^2*sec(c+d*x)^(1/2), x) == :(2//3*b^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*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*cos(c+d*x))^2*sec(c+d*x)^-1//2, x) == :(2//5*b^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*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)^-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*cos(c+d*x))^2*sec(c+d*x)^-3//2, x) == :(1//21*d^-1*sec(c+d*x)^-1//2*(10*b^2+14*a^2)*sin(c+d*x)+2//7*b^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*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)^-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*cos(c+d*x))^2*sec(c+d*x)^-5//2, x) == :(1//45*d^-1*sec(c+d*x)^-3//2*(14*b^2+18*a^2)*sin(c+d*x)+2//9*b^2*d^-1*sec(c+d*x)^-7//2*sin(c+d*x)+1//15*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(14*b^2+18*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//7*a*b*d^-1*sec(c+d*x)^-5//2*sin(c+d*x)+20//21*a*b*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+20//21*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*cos(c+d*x))^3*sec(c+d*x)^9//2, x) == :(2//5*b*d^-1*sec(c+d*x)^(1/2)*(5*b^2+9*a^2)*sin(c+d*x)+2//7*a^2*d^-1*sec(c+d*x)^5//2*(b+a*sec(c+d*x))*sin(c+d*x)+2//21*a*d^-1*sec(c+d*x)^3//2*(5*a^2+21*b^2)*sin(c+d*x)+32//35*b*a^2*d^-1*sec(c+d*x)^5//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*cos(c+d*x))^3*sec(c+d*x)^7//2, x) == :(2//5*a^2*d^-1*sec(c+d*x)^3//2*(b+a*sec(c+d*x))*sin(c+d*x)+6//5*a*d^-1*sec(c+d*x)^(1/2)*(a^2+5*b^2)*sin(c+d*x)+8//5*b*a^2*d^-1*sec(c+d*x)^3//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*cos(c+d*x))^3*sec(c+d*x)^5//2, x) == :(2//3*a^2*d^-1*sec(c+d*x)^(1/2)*(b+a*sec(c+d*x))*sin(c+d*x)+16//3*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)*(-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*cos(c+d*x))^3*sec(c+d*x)^3//2, x) == :(2//3*a*d^-1*sec(c+d*x)^(1/2)*(-1*b^2+3*a^2)*sin(c+d*x)+2//3*b^2*d^-1*sec(c+d*x)^-1//2*(b+a*sec(c+d*x))*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*cos(c+d*x))^3*sec(c+d*x)^(1/2), x) == :(2//5*b^2*d^-1*sec(c+d*x)^-3//2*(b+a*sec(c+d*x))*sin(c+d*x)+8//5*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+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*cos(c+d*x))^3*sec(c+d*x)^-1//2, x) == :(2//7*b^2*d^-1*sec(c+d*x)^-5//2*(b+a*sec(c+d*x))*sin(c+d*x)+2//21*b*d^-1*sec(c+d*x)^-1//2*(5*b^2+21*a^2)*sin(c+d*x)+32//35*a*b^2*d^-1*sec(c+d*x)^-3//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*cos(c+d*x))^3*sec(c+d*x)^-3//2, x) == :(2//9*b^2*d^-1*sec(c+d*x)^-7//2*(b+a*sec(c+d*x))*sin(c+d*x)+2//21*a*d^-1*sec(c+d*x)^-1//2*(7*a^2+15*b^2)*sin(c+d*x)+2//45*b*d^-1*sec(c+d*x)^-3//2*(7*b^2+27*a^2)*sin(c+d*x)+40//63*a*b^2*d^-1*sec(c+d*x)^-5//2*sin(c+d*x)+2//15*b*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(7*b^2+27*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)*(7*a^2+15*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+b*cos(c+d*x))^(1/2)*sec(c+d*x)^7//2, x) == :(2//5*d^-1*(a+b*cos(c+d*x))^(1/2)*sec(c+d*x)^5//2*sin(c+d*x)+2//15*b*a^-1*d^-1*(a+b*cos(c+d*x))^(1/2)*sec(c+d*x)^3//2*sin(c+d*x)+-1//15*a^-2*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-2b+2a)*(2b+9a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x)+1//15*a^-3*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-2b+2a)*(-2*b^2+9*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x))
@test integrate((a+b*cos(c+d*x))^(1/2)*sec(c+d*x)^5//2, x) == :(2//3*d^-1*(a+b*cos(c+d*x))^(1/2)*sec(c+d*x)^3//2*sin(c+d*x)+1//3*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-2b+2a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x)+1//3*b*a^-2*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-2b+2a)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x))
@test integrate((a+b*cos(c+d*x))^(1/2)*sec(c+d*x)^3//2, x) == :(a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-2b+2a)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x)+-1*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-2b+2a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x))
@test integrate((a+b*cos(c+d*x))^3//2*sec(c+d*x)^9//2, x) == :(2//7*a*d^-1*(a+b*cos(c+d*x))^(1/2)*sec(c+d*x)^7//2*sin(c+d*x)+16//35*b*d^-1*(a+b*cos(c+d*x))^(1/2)*sec(c+d*x)^5//2*sin(c+d*x)+1//105*a^-1*d^-1*(a+b*cos(c+d*x))^(1/2)*sec(c+d*x)^3//2*(6*b^2+50*a^2)*sin(c+d*x)+1//105*a^-2*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-2b+2a)*(-6*b^2+25*a^2+-57*a*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x)+1//105*b*a^-3*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-4b+4a)*(-3*b^2+41*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x))
@test integrate((a+b*cos(c+d*x))^3//2*sec(c+d*x)^7//2, x) == :(2//5*a*d^-1*(a+b*cos(c+d*x))^(1/2)*sec(c+d*x)^5//2*sin(c+d*x)+4//5*b*d^-1*(a+b*cos(c+d*x))^(1/2)*sec(c+d*x)^3//2*sin(c+d*x)+-1//5*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-1b+3a)*(-2b+2a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x)+1//5*a^-2*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(b^2+3*a^2)*(-2b+2a)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x))
@test integrate((a+b*cos(c+d*x))^3//2*sec(c+d*x)^5//2, x) == :(2//3*a*d^-1*(a+b*cos(c+d*x))^(1/2)*sec(c+d*x)^3//2*sin(c+d*x)+1//3*b*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-8b+8a)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x)+1//3*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(a+-1b)*(-6b+2a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x))
@test integrate((a+b*cos(c+d*x))^5//2*sec(c+d*x)^11//2, x) == :(1//315*d^-1*(a+b*cos(c+d*x))^(1/2)*sec(c+d*x)^5//2*(98*a^2+150*b^2)*sin(c+d*x)+2//9*a^2*d^-1*(a+b*cos(c+d*x))^(1/2)*sec(c+d*x)^9//2*sin(c+d*x)+38//63*a*b*d^-1*(a+b*cos(c+d*x))^(1/2)*sec(c+d*x)^7//2*sin(c+d*x)+2//315*b*a^-1*d^-1*(a+b*cos(c+d*x))^(1/2)*sec(c+d*x)^3//2*(5*b^2+163*a^2)*sin(c+d*x)+-1//315*a^-2*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-2b+2a)*(10*b^3+147*a^3+-114*b*a^2+165*a*b^2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x)+1//315*a^-3*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-2b+2a)*(-10*b^4+147*a^4+279*a^2*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x))
@test integrate((a+b*cos(c+d*x))^5//2*sec(c+d*x)^9//2, x) == :(1//21*d^-1*(a+b*cos(c+d*x))^(1/2)*sec(c+d*x)^3//2*(10*a^2+18*b^2)*sin(c+d*x)+2//7*a^2*d^-1*(a+b*cos(c+d*x))^(1/2)*sec(c+d*x)^7//2*sin(c+d*x)+6//7*a*b*d^-1*(a+b*cos(c+d*x))^(1/2)*sec(c+d*x)^5//2*sin(c+d*x)+1//21*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-2b+2a)*(3*b^2+5*a^2+-24*a*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x)+1//21*b*a^-2*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-2b+2a)*(3*b^2+29*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x))
@test integrate((a+b*cos(c+d*x))^5//2*sec(c+d*x)^7//2, x) == :(2//5*a^2*d^-1*(a+b*cos(c+d*x))^(1/2)*sec(c+d*x)^5//2*sin(c+d*x)+22//15*a*b*d^-1*(a+b*cos(c+d*x))^(1/2)*sec(c+d*x)^3//2*sin(c+d*x)+-1//15*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-2b+2a)*(9*a^2+15*b^2+-8*a*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x)+1//15*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-2b+2a)*(9*a^2+23*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x))
@test integrate((a+b*cos(c+d*x))^-1//2*sec(c+d*x)^5//2, x) == :(2//3*a^-1*d^-1*(a+b*cos(c+d*x))^(1/2)*sec(c+d*x)^3//2*sin(c+d*x)+2//3*a^-2*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(a+2b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x)+1//3*b*a^-3*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-4a+4b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x))
@test integrate((a+b*cos(c+d*x))^-1//2*sec(c+d*x)^3//2, x) == :(-2*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x)+a^-2*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-2b+2a)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x))
@test integrate((a+b*cos(c+d*x))^-1//2*sec(c+d*x)^(1/2), x) == :(2*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x))
@test integrate((a+b*cos(c+d*x))^-3//2*sec(c+d*x)^5//2, x) == :(2*a^-1*b^2*d^-1*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^3//2*sin(c+d*x)+1//3*a^-2*d^-1*(a+b*cos(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*sec(c+d*x)^3//2*(-8*b^2+2*a^2)*sin(c+d*x)+-2//3*b*a^-4*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-8*b^2+5*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x)+1//3*a^-3*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(a+4b)*(2a+4b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x))
@test integrate((a+b*cos(c+d*x))^-3//2*sec(c+d*x)^3//2, x) == :(2*a^-1*b^2*d^-1*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+a^-3*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-4*b^2+2*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x)+-1*a^-2*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(2a+4b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x))
@test integrate((a+b*cos(c+d*x))^-3//2*sec(c+d*x)^(1/2), x) == :(-2*b*d^-1*(a+b*cos(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*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x)+2*b*a^-2*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x))
@test integrate((a+b*cos(c+d*x))^-3//2*sec(c+d*x)^-1//2, x) == :(2*a*d^-1*(a+b*cos(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*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x)+2*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x))
@test integrate((a+b*cos(c+d*x))^-5//2*sec(c+d*x)^5//2, x) == :(1//3*a^-3*d^-1*(a+b*cos(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*sec(c+d*x)^3//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*cos(c+d*x))^-3//2*(a^2+-1*b^2)^-1*sec(c+d*x)^3//2*sin(c+d*x)+4//3*a^-2*b^2*d^-1*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-2*sec(c+d*x)^3//2*(-3*b^2+5*a^2)*sin(c+d*x)+1//3*a^-4*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(a+-1b)^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-32*b^4+2*a^4+-24*a*b^3+18*b*a^3+32*a^2*b^2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x)+-8//3*b*a^-5*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(a+-1b)^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(2*a^4+4*b^4+-7*a^2*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x))
@test integrate((a+b*cos(c+d*x))^-5//2*sec(c+d*x)^3//2, x) == :(2//3*a^-1*b^2*d^-1*(a+b*cos(c+d*x))^-3//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+8//3*a^-2*b^2*d^-1*(a+b*cos(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)+-1//3*a^-3*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(a+-1b)^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-16*b^3+6*a^3+-12*a*b^2+18*b*a^2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x)+1//3*a^-4*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(a+-1b)^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(6*a^4+16*b^4+-30*a^2*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x))
@test integrate((a+b*cos(c+d*x))^-5//2*sec(c+d*x)^(1/2), x) == :(2//3*a^-1*b^2*d^-1*(a+b*cos(c+d*x))^-3//2*(a^2+-1*b^2)^-1*sec(c+d*x)^-1//2*sin(c+d*x)+-4//3*b*a^-1*d^-1*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-2*sec(c+d*x)^(1/2)*(-1*b^2+3*a^2)*sin(c+d*x)+1//3*a^-2*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(a+-1b)^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-4*b^2+6*a^2+-6*a*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x)+4//3*b*a^-3*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(a+-1b)^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-1*b^2+3*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x))
@test integrate((a+b*cos(c+d*x))^-5//2*sec(c+d*x)^-1//2, x) == :(-2*b*d^-1*(a+b*cos(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*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-2*sec(c+d*x)^(1/2)*(2*b^2+6*a^2)*sin(c+d*x)+-1//3*a^-2*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(a+-1b)^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(2*b^2+6*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x)+1//3*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(a+-1b)^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-2b+6a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x))
@test integrate((a+b*cos(c+d*x))^-5//2*sec(c+d*x)^-3//2, x) == :(2*a*d^-1*(a+b*cos(c+d*x))^-3//2*(-3*b^2+3*a^2)^-1*sec(c+d*x)^-1//2*sin(c+d*x)+-8//3*a*b*d^-1*(a+b*cos(c+d*x))^-1//2*(a^2+-1*b^2)^-2*sec(c+d*x)^(1/2)*sin(c+d*x)+1//3*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(a+-1b)^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*(-6b+2a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x)+8//3*b*a^-1*d^-1*(a*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(a*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(a+-1b)^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^-1//2*Elliptic.E(arcsin((a+b)^-1//2*(a+b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2),-1*(a+-1b)^-1*(a+b))*csc(c+d*x))
@test integrate((1+-1*cos(x))^(1/2)*(a+-1*cos(x))^-1//2, x) == :(-2*arctan((1+-1*cos(x))^-1//2*(a+-1*cos(x))^-1//2*sin(x)))
@test integrate(((a+-1*cos(x))^-1*(1+-1*cos(x)))^(1/2), x) == :(-2*((a+-1*cos(x))^-1*(1+-1*cos(x)))^(1/2)*(1+-1*cos(x))^-1//2*(a+-1*cos(x))^(1/2)*arctan((1+-1*cos(x))^-1//2*(a+-1*cos(x))^-1//2*sin(x)))
@test integrate((a+a*cos(c+d*x))*(-1//2*B+B*cos(c+d*x)), x) == :((1/2)*B*a*d^-1*sin(c+d*x)+(1/2)*B*a*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^4*(-4//5*B+B*cos(c+d*x)), x) == :(1//5*B*d^-1*(a+a*cos(c+d*x))^4*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^n*(B*cos(c+d*x)+-1*B*n*(1+n)^-1), x) == :(B*d^-1*(1+n)^-1*(a+a*cos(c+d*x))^n*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-3*(-3//2*B+B*cos(c+d*x)), x) == :(-1//2*B*d^-1*(a+a*cos(c+d*x))^-3*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^3//2*(-3//5*B+B*cos(c+d*x)), x) == :(2//5*B*d^-1*(a+a*cos(c+d*x))^3//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-1//2*(B+B*cos(c+d*x)), x) == :(2*B*d^-1*(a+a*cos(c+d*x))^-1//2*sin(c+d*x))
@test integrate((a+a*cos(c+d*x))^-5//2*(-5//3*B+B*cos(c+d*x)), x) == :(-2//3*B*d^-1*(a+a*cos(c+d*x))^-5//2*sin(c+d*x))
@test integrate((a+b*cos(c+d*x))^-1*(B*cos(c+d*x)+B*b*a^-1), x) == :(B*x*b^-1+-2*B*a^-1*b^-1*d^-1*(a+b)^(1/2)*(a+-1b)^(1/2)*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((b+a*cos(c+d*x))^-2*(a+b*cos(c+d*x)), x) == :(d^-1*(b+a*cos(c+d*x))^-1*sin(c+d*x))
@test integrate((2+-1*cos(c+d*x))^-1*(3+cos(c+d*x)), x) == :(-1x+5//3*x*3^(1/2)+10//3*3^(1/2)*d^-1*arctan((2+3^(1/2)+-1*cos(c+d*x))^-1*sin(c+d*x)))
@test integrate((a+b*cos(c+d*x))^-1//2*(B*a+B*b*cos(c+d*x)), x) == :(2*B*d^-1*((a+b)^-1*(a+b*cos(c+d*x)))^-1//2*(a+b*cos(c+d*x))^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((b*cos(c+d*x))^(1/2)*cos(c+d*x)^2*(A+B*cos(c+d*x)), x) == :(10//21*B*d^-1*(b*cos(c+d*x))^(1/2)*sin(c+d*x)+2//5*A*b^-1*d^-1*(b*cos(c+d*x))^3//2*sin(c+d*x)+2//7*B*b^-2*d^-1*(b*cos(c+d*x))^5//2*sin(c+d*x)+6//5*A*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+10//21*B*b*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^(1/2)*(A+B*cos(c+d*x))*cos(c+d*x), x) == :(2//3*A*d^-1*(b*cos(c+d*x))^(1/2)*sin(c+d*x)+2//5*B*b^-1*d^-1*(b*cos(c+d*x))^3//2*sin(c+d*x)+6//5*B*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*A*b*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^(1/2)*(A+B*cos(c+d*x)), x) == :(2//3*B*d^-1*(b*cos(c+d*x))^(1/2)*sin(c+d*x)+2*A*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*B*b*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^(1/2)*(A+B*cos(c+d*x))*sec(c+d*x), x) == :(2*B*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*A*b*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^(1/2)*sec(c+d*x)^2*(A+B*cos(c+d*x)), x) == :(-2*A*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*A*b*d^-1*(b*cos(c+d*x))^-1//2*sin(c+d*x)+2*B*b*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^(1/2)*sec(c+d*x)^3*(A+B*cos(c+d*x)), x) == :(-2*B*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*B*b*d^-1*(b*cos(c+d*x))^-1//2*sin(c+d*x)+2//3*A*b^2*d^-1*(b*cos(c+d*x))^-3//2*sin(c+d*x)+2//3*A*b*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^(1/2)*sec(c+d*x)^4*(A+B*cos(c+d*x)), x) == :(-6//5*A*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*B*b^2*d^-1*(b*cos(c+d*x))^-3//2*sin(c+d*x)+2//5*A*b^3*d^-1*(b*cos(c+d*x))^-5//2*sin(c+d*x)+6//5*A*b*d^-1*(b*cos(c+d*x))^-1//2*sin(c+d*x)+2//3*B*b*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^3//2*(A+B*cos(c+d*x))*cos(c+d*x), x) == :(2//5*A*d^-1*(b*cos(c+d*x))^3//2*sin(c+d*x)+2//7*B*b^-1*d^-1*(b*cos(c+d*x))^5//2*sin(c+d*x)+10//21*B*b*d^-1*(b*cos(c+d*x))^(1/2)*sin(c+d*x)+6//5*A*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+10//21*B*b^2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^3//2*(A+B*cos(c+d*x)), x) == :(2//5*B*d^-1*(b*cos(c+d*x))^3//2*sin(c+d*x)+2//3*A*b*d^-1*(b*cos(c+d*x))^(1/2)*sin(c+d*x)+2//3*A*b^2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+6//5*B*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^3//2*(A+B*cos(c+d*x))*sec(c+d*x), x) == :(2//3*B*b*d^-1*(b*cos(c+d*x))^(1/2)*sin(c+d*x)+2*A*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*B*b^2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^3//2*sec(c+d*x)^2*(A+B*cos(c+d*x)), x) == :(2*A*b^2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*B*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^3//2*sec(c+d*x)^3*(A+B*cos(c+d*x)), x) == :(2*A*b^2*d^-1*(b*cos(c+d*x))^-1//2*sin(c+d*x)+-2*A*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*B*b^2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^3//2*sec(c+d*x)^4*(A+B*cos(c+d*x)), x) == :(2*B*b^2*d^-1*(b*cos(c+d*x))^-1//2*sin(c+d*x)+2//3*A*b^3*d^-1*(b*cos(c+d*x))^-3//2*sin(c+d*x)+-2*B*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*A*b^2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^3//2*sec(c+d*x)^5*(A+B*cos(c+d*x)), x) == :(2//3*B*b^3*d^-1*(b*cos(c+d*x))^-3//2*sin(c+d*x)+2//5*A*b^4*d^-1*(b*cos(c+d*x))^-5//2*sin(c+d*x)+6//5*A*b^2*d^-1*(b*cos(c+d*x))^-1//2*sin(c+d*x)+-6//5*A*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*B*b^2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^5//2*(A+B*cos(c+d*x)), x) == :(2//7*B*d^-1*(b*cos(c+d*x))^5//2*sin(c+d*x)+2//5*A*b*d^-1*(b*cos(c+d*x))^3//2*sin(c+d*x)+10//21*B*b^2*d^-1*(b*cos(c+d*x))^(1/2)*sin(c+d*x)+6//5*A*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+10//21*B*b^3*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^5//2*(A+B*cos(c+d*x))*sec(c+d*x), x) == :(2//3*A*b^2*d^-1*(b*cos(c+d*x))^(1/2)*sin(c+d*x)+2//5*B*b*d^-1*(b*cos(c+d*x))^3//2*sin(c+d*x)+2//3*A*b^3*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+6//5*B*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^5//2*sec(c+d*x)^2*(A+B*cos(c+d*x)), x) == :(2//3*B*b^2*d^-1*(b*cos(c+d*x))^(1/2)*sin(c+d*x)+2*A*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*B*b^3*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^5//2*sec(c+d*x)^3*(A+B*cos(c+d*x)), x) == :(2*A*b^3*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*B*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^5//2*sec(c+d*x)^4*(A+B*cos(c+d*x)), x) == :(2*A*b^3*d^-1*(b*cos(c+d*x))^-1//2*sin(c+d*x)+-2*A*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*B*b^3*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^5//2*sec(c+d*x)^5*(A+B*cos(c+d*x)), x) == :(2*B*b^3*d^-1*(b*cos(c+d*x))^-1//2*sin(c+d*x)+2//3*A*b^4*d^-1*(b*cos(c+d*x))^-3//2*sin(c+d*x)+-2*B*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*A*b^3*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^5//2*sec(c+d*x)^6*(A+B*cos(c+d*x)), x) == :(2//3*B*b^4*d^-1*(b*cos(c+d*x))^-3//2*sin(c+d*x)+2//5*A*b^5*d^-1*(b*cos(c+d*x))^-5//2*sin(c+d*x)+6//5*A*b^3*d^-1*(b*cos(c+d*x))^-1//2*sin(c+d*x)+-6//5*A*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*B*b^3*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^-1//2*cos(c+d*x)^3*(A+B*cos(c+d*x)), x) == :(2//5*A*b^-2*d^-1*(b*cos(c+d*x))^3//2*sin(c+d*x)+2//7*B*b^-3*d^-1*(b*cos(c+d*x))^5//2*sin(c+d*x)+10//21*B*b^-1*d^-1*(b*cos(c+d*x))^(1/2)*sin(c+d*x)+10//21*B*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+6//5*A*b^-1*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^-1//2*cos(c+d*x)^2*(A+B*cos(c+d*x)), x) == :(2//3*A*b^-1*d^-1*(b*cos(c+d*x))^(1/2)*sin(c+d*x)+2//3*A*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*B*b^-2*d^-1*(b*cos(c+d*x))^3//2*sin(c+d*x)+6//5*B*b^-1*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^-1//2*(A+B*cos(c+d*x))*cos(c+d*x), x) == :(2//3*B*b^-1*d^-1*(b*cos(c+d*x))^(1/2)*sin(c+d*x)+2//3*B*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*A*b^-1*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^-1//2*(A+B*cos(c+d*x)), x) == :(2*A*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*B*b^-1*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^-1//2*(A+B*cos(c+d*x))*sec(c+d*x), x) == :(2*A*d^-1*(b*cos(c+d*x))^-1//2*sin(c+d*x)+2*B*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-2*A*b^-1*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^-1//2*sec(c+d*x)^2*(A+B*cos(c+d*x)), x) == :(2*B*d^-1*(b*cos(c+d*x))^-1//2*sin(c+d*x)+2//3*A*b*d^-1*(b*cos(c+d*x))^-3//2*sin(c+d*x)+2//3*A*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-2*B*b^-1*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^-1//2*sec(c+d*x)^3*(A+B*cos(c+d*x)), x) == :(6//5*A*d^-1*(b*cos(c+d*x))^-1//2*sin(c+d*x)+2//3*B*b*d^-1*(b*cos(c+d*x))^-3//2*sin(c+d*x)+2//3*B*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*A*b^2*d^-1*(b*cos(c+d*x))^-5//2*sin(c+d*x)+-6//5*A*b^-1*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^-3//2*cos(c+d*x)^4*(A+B*cos(c+d*x)), x) == :(2//5*A*b^-3*d^-1*(b*cos(c+d*x))^3//2*sin(c+d*x)+2//7*B*b^-4*d^-1*(b*cos(c+d*x))^5//2*sin(c+d*x)+10//21*B*b^-2*d^-1*(b*cos(c+d*x))^(1/2)*sin(c+d*x)+6//5*A*b^-2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+10//21*B*b^-1*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^-3//2*cos(c+d*x)^3*(A+B*cos(c+d*x)), x) == :(2//3*A*b^-2*d^-1*(b*cos(c+d*x))^(1/2)*sin(c+d*x)+2//5*B*b^-3*d^-1*(b*cos(c+d*x))^3//2*sin(c+d*x)+2//3*A*b^-1*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+6//5*B*b^-2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^-3//2*cos(c+d*x)^2*(A+B*cos(c+d*x)), x) == :(2//3*B*b^-2*d^-1*(b*cos(c+d*x))^(1/2)*sin(c+d*x)+2*A*b^-2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*B*b^-1*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^-3//2*(A+B*cos(c+d*x))*cos(c+d*x), x) == :(2*A*b^-1*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*B*b^-2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^-3//2*(A+B*cos(c+d*x)), x) == :(2*A*b^-1*d^-1*(b*cos(c+d*x))^-1//2*sin(c+d*x)+-2*A*b^-2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*B*b^-1*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^-3//2*(A+B*cos(c+d*x))*sec(c+d*x), x) == :(2//3*A*d^-1*(b*cos(c+d*x))^-3//2*sin(c+d*x)+2*B*b^-1*d^-1*(b*cos(c+d*x))^-1//2*sin(c+d*x)+-2*B*b^-2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*A*b^-1*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^-3//2*sec(c+d*x)^2*(A+B*cos(c+d*x)), x) == :(2//3*B*d^-1*(b*cos(c+d*x))^-3//2*sin(c+d*x)+2//5*A*b*d^-1*(b*cos(c+d*x))^-5//2*sin(c+d*x)+6//5*A*b^-1*d^-1*(b*cos(c+d*x))^-1//2*sin(c+d*x)+-6//5*A*b^-2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*B*b^-1*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^-5//2*cos(c+d*x)^5*(A+B*cos(c+d*x)), x) == :(2//5*A*b^-4*d^-1*(b*cos(c+d*x))^3//2*sin(c+d*x)+2//7*B*b^-5*d^-1*(b*cos(c+d*x))^5//2*sin(c+d*x)+10//21*B*b^-3*d^-1*(b*cos(c+d*x))^(1/2)*sin(c+d*x)+6//5*A*b^-3*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+10//21*B*b^-2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^-5//2*cos(c+d*x)^4*(A+B*cos(c+d*x)), x) == :(2//3*A*b^-3*d^-1*(b*cos(c+d*x))^(1/2)*sin(c+d*x)+2//5*B*b^-4*d^-1*(b*cos(c+d*x))^3//2*sin(c+d*x)+2//3*A*b^-2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+6//5*B*b^-3*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^-5//2*cos(c+d*x)^3*(A+B*cos(c+d*x)), x) == :(2//3*B*b^-3*d^-1*(b*cos(c+d*x))^(1/2)*sin(c+d*x)+2*A*b^-3*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*B*b^-2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^-5//2*cos(c+d*x)^2*(A+B*cos(c+d*x)), x) == :(2*A*b^-2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*B*b^-3*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^-5//2*(A+B*cos(c+d*x))*cos(c+d*x), x) == :(2*A*b^-2*d^-1*(b*cos(c+d*x))^-1//2*sin(c+d*x)+-2*A*b^-3*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*B*b^-2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^-5//2*(A+B*cos(c+d*x)), x) == :(2*B*b^-2*d^-1*(b*cos(c+d*x))^-1//2*sin(c+d*x)+2//3*A*b^-1*d^-1*(b*cos(c+d*x))^-3//2*sin(c+d*x)+-2*B*b^-3*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*A*b^-2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^-5//2*(A+B*cos(c+d*x))*sec(c+d*x), x) == :(2//5*A*d^-1*(b*cos(c+d*x))^-5//2*sin(c+d*x)+2//3*B*b^-1*d^-1*(b*cos(c+d*x))^-3//2*sin(c+d*x)+6//5*A*b^-2*d^-1*(b*cos(c+d*x))^-1//2*sin(c+d*x)+-6//5*A*b^-3*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*B*b^-2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^-7//2*(A+B*cos(c+d*x)), x) == :(2//3*B*b^-2*d^-1*(b*cos(c+d*x))^-3//2*sin(c+d*x)+2//5*A*b^-1*d^-1*(b*cos(c+d*x))^-5//2*sin(c+d*x)+6//5*A*b^-3*d^-1*(b*cos(c+d*x))^-1//2*sin(c+d*x)+-6//5*A*b^-4*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*B*b^-3*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*cos(c+d*x))^(1/2)*cos(c+d*x)^5//2*(A+B*cos(c+d*x)), x) == :(3//8*B*x*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2+A*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*sin(c+d*x)+-1//3*A*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*sin(c+d*x)^3+1//4*B*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^5//2*sin(c+d*x)+3//8*B*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((b*cos(c+d*x))^(1/2)*cos(c+d*x)^3//2*(A+B*cos(c+d*x)), x) == :((1/2)*A*x*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2+B*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*sin(c+d*x)+(1/2)*A*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x)+-1//3*B*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*sin(c+d*x)^3)
@test integrate((b*cos(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(A+B*cos(c+d*x)), x) == :((1/2)*B*x*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2+A*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*sin(c+d*x)+(1/2)*B*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*(A+B*cos(c+d*x)), x) == :(A*x*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2+B*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((b*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2*(A+B*cos(c+d*x)), x) == :(B*x*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2+A*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*arctanh(sin(c+d*x)))
@test integrate((b*cos(c+d*x))^(1/2)*cos(c+d*x)^-5//2*(A+B*cos(c+d*x)), x) == :(A*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2*sin(c+d*x)+B*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*arctanh(sin(c+d*x)))
@test integrate((b*cos(c+d*x))^(1/2)*cos(c+d*x)^-7//2*(A+B*cos(c+d*x)), x) == :(B*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2*sin(c+d*x)+(1/2)*A*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-5//2*sin(c+d*x)+(1/2)*A*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*arctanh(sin(c+d*x)))
@test integrate((b*cos(c+d*x))^(1/2)*cos(c+d*x)^-9//2*(A+B*cos(c+d*x)), x) == :(A*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2*sin(c+d*x)+(1/2)*B*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-5//2*sin(c+d*x)+(1/2)*B*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*arctanh(sin(c+d*x))+1//3*A*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-7//2*sin(c+d*x)^3)
@test integrate((b*cos(c+d*x))^3//2*cos(c+d*x)^3//2*(A+B*cos(c+d*x)), x) == :(3//8*B*b*x*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2+A*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*sin(c+d*x)+-1//3*A*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*sin(c+d*x)^3+1//4*B*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^5//2*sin(c+d*x)+3//8*B*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((b*cos(c+d*x))^3//2*cos(c+d*x)^(1/2)*(A+B*cos(c+d*x)), x) == :((1/2)*A*b*x*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2+B*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*sin(c+d*x)+(1/2)*A*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x)+-1//3*B*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*sin(c+d*x)^3)
@test integrate((b*cos(c+d*x))^3//2*cos(c+d*x)^-1//2*(A+B*cos(c+d*x)), x) == :((1/2)*B*b*x*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2+A*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*sin(c+d*x)+(1/2)*B*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((b*cos(c+d*x))^3//2*cos(c+d*x)^-3//2*(A+B*cos(c+d*x)), x) == :(A*b*x*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2+B*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((b*cos(c+d*x))^3//2*cos(c+d*x)^-5//2*(A+B*cos(c+d*x)), x) == :(B*b*x*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2+A*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*arctanh(sin(c+d*x)))
@test integrate((b*cos(c+d*x))^3//2*cos(c+d*x)^-7//2*(A+B*cos(c+d*x)), x) == :(A*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2*sin(c+d*x)+B*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*arctanh(sin(c+d*x)))
@test integrate((b*cos(c+d*x))^3//2*cos(c+d*x)^-9//2*(A+B*cos(c+d*x)), x) == :(B*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2*sin(c+d*x)+(1/2)*A*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-5//2*sin(c+d*x)+(1/2)*A*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*arctanh(sin(c+d*x)))
@test integrate((b*cos(c+d*x))^3//2*cos(c+d*x)^-11//2*(A+B*cos(c+d*x)), x) == :(A*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2*sin(c+d*x)+(1/2)*B*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-5//2*sin(c+d*x)+(1/2)*B*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*arctanh(sin(c+d*x))+1//3*A*b*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-7//2*sin(c+d*x)^3)
@test integrate((b*cos(c+d*x))^5//2*cos(c+d*x)^(1/2)*(A+B*cos(c+d*x)), x) == :(3//8*B*x*b^2*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2+A*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*sin(c+d*x)+-1//3*A*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*sin(c+d*x)^3+1//4*B*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^5//2*sin(c+d*x)+3//8*B*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((b*cos(c+d*x))^5//2*cos(c+d*x)^-1//2*(A+B*cos(c+d*x)), x) == :((1/2)*A*x*b^2*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2+B*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*sin(c+d*x)+(1/2)*A*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x)+-1//3*B*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*sin(c+d*x)^3)
@test integrate((b*cos(c+d*x))^5//2*cos(c+d*x)^-3//2*(A+B*cos(c+d*x)), x) == :((1/2)*B*x*b^2*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2+A*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*sin(c+d*x)+(1/2)*B*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((b*cos(c+d*x))^5//2*cos(c+d*x)^-5//2*(A+B*cos(c+d*x)), x) == :(A*x*b^2*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2+B*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate((b*cos(c+d*x))^5//2*cos(c+d*x)^-7//2*(A+B*cos(c+d*x)), x) == :(B*x*b^2*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2+A*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*arctanh(sin(c+d*x)))
@test integrate((b*cos(c+d*x))^5//2*cos(c+d*x)^-9//2*(A+B*cos(c+d*x)), x) == :(A*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2*sin(c+d*x)+B*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*arctanh(sin(c+d*x)))
@test integrate((b*cos(c+d*x))^5//2*cos(c+d*x)^-11//2*(A+B*cos(c+d*x)), x) == :(B*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2*sin(c+d*x)+(1/2)*A*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-5//2*sin(c+d*x)+(1/2)*A*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*arctanh(sin(c+d*x)))
@test integrate((b*cos(c+d*x))^5//2*cos(c+d*x)^-13//2*(A+B*cos(c+d*x)), x) == :(A*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-3//2*sin(c+d*x)+(1/2)*B*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-5//2*sin(c+d*x)+(1/2)*B*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-1//2*arctanh(sin(c+d*x))+1//3*A*b^2*d^-1*(b*cos(c+d*x))^(1/2)*cos(c+d*x)^-7//2*sin(c+d*x)^3)
@test integrate((b*cos(c+d*x))^-1//2*cos(c+d*x)^5//2*(A+B*cos(c+d*x)), x) == :((1/2)*A*x*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)+B*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)+(1/2)*A*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x)+-1//3*B*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)^3)
@test integrate((b*cos(c+d*x))^-1//2*cos(c+d*x)^3//2*(A+B*cos(c+d*x)), x) == :((1/2)*B*x*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)+A*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)+(1/2)*B*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate((b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(A+B*cos(c+d*x)), x) == :(A*x*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)+B*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((b*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*(A+B*cos(c+d*x)), x) == :(B*x*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)+A*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*arctanh(sin(c+d*x)))
@test integrate((b*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*(A+B*cos(c+d*x)), x) == :(A*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+B*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*arctanh(sin(c+d*x)))
@test integrate((b*cos(c+d*x))^-1//2*cos(c+d*x)^-5//2*(A+B*cos(c+d*x)), x) == :(B*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+(1/2)*A*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*arctanh(sin(c+d*x))+(1/2)*A*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((b*cos(c+d*x))^-1//2*cos(c+d*x)^-7//2*(A+B*cos(c+d*x)), x) == :(A*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+(1/2)*B*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*arctanh(sin(c+d*x))+(1/2)*B*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+1//3*A*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x)^3)
@test integrate((b*cos(c+d*x))^-3//2*cos(c+d*x)^7//2*(A+B*cos(c+d*x)), x) == :((1/2)*A*x*b^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)+B*b^-1*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)+(1/2)*A*b^-1*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x)+-1//3*B*b^-1*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)^3)
@test integrate((b*cos(c+d*x))^-3//2*cos(c+d*x)^5//2*(A+B*cos(c+d*x)), x) == :((1/2)*B*x*b^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)+A*b^-1*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)+(1/2)*B*b^-1*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate((b*cos(c+d*x))^-3//2*cos(c+d*x)^3//2*(A+B*cos(c+d*x)), x) == :(A*x*b^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)+B*b^-1*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((b*cos(c+d*x))^-3//2*cos(c+d*x)^(1/2)*(A+B*cos(c+d*x)), x) == :(B*x*b^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)+A*b^-1*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*arctanh(sin(c+d*x)))
@test integrate((b*cos(c+d*x))^-3//2*cos(c+d*x)^-1//2*(A+B*cos(c+d*x)), x) == :(A*b^-1*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+B*b^-1*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*arctanh(sin(c+d*x)))
@test integrate((b*cos(c+d*x))^-3//2*cos(c+d*x)^-3//2*(A+B*cos(c+d*x)), x) == :(B*b^-1*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+(1/2)*A*b^-1*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*arctanh(sin(c+d*x))+(1/2)*A*b^-1*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((b*cos(c+d*x))^-3//2*cos(c+d*x)^-5//2*(A+B*cos(c+d*x)), x) == :(A*b^-1*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+(1/2)*B*b^-1*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*arctanh(sin(c+d*x))+(1/2)*B*b^-1*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+1//3*A*b^-1*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x)^3)
@test integrate((b*cos(c+d*x))^-5//2*cos(c+d*x)^9//2*(A+B*cos(c+d*x)), x) == :((1/2)*A*x*b^-2*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)+B*b^-2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)+(1/2)*A*b^-2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x)+-1//3*B*b^-2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)^3)
@test integrate((b*cos(c+d*x))^-5//2*cos(c+d*x)^7//2*(A+B*cos(c+d*x)), x) == :((1/2)*B*x*b^-2*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)+A*b^-2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)+(1/2)*B*b^-2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate((b*cos(c+d*x))^-5//2*cos(c+d*x)^5//2*(A+B*cos(c+d*x)), x) == :(A*x*b^-2*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)+B*b^-2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((b*cos(c+d*x))^-5//2*cos(c+d*x)^3//2*(A+B*cos(c+d*x)), x) == :(B*x*b^-2*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)+A*b^-2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*arctanh(sin(c+d*x)))
@test integrate((b*cos(c+d*x))^-5//2*cos(c+d*x)^(1/2)*(A+B*cos(c+d*x)), x) == :(A*b^-2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+B*b^-2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*arctanh(sin(c+d*x)))
@test integrate((b*cos(c+d*x))^-5//2*cos(c+d*x)^-1//2*(A+B*cos(c+d*x)), x) == :(B*b^-2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+(1/2)*A*b^-2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*arctanh(sin(c+d*x))+(1/2)*A*b^-2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((b*cos(c+d*x))^-5//2*cos(c+d*x)^-3//2*(A+B*cos(c+d*x)), x) == :(A*b^-2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+(1/2)*B*b^-2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^(1/2)*arctanh(sin(c+d*x))+(1/2)*B*b^-2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+1//3*A*b^-2*d^-1*(b*cos(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x)^3)

max_stars_repo_path: test/4 Trig functions/4.2 Cosine/4.2.2.1 (a+b cos)^m (c+d cos)^n.jl