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

@test integrate((a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^7//2*cos(e+f*x)^2, x) == :(-1//6*c^-1*f^-1*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^9//2*cos(e+f*x)+-1//15*a*c^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^9//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^5//2*cos(e+f*x)^2, x) == :(-1//5*c^-1*f^-1*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^7//2*cos(e+f*x)+-1//10*a*c^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^7//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^3//2*cos(e+f*x)^2, x) == :(-1//4*c^-1*f^-1*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^5//2*cos(e+f*x)+-1//6*a*c^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^5//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^(1/2)*cos(e+f*x)^2, x) == :(-1//3*c^-1*f^-1*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^3//2*cos(e+f*x)+-1//3*a*c^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^3//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^2, x) == :((1/2)*a^-1*f^-1*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-3//2*cos(e+f*x)^2, x) == :(-1*c^-1*f^-1*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)+-2*a*c^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)*log(1+-1*sin(e+f*x)))
@test integrate((a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-5//2*cos(e+f*x)^2, x) == :(c^-1*f^-1*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-3//2*cos(e+f*x)+a*c^-2*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)*log(1+-1*sin(e+f*x)))
@test integrate((a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-7//2*cos(e+f*x)^2, x) == :(1//4*a^-1*c^-1*f^-1*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-5//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^7//2*cos(e+f*x)^2, x) == :(-1//7*c^-1*f^-1*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^9//2*cos(e+f*x)+-4//105*a^2*c^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^9//2*cos(e+f*x)+-2//21*a*c^-1*f^-1*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^9//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^5//2*cos(e+f*x)^2, x) == :(-1//6*c^-1*f^-1*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^7//2*cos(e+f*x)+-2//15*a*c^-1*f^-1*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^7//2*cos(e+f*x)+-1//15*a^2*c^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^7//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^3//2*cos(e+f*x)^2, x) == :(-1//5*c^-1*f^-1*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^5//2*cos(e+f*x)+-2//15*a^2*c^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^5//2*cos(e+f*x)+-1//5*a*c^-1*f^-1*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^5//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^(1/2)*cos(e+f*x)^2, x) == :(1//4*a^-1*f^-1*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^(1/2)*cos(e+f*x)+1//6*c*a^-1*f^-1*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^2, x) == :(1//3*a^-1*f^-1*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-3//2*cos(e+f*x)^2, x) == :(-1//2*c^-1*f^-1*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)+-2*a*c^-1*f^-1*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)+-4*a^2*c^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)*log(1+-1*sin(e+f*x)))
@test integrate((a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-5//2*cos(e+f*x)^2, x) == :(c^-1*f^-1*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-3//2*cos(e+f*x)+2*a*c^-2*f^-1*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)+4*a^2*c^-2*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)*log(1+-1*sin(e+f*x)))
@test integrate((a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-7//2*cos(e+f*x)^2, x) == :((1/2)*c^-1*f^-1*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-5//2*cos(e+f*x)+-1*a*c^-2*f^-1*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-3//2*cos(e+f*x)+-1*a^2*c^-3*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)*log(1+-1*sin(e+f*x)))
@test integrate((a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-9//2*cos(e+f*x)^2, x) == :(1//6*a^-1*c^-1*f^-1*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-7//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-11//2*cos(e+f*x)^2, x) == :(1//8*a^-1*c^-1*f^-1*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-9//2*cos(e+f*x)+1//48*a^-1*c^-2*f^-1*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-7//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^7//2*cos(e+f*x)^2, x) == :(-1//8*c^-1*f^-1*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^9//2*cos(e+f*x)+-3//28*a*c^-1*f^-1*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^9//2*cos(e+f*x)+-1//14*a^2*c^-1*f^-1*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^9//2*cos(e+f*x)+-1//35*a^3*c^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^9//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^5//2*cos(e+f*x)^2, x) == :(-1//7*c^-1*f^-1*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^7//2*cos(e+f*x)+-4//35*a^2*c^-1*f^-1*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^7//2*cos(e+f*x)+-2//35*a^3*c^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^7//2*cos(e+f*x)+-1//7*a*c^-1*f^-1*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^7//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^3//2*cos(e+f*x)^2, x) == :(1//6*a^-1*f^-1*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^3//2*cos(e+f*x)+1//15*a^-1*c^2*f^-1*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)+2//15*c*a^-1*f^-1*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^(1/2)*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^(1/2)*cos(e+f*x)^2, x) == :(1//5*a^-1*f^-1*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^(1/2)*cos(e+f*x)+1//10*c*a^-1*f^-1*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^2, x) == :(1//4*a^-1*f^-1*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-3//2*cos(e+f*x)^2, x) == :(-1//3*c^-1*f^-1*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)+-1*a*c^-1*f^-1*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)+-4*a^2*c^-1*f^-1*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)+-8*a^3*c^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)*log(1+-1*sin(e+f*x)))
@test integrate((a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-5//2*cos(e+f*x)^2, x) == :(c^-1*f^-1*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-3//2*cos(e+f*x)+6*a^2*c^-2*f^-1*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)+3//2*a*c^-2*f^-1*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)+12*a^3*c^-2*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)*log(1+-1*sin(e+f*x)))
@test integrate((a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-7//2*cos(e+f*x)^2, x) == :((1/2)*c^-1*f^-1*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-5//2*cos(e+f*x)+-3*a^2*c^-3*f^-1*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)+-3//2*a*c^-2*f^-1*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-3//2*cos(e+f*x)+-6*a^3*c^-3*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)*log(1+-1*sin(e+f*x)))
@test integrate((a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-9//2*cos(e+f*x)^2, x) == :(1//3*c^-1*f^-1*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-7//2*cos(e+f*x)+a^2*c^-3*f^-1*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-3//2*cos(e+f*x)+-1//2*a*c^-2*f^-1*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-5//2*cos(e+f*x)+a^3*c^-4*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)*log(1+-1*sin(e+f*x)))
@test integrate((a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-11//2*cos(e+f*x)^2, x) == :(1//8*a^-1*c^-1*f^-1*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-9//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-13//2*cos(e+f*x)^2, x) == :(1//10*a^-1*c^-1*f^-1*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-11//2*cos(e+f*x)+1//80*a^-1*c^-2*f^-1*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-9//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^9//2*cos(e+f*x)^2, x) == :(-1//10*c^-1*f^-1*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^11//2*cos(e+f*x)+-4//45*a*c^-1*f^-1*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^11//2*cos(e+f*x)+-4//105*a^3*c^-1*f^-1*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^11//2*cos(e+f*x)+-4//315*a^4*c^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^11//2*cos(e+f*x)+-1//15*a^2*c^-1*f^-1*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^11//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^7//2*cos(e+f*x)^2, x) == :(-1//9*c^-1*f^-1*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^9//2*cos(e+f*x)+-8//315*a^4*c^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^9//2*cos(e+f*x)+-4//63*a^3*c^-1*f^-1*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^9//2*cos(e+f*x)+-2//21*a^2*c^-1*f^-1*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^9//2*cos(e+f*x)+-1//9*a*c^-1*f^-1*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^9//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^5//2*cos(e+f*x)^2, x) == :(1//8*a^-1*f^-1*(a+a*sin(e+f*x))^9//2*(c+-1*c*sin(e+f*x))^5//2*cos(e+f*x)+1//14*a^-1*c^2*f^-1*(a+a*sin(e+f*x))^9//2*(c+-1*c*sin(e+f*x))^(1/2)*cos(e+f*x)+1//35*a^-1*c^3*f^-1*(a+a*sin(e+f*x))^9//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)+3//28*c*a^-1*f^-1*(a+a*sin(e+f*x))^9//2*(c+-1*c*sin(e+f*x))^3//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^3//2*cos(e+f*x)^2, x) == :(1//7*a^-1*f^-1*(a+a*sin(e+f*x))^9//2*(c+-1*c*sin(e+f*x))^3//2*cos(e+f*x)+2//21*c*a^-1*f^-1*(a+a*sin(e+f*x))^9//2*(c+-1*c*sin(e+f*x))^(1/2)*cos(e+f*x)+4//105*a^-1*c^2*f^-1*(a+a*sin(e+f*x))^9//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^(1/2)*cos(e+f*x)^2, x) == :(1//6*a^-1*f^-1*(a+a*sin(e+f*x))^9//2*(c+-1*c*sin(e+f*x))^(1/2)*cos(e+f*x)+1//15*c*a^-1*f^-1*(a+a*sin(e+f*x))^9//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^2, x) == :(1//5*a^-1*f^-1*(a+a*sin(e+f*x))^9//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-3//2*cos(e+f*x)^2, x) == :(-1//4*c^-1*f^-1*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)+-8*a^3*c^-1*f^-1*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)+-2*a^2*c^-1*f^-1*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)+-2//3*a*c^-1*f^-1*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)+-16*a^4*c^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)*log(1+-1*sin(e+f*x)))
@test integrate((a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-5//2*cos(e+f*x)^2, x) == :(c^-1*f^-1*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-3//2*cos(e+f*x)+4*a^2*c^-2*f^-1*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)+16*a^3*c^-2*f^-1*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)+4//3*a*c^-2*f^-1*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)+32*a^4*c^-2*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)*log(1+-1*sin(e+f*x)))
@test integrate((a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-7//2*cos(e+f*x)^2, x) == :((1/2)*c^-1*f^-1*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-5//2*cos(e+f*x)+-12*a^3*c^-3*f^-1*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)+-3*a^2*c^-3*f^-1*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)+-2*a*c^-2*f^-1*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-3//2*cos(e+f*x)+-24*a^4*c^-3*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)*log(1+-1*sin(e+f*x)))
@test integrate((a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-9//2*cos(e+f*x)^2, x) == :(1//3*c^-1*f^-1*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-7//2*cos(e+f*x)+2*a^2*c^-3*f^-1*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-3//2*cos(e+f*x)+4*a^3*c^-4*f^-1*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)+-2//3*a*c^-2*f^-1*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-5//2*cos(e+f*x)+8*a^4*c^-4*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)*log(1+-1*sin(e+f*x)))
@test integrate((a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-11//2*cos(e+f*x)^2, x) == :(1//4*c^-1*f^-1*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-9//2*cos(e+f*x)+(1/2)*a^2*c^-3*f^-1*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-5//2*cos(e+f*x)+-1*a^3*c^-4*f^-1*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-3//2*cos(e+f*x)+-1//3*a*c^-2*f^-1*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-7//2*cos(e+f*x)+-1*a^4*c^-5*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)*log(1+-1*sin(e+f*x)))
@test integrate((a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-13//2*cos(e+f*x)^2, x) == :(1//10*a^-1*c^-1*f^-1*(a+a*sin(e+f*x))^9//2*(c+-1*c*sin(e+f*x))^-11//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-15//2*cos(e+f*x)^2, x) == :(1//12*a^-1*c^-1*f^-1*(a+a*sin(e+f*x))^9//2*(c+-1*c*sin(e+f*x))^-13//2*cos(e+f*x)+1//120*a^-1*c^-2*f^-1*(a+a*sin(e+f*x))^9//2*(c+-1*c*sin(e+f*x))^-11//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-17//2*cos(e+f*x)^2, x) == :(1//14*a^-1*c^-1*f^-1*(a+a*sin(e+f*x))^9//2*(c+-1*c*sin(e+f*x))^-15//2*cos(e+f*x)+1//84*a^-1*c^-2*f^-1*(a+a*sin(e+f*x))^9//2*(c+-1*c*sin(e+f*x))^-13//2*cos(e+f*x)+1//840*a^-1*c^-3*f^-1*(a+a*sin(e+f*x))^9//2*(c+-1*c*sin(e+f*x))^-11//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^5//2*cos(e+f*x)^2, x) == :(-1//4*c^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^7//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^3//2*cos(e+f*x)^2, x) == :(-1//3*c^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^5//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^(1/2)*cos(e+f*x)^2, x) == :(-1//2*c^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^3//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^2, x) == :(-1*c^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^(1/2)*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2*cos(e+f*x)^2, x) == :(-1*c^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)*log(1+-1*sin(e+f*x)))
@test integrate((a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-5//2*cos(e+f*x)^2, x) == :(c^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^7//2*cos(e+f*x)^2, x) == :(1//4*a^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^7//2*cos(e+f*x)+2*a^-1*c^2*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^3//2*cos(e+f*x)+8*a^-1*c^3*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^(1/2)*cos(e+f*x)+2//3*c*a^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^5//2*cos(e+f*x)+16*a^-1*c^4*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)*log(1+sin(e+f*x)))
@test integrate((a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^5//2*cos(e+f*x)^2, x) == :(1//3*a^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^5//2*cos(e+f*x)+c*a^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^3//2*cos(e+f*x)+4*a^-1*c^2*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^(1/2)*cos(e+f*x)+8*a^-1*c^3*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)*log(1+sin(e+f*x)))
@test integrate((a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^3//2*cos(e+f*x)^2, x) == :((1/2)*a^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^3//2*cos(e+f*x)+2*c*a^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^(1/2)*cos(e+f*x)+4*a^-1*c^2*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)*log(1+sin(e+f*x)))
@test integrate((a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^(1/2)*cos(e+f*x)^2, x) == :(a^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^(1/2)*cos(e+f*x)+2*c*a^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)*log(1+sin(e+f*x)))
@test integrate((a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^2, x) == :(a^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)*log(1+sin(e+f*x)))
@test integrate((a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^-3//2*cos(e+f*x)^2, x) == :(a^-1*c^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*arctanh(sin(e+f*x))*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^-5//2*cos(e+f*x)^2, x) == :((1/2)*a^-1*c^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2*cos(e+f*x)+(1/2)*a^-1*c^-2*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*arctanh(sin(e+f*x))*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^9//2*cos(e+f*x)^2, x) == :(-1*a^-1*f^-1*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^9//2*cos(e+f*x)+-40*a^-2*c^4*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^(1/2)*cos(e+f*x)+-10*a^-2*c^3*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^3//2*cos(e+f*x)+-10//3*a^-2*c^2*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^5//2*cos(e+f*x)+-5//4*c*a^-2*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^7//2*cos(e+f*x)+-80*a^-2*c^5*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)*log(1+sin(e+f*x)))
@test integrate((a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^7//2*cos(e+f*x)^2, x) == :(-1*a^-1*f^-1*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^7//2*cos(e+f*x)+-16*a^-2*c^3*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^(1/2)*cos(e+f*x)+-4*a^-2*c^2*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^3//2*cos(e+f*x)+-4//3*c*a^-2*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^5//2*cos(e+f*x)+-32*a^-2*c^4*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)*log(1+sin(e+f*x)))
@test integrate((a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^5//2*cos(e+f*x)^2, x) == :(-1*a^-1*f^-1*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^5//2*cos(e+f*x)+-6*a^-2*c^2*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^(1/2)*cos(e+f*x)+-3//2*c*a^-2*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^3//2*cos(e+f*x)+-12*a^-2*c^3*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)*log(1+sin(e+f*x)))
@test integrate((a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^3//2*cos(e+f*x)^2, x) == :(-1*a^-1*f^-1*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^3//2*cos(e+f*x)+-2*c*a^-2*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^(1/2)*cos(e+f*x)+-4*a^-2*c^2*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)*log(1+sin(e+f*x)))
@test integrate((a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^(1/2)*cos(e+f*x)^2, x) == :(-1*a^-1*f^-1*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^(1/2)*cos(e+f*x)+-1*c*a^-2*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)*log(1+sin(e+f*x)))
@test integrate((a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^2, x) == :(-1*a^-1*f^-1*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^-3//2*cos(e+f*x)^2, x) == :(-1//2*a^-1*c^-1*f^-1*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)+(1/2)*a^-2*c^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*arctanh(sin(e+f*x))*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^-5//2*cos(e+f*x)^2, x) == :((1/2)*a^-2*c^-1*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2*cos(e+f*x)+-1//2*a^-1*c^-1*f^-1*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^-3//2*cos(e+f*x)+(1/2)*a^-2*c^-2*f^-1*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*arctanh(sin(e+f*x))*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^(1/2)*cos(e+f*x)^2, x) == :(2*a^-1*f^-1*(5+2m)^-1*(a+a*sin(e+f*x))^(1+m)*(c+-1*c*sin(e+f*x))^(1/2)*cos(e+f*x)+8*c*a^-1*f^-1*(a+a*sin(e+f*x))^(1+m)*(c+-1*c*sin(e+f*x))^-1//2*(15+4*m^2+16m)^-1*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^2, x) == :(2*a^-1*f^-1*(3+2m)^-1*(a+a*sin(e+f*x))^(1+m)*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^2, x) == :(2*a^-1*f^-1*(3+2m)^-1*(a+a*sin(e+f*x))^(1+m)*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x))
@test integrate((a+-1*a*sin(e+f*x))^-1//2*(c+c*sin(e+f*x))^m*cos(e+f*x)^2, x) == :(2*c^-1*f^-1*(3+2m)^-1*(a+-1*a*sin(e+f*x))^-1//2*(c+c*sin(e+f*x))^(1+m)*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^(-4+-1m)*cos(e+f*x)^2, x) == :(a^-1*c^-1*f^-1*(5+2m)^-1*(a+a*sin(e+f*x))^(1+m)*(c+-1*c*sin(e+f*x))^(-3+-1m)*cos(e+f*x)+a^-1*c^-2*f^-1*(a+a*sin(e+f*x))^(1+m)*(c+-1*c*sin(e+f*x))^(-2+-1m)*(15+4*m^2+16m)^-1*cos(e+f*x))
@test integrate((a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^(-3+-1m)*cos(e+f*x)^2, x) == :(a^-1*c^-1*f^-1*(3+2m)^-1*(a+a*sin(e+f*x))^(1+m)*(c+-1*c*sin(e+f*x))^(-2+-1m)*cos(e+f*x))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^7//2, x) == :(-2//11*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^7//2+2//3*a*c^4*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+2//7*a*c^3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^(1/2)+2//33*a*c*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^5//2+10//77*a*c^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^3//2+2*a*g*c^4*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^5//2, x) == :(-2//9*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^5//2+2//21*a*c*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^3//2+22//45*a*c^3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+22//105*a*c^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^(1/2)+22//15*a*g*c^3*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^3//2, x) == :(-2//7*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^3//2+2//5*a*c^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+6//35*a*c*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^(1/2)+6//5*a*g*c^2*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^(1/2), x) == :(-2//5*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^(1/2)+2//5*a*c*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+6//5*a*c*g*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-1//2, x) == :(-2//3*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+2*a*g*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-3//2, x) == :(4*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2+-6*a*g*c^-1*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-5//2, x) == :(4//5*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-5//2+-6//5*a*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2+6//5*a*g*c^-2*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-7//2, x) == :(4//9*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-7//2+-2//15*a*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-5//2+-2//15*a*c^-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2+2//15*a*g*c^-3*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-9//2, x) == :(4//13*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-9//2+-2//39*a*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-7//2+-2//65*a*c^-3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2+-2//65*a*c^-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-5//2+2//65*a*g*c^-4*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^5//2, x) == :(-14//99*a^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^5//2+-2//11*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^5//2+2//15*a^2*c^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^(1/2)+2//33*c*a^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^3//2+14//45*a^2*c^3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+14//15*g*a^2*c^3*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^3//2, x) == :(-2//9*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^3//2+-2//9*a^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^3//2+2//15*c*a^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^(1/2)+14//45*a^2*c^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+14//15*g*a^2*c^2*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^(1/2), x) == :(2//7*c*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-1//2+-6//35*a*c*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-1//2+-2//5*c*a^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+6//5*c*g*a^2*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-1//2, x) == :(-14//15*a^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+-2//5*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-1//2+14//5*g*a^2*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-3//2, x) == :(4*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-3//2+14//3*a^2*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+-14*g*a^2*c^-1*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-5//2, x) == :(4//5*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-5//2+-28//5*a^2*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2+42//5*g*a^2*c^-2*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-7//2, x) == :(4//9*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-7//2+-28//45*a^2*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-5//2+14//15*a^2*c^-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2+-14//15*g*a^2*c^-3*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-9//2, x) == :(4//13*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-9//2+-28//117*a^2*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-7//2+14//195*a^2*c^-3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2+14//195*a^2*c^-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-5//2+-14//195*g*a^2*c^-4*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-11//2, x) == :(4//17*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-11//2+-28//221*a^2*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-9//2+14//663*a^2*c^-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-7//2+14//1105*a^2*c^-4*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2+14//1105*a^2*c^-3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-5//2+-14//1105*g*a^2*c^-5*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^5//2, x) == :(-14//117*a^3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^5//2+-2//13*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^5//2+-2//13*a^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^5//2+2//39*c*a^3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^3//2+22//195*a^3*c^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^(1/2)+154//585*a^3*c^3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+154//195*g*a^3*c^3*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^3//2, x) == :(2//11*c*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^(1/2)+14//99*c^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-1//2+-14//45*a^3*c^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+-2//15*a^2*c^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-1//2+-2//33*a*c^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-1//2+14//15*g*a^3*c^2*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^(1/2), x) == :(2//9*c*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-1//2+-22//45*c*a^3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+-22//105*c*a^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-1//2+-2//21*a*c*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-1//2+22//15*c*g*a^3*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-1//2, x) == :(-22//15*a^3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+-22//35*a^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-1//2+-2//7*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-1//2+22//5*g*a^3*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-3//2, x) == :(4*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-3//2+22//5*a^2*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-1//2+154//15*a^3*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+-154//5*g*a^3*c^-1*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-5//2, x) == :(4//5*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-5//2+-154//15*a^3*c^-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+-44//5*a^2*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-3//2+154//5*g*a^3*c^-2*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-7//2, x) == :(4//9*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-7//2+-44//45*a^2*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-5//2+308//45*a^3*c^-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2+-154//15*g*a^3*c^-3*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-9//2, x) == :(4//13*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-9//2+-154//195*a^3*c^-3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2+-44//117*a^2*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-7//2+308//585*a^3*c^-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-5//2+154//195*g*a^3*c^-4*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-11//2, x) == :(4//17*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-11//2+-154//3315*a^3*c^-4*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2+-154//3315*a^3*c^-3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-5//2+-44//221*a^2*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-9//2+308//1989*a^3*c^-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-7//2+154//3315*g*a^3*c^-5*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-13//2, x) == :(4//21*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-13//2+-44//357*a^2*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-11//2+-22//1989*a^3*c^-3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-7//2+-22//3315*a^3*c^-5*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2+-22//3315*a^3*c^-4*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-5//2+44//663*a^3*c^-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-9//2+22//3315*g*a^3*c^-6*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^5//2, x) == :(2//15*c*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^3//2+14//195*c^3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-1//2+22//195*c^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^(1/2)+-154//585*a^4*c^3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+-22//195*a^3*c^3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-1//2+-14//585*a*c^3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-1//2+-2//39*a^2*c^3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-1//2+154//195*g*a^4*c^3*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^3//2, x) == :(2//13*c*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^(1/2)+14//143*c^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-1//2+-14//39*a^4*c^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+-14//429*a*c^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-1//2+-10//143*a^2*c^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-1//2+-2//13*a^3*c^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-1//2+14//13*g*a^4*c^2*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^(1/2), x) == :(2//11*c*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-1//2+-10//77*c*a^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-1//2+-2//3*c*a^4*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+-2//7*c*a^3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-1//2+-2//33*a*c*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-1//2+2*c*g*a^4*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-1//2, x) == :(-22//9*a^4*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+-22//21*a^3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-1//2+-10//21*a^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-1//2+-2//9*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-1//2+22//3*g*a^4*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-3//2, x) == :(4*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-3//2+22*a^4*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+30//7*a^2*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-1//2+66//7*a^3*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-1//2+-66*g*a^4*c^-1*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-5//2, x) == :(4//5*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-5//2+-12*a^2*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-3//2+-154//5*a^4*c^-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+-66//5*a^3*c^-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-1//2+462//5*g*a^4*c^-2*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-7//2, x) == :(4//9*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-7//2+-4//3*a^2*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-5//2+44//3*a^3*c^-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-3//2+154//9*a^4*c^-3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+-154//3*g*a^4*c^-3*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-9//2, x) == :(4//13*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-9//2+-308//39*a^4*c^-3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2+-20//39*a^2*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-7//2+44//39*a^3*c^-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-5//2+154//13*g*a^4*c^-4*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-11//2, x) == :(4//17*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-11//2+-308//663*a^4*c^-3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-5//2+-60//221*a^2*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-9//2+154//221*a^4*c^-4*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2+220//663*a^3*c^-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-7//2+-154//221*g*a^4*c^-5*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-13//2, x) == :(4//21*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-13//2+-220//1989*a^4*c^-3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-7//2+-20//119*a^2*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-11//2+22//663*a^4*c^-5*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2+22//663*a^4*c^-4*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-5//2+220//1547*a^3*c^-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-9//2+-22//663*g*a^4*c^-6*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^7//2*(c+-1*c*sin(e+f*x))^-15//2, x) == :(4//25*a*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^5//2*(c+-1*c*sin(e+f*x))^-15//2+-44//1105*a^4*c^-3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-9//2+-4//35*a^2*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^3//2*(c+-1*c*sin(e+f*x))^-13//2+22//3315*a^4*c^-4*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-7//2+22//5525*a^4*c^-6*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2+22//5525*a^4*c^-5*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-5//2+44//595*a^3*c^-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^(1/2)*(c+-1*c*sin(e+f*x))^-11//2+-22//5525*g*a^4*c^-7*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^5//2, x) == :(2//7*c*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^3//2+22//15*c^3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+22//35*c^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^(1/2)+22//5*g*c^3*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^3//2, x) == :(2//5*c*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^(1/2)+14//15*c^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+14//5*g*c^2*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^(1/2), x) == :(2//3*c*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+2*c*g*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2, x) == :(2*g*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2, x) == :(2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2+-2*g*c^-1*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-5//2, x) == :(2//5*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-5//2+2//5*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2+-2//5*g*c^-2*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-7//2, x) == :(2//9*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-7//2+2//15*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-5//2+2//15*c^-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2+-2//15*g*c^-3*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^7//2, x) == :(-4*c*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^5//2+-22*a^-1*c^4*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+-66//7*a^-1*c^3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^(1/2)+-30//7*a^-1*c^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^3//2+-66*g*a^-1*c^4*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^5//2, x) == :(-4*c*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^3//2+-154//15*a^-1*c^3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+-22//5*a^-1*c^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^(1/2)+-154//5*g*a^-1*c^3*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^3//2, x) == :(-4*c*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^(1/2)+-14//3*a^-1*c^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+-14*g*a^-1*c^2*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^(1/2), x) == :(-4*c*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^-1//2+-6*c*g*a^-1*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^-1//2, x) == :(-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^-1//2+-2*g*a^-1*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^-3//2, x) == :(-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^-3//2+2*a^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2+-2*g*a^-1*c^-1*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^-5//2, x) == :(-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^-5//2+6//5*a^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-5//2+6//5*a^-1*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2+-6//5*g*a^-1*c^-2*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^-7//2, x) == :(-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^-7//2+10//9*a^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-7//2+2//3*a^-1*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-5//2+2//3*a^-1*c^-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2+-2//3*g*a^-1*c^-3*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^9//2, x) == :(-4//5*c*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^7//2+76//5*a^-1*c^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^5//2+114//7*a^-2*c^3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^3//2+418//5*a^-2*c^5*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+1254//35*a^-2*c^4*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^(1/2)+1254//5*g*a^-2*c^5*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^7//2, x) == :(-4//5*c*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^5//2+12*a^-1*c^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^3//2+66//5*a^-2*c^3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^(1/2)+154//5*a^-2*c^4*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+462//5*g*a^-2*c^4*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^5//2, x) == :(-4//5*c*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^3//2+44//5*a^-1*c^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^(1/2)+154//15*a^-2*c^3*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2+154//5*g*a^-2*c^3*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^3//2, x) == :(-4//5*c*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^(1/2)+28//5*a^-1*c^2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^-1//2+42//5*g*a^-2*c^2*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^(1/2), x) == :(-4//5*c*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^-1//2+6//5*c*a^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^-1//2+6//5*c*g*a^-2*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^-1//2, x) == :(-2//5*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^-1//2+-2//5*a^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^-1//2+-2//5*g*a^-2*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^-3//2, x) == :(2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^-3//2+-6//5*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^-1//2+-6//5*a^-1*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^-1//2+-6//5*g*a^-2*c^-1*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^-5//2, x) == :(-2//5*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^-5//2+-2*a^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^-5//2+6//5*a^-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-5//2+6//5*a^-2*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2+-6//5*g*a^-2*c^-2*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^3//2*(a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^-7//2, x) == :(-2//5*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-5//2*(c+-1*c*sin(e+f*x))^-7//2+-14//5*a^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-3//2*(c+-1*c*sin(e+f*x))^-7//2+14//9*a^-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-7//2+14//15*a^-2*c^-1*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-5//2+14//15*a^-2*c^-2*f^-1*g^-1*(g*cos(e+f*x))^5//2*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-3//2+-14//15*g*a^-2*c^-3*f^-1*(g*cos(e+f*x))^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1*c*sin(e+f*x))^-1//2*cos(e+f*x)^(1/2)*Elliptic.E((1/2)*e+(1/2)*f*x,2))
@test integrate((g*cos(e+f*x))^(1+-2m)*(a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^(-1+m), x) == :(-1*g*c^-1*f^-1*(g*cos(e+f*x))^(-2m)*(a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^m*log(1+-1*sin(e+f*x)))
@test integrate((g*cos(e+f*x))^(5+-2m)*(a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^n, x) == :(-1*a*f^-1*g^-1*(g*cos(e+f*x))^(6+-2m)*(a+a*sin(e+f*x))^(-1+m)*(c+-1*c*sin(e+f*x))^n*(5+n+-1m)^-1+-4*a^2*f^-1*g^-1*(g*cos(e+f*x))^(6+-2m)*(a+a*sin(e+f*x))^(-2+m)*(c+-1*c*sin(e+f*x))^n*(4+n+-1m)^-1*(5+n+-1m)^-1+-8*a^3*f^-1*g^-1*(g*cos(e+f*x))^(6+-2m)*(a+a*sin(e+f*x))^(-3+m)*(c+-1*c*sin(e+f*x))^n*(3+n+-1m)^-1*(4+n+-1m)^-1*(5+n+-1m)^-1)
@test integrate((g*cos(e+f*x))^(3+-2m)*(a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^n, x) == :(-1*a*f^-1*g^-1*(g*cos(e+f*x))^(4+-2m)*(a+a*sin(e+f*x))^(-1+m)*(c+-1*c*sin(e+f*x))^n*(3+n+-1m)^-1+-2*a^2*f^-1*g^-1*(g*cos(e+f*x))^(4+-2m)*(a+a*sin(e+f*x))^(-2+m)*(c+-1*c*sin(e+f*x))^n*(2+n+-1m)^-1*(3+n+-1m)^-1)
@test integrate((g*cos(e+f*x))^(1+-2m)*(a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^n, x) == :(-1*a*f^-1*g^-1*(g*cos(e+f*x))^(2+-2m)*(a+a*sin(e+f*x))^(-1+m)*(c+-1*c*sin(e+f*x))^n*(1+n+-1m)^-1)
@test integrate((g*cos(e+f*x))^(-1+-2m)*(a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^m, x) == :(f^-1*g^-1*(g*cos(e+f*x))^(-2m)*(a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^m*arctanh(sin(e+f*x)))
@test integrate((g*cos(e+f*x))^(-1+-1m+-1n)*(a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^n, x) == :(f^-1*g^-1*(g*cos(e+f*x))^(-1m+-1n)*(a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^n*(m+-1n)^-1)
@test integrate((g*cos(e+f*x))^(-1+-1m+-1n)*(a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^(-1+n), x) == :(f^-1*g^-1*(g*cos(e+f*x))^(-1m+-1n)*(a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^(-1+n)*(2+m+-1n)^-1+c^-1*f^-1*g^-1*(g*cos(e+f*x))^(-1m+-1n)*(a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^n*(m+-1n)^-1*(2+m+-1n)^-1)
@test integrate((g*cos(e+f*x))^(-1+-1m+-1n)*(a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^(-2+n), x) == :(f^-1*g^-1*(g*cos(e+f*x))^(-1m+-1n)*(a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^(-2+n)*(4+m+-1n)^-1+2*c^-1*f^-1*g^-1*(g*cos(e+f*x))^(-1m+-1n)*(a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^(-1+n)*(2+m+-1n)^-1*(4+m+-1n)^-1+2*c^-2*f^-1*g^-1*(g*cos(e+f*x))^(-1m+-1n)*(a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^n*(m+-1n)^-1*(2+m+-1n)^-1*(4+m+-1n)^-1)
@test integrate((g*cos(e+f*x))^(-1+-1m+-1n)*(a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^(-3+n), x) == :(f^-1*g^-1*(g*cos(e+f*x))^(-1m+-1n)*(a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^(-3+n)*(6+m+-1n)^-1+3*c^-1*f^-1*g^-1*(g*cos(e+f*x))^(-1m+-1n)*(a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^(-2+n)*(4+m+-1n)^-1*(6+m+-1n)^-1+6*c^-2*f^-1*g^-1*(g*cos(e+f*x))^(-1m+-1n)*(a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^(-1+n)*(2+m+-1n)^-1*(4+m+-1n)^-1*(6+m+-1n)^-1+6*c^-3*f^-1*g^-1*(g*cos(e+f*x))^(-1m+-1n)*(a+a*sin(e+f*x))^m*(c+-1*c*sin(e+f*x))^n*(m+-1n)^-1*(2+m+-1n)^-1*(4+m+-1n)^-1*(6+m+-1n)^-1)
@test integrate(sin(c+d*x)^2*(a+a*sin(c+d*x))*cos(c+d*x), x) == :(1//3*a*d^-1*sin(c+d*x)^3+1//4*a*d^-1*sin(c+d*x)^4)
@test integrate((a+a*sin(c+d*x))*cos(c+d*x)*sin(c+d*x), x) == :((1/2)*a*d^-1*sin(c+d*x)^2+1//3*a*d^-1*sin(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))*cos(c+d*x)*csc(c+d*x), x) == :(a*d^-1*log(sin(c+d*x))+a*d^-1*sin(c+d*x))
@test integrate(csc(c+d*x)^2*(a+a*sin(c+d*x))*cos(c+d*x), x) == :(a*d^-1*log(sin(c+d*x))+-1*a*d^-1*csc(c+d*x))
@test integrate(csc(c+d*x)^3*(a+a*sin(c+d*x))*cos(c+d*x), x) == :(-1//2*a^-1*d^-1*(a+a*sin(c+d*x))^2*csc(c+d*x)^2)
@test integrate(csc(c+d*x)^4*(a+a*sin(c+d*x))*cos(c+d*x), x) == :(-1//2*a*d^-1*csc(c+d*x)^2+-1//3*a*d^-1*csc(c+d*x)^3)
@test integrate(csc(c+d*x)^5*(a+a*sin(c+d*x))*cos(c+d*x), x) == :(-1//3*a*d^-1*csc(c+d*x)^3+-1//4*a*d^-1*csc(c+d*x)^4)
@test integrate((a+a*sin(c+d*x))^2*sin(c+d*x)^2*cos(c+d*x), x) == :((1/2)*a^2*d^-1*sin(c+d*x)^4+1//3*a^2*d^-1*sin(c+d*x)^3+1//5*a^2*d^-1*sin(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)*sin(c+d*x), x) == :((1/2)*a^2*d^-1*sin(c+d*x)^2+1//4*a^2*d^-1*sin(c+d*x)^4+2//3*a^2*d^-1*sin(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)*csc(c+d*x), x) == :(a^2*d^-1*log(sin(c+d*x))+(1/2)*a^2*d^-1*sin(c+d*x)^2+2*a^2*d^-1*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*csc(c+d*x)^2*cos(c+d*x), x) == :(a^2*d^-1*sin(c+d*x)+-1*a^2*d^-1*csc(c+d*x)+2*a^2*d^-1*log(sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^2*csc(c+d*x)^3*cos(c+d*x), x) == :(a^2*d^-1*log(sin(c+d*x))+-2*a^2*d^-1*csc(c+d*x)+-1//2*a^2*d^-1*csc(c+d*x)^2)
@test integrate((a+a*sin(c+d*x))^2*csc(c+d*x)^4*cos(c+d*x), x) == :(-1//3*a^-1*d^-1*(a+a*sin(c+d*x))^3*csc(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^2*csc(c+d*x)^5*cos(c+d*x), x) == :(-2//3*a^2*d^-1*csc(c+d*x)^3+-1//2*a^2*d^-1*csc(c+d*x)^2+-1//4*a^2*d^-1*csc(c+d*x)^4)
@test integrate((a+a*sin(c+d*x))^2*csc(c+d*x)^6*cos(c+d*x), x) == :(-1//2*a^2*d^-1*csc(c+d*x)^4+-1//3*a^2*d^-1*csc(c+d*x)^3+-1//5*a^2*d^-1*csc(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^2*csc(c+d*x)^7*cos(c+d*x), x) == :(-2//5*a^2*d^-1*csc(c+d*x)^5+-1//4*a^2*d^-1*csc(c+d*x)^4+-1//6*a^2*d^-1*csc(c+d*x)^6)
@test integrate((a+a*sin(c+d*x))^3*sin(c+d*x)^3*cos(c+d*x), x) == :((1/2)*a^3*d^-1*sin(c+d*x)^6+1//4*a^3*d^-1*sin(c+d*x)^4+1//7*a^3*d^-1*sin(c+d*x)^7+3//5*a^3*d^-1*sin(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^3*sin(c+d*x)^2*cos(c+d*x), x) == :(1//3*a^3*d^-1*sin(c+d*x)^3+1//6*a^3*d^-1*sin(c+d*x)^6+3//4*a^3*d^-1*sin(c+d*x)^4+3//5*a^3*d^-1*sin(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)*sin(c+d*x), x) == :(-1//4*a^-1*d^-1*(a+a*sin(c+d*x))^4+1//5*a^-2*d^-1*(a+a*sin(c+d*x))^5)
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)*csc(c+d*x), x) == :(a^3*d^-1*log(sin(c+d*x))+3*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*sin(c+d*x)^2)
@test integrate((a+a*sin(c+d*x))^3*csc(c+d*x)^2*cos(c+d*x), x) == :((1/2)*a^3*d^-1*sin(c+d*x)^2+-1*a^3*d^-1*csc(c+d*x)+3*a^3*d^-1*log(sin(c+d*x))+3*a^3*d^-1*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*csc(c+d*x)^3*cos(c+d*x), x) == :(a^3*d^-1*sin(c+d*x)+-3*a^3*d^-1*csc(c+d*x)+3*a^3*d^-1*log(sin(c+d*x))+-1//2*a^3*d^-1*csc(c+d*x)^2)
@test integrate((a+a*sin(c+d*x))^3*csc(c+d*x)^4*cos(c+d*x), x) == :(a^3*d^-1*log(sin(c+d*x))+-3*a^3*d^-1*csc(c+d*x)+-3//2*a^3*d^-1*csc(c+d*x)^2+-1//3*a^3*d^-1*csc(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^3*csc(c+d*x)^5*cos(c+d*x), x) == :(-1//4*a^-1*d^-1*(a+a*sin(c+d*x))^4*csc(c+d*x)^4)
@test integrate((a+a*sin(c+d*x))^3*csc(c+d*x)^6*cos(c+d*x), x) == :(-1//5*a^-1*d^-1*(a+a*sin(c+d*x))^4*csc(c+d*x)^5+1//20*a^-1*d^-1*(a+a*sin(c+d*x))^4*csc(c+d*x)^4)
@test integrate((a+a*sin(c+d*x))^3*csc(c+d*x)^7*cos(c+d*x), x) == :(-3//4*a^3*d^-1*csc(c+d*x)^4+-3//5*a^3*d^-1*csc(c+d*x)^5+-1//3*a^3*d^-1*csc(c+d*x)^3+-1//6*a^3*d^-1*csc(c+d*x)^6)
@test integrate((a+a*sin(c+d*x))^3*csc(c+d*x)^8*cos(c+d*x), x) == :(-3//5*a^3*d^-1*csc(c+d*x)^5+-1//2*a^3*d^-1*csc(c+d*x)^6+-1//4*a^3*d^-1*csc(c+d*x)^4+-1//7*a^3*d^-1*csc(c+d*x)^7)
@test integrate((a+a*sin(c+d*x))^4*sin(c+d*x)^4*cos(c+d*x), x) == :((1/2)*a^4*d^-1*sin(c+d*x)^8+1//5*a^4*d^-1*sin(c+d*x)^5+1//9*a^4*d^-1*sin(c+d*x)^9+2//3*a^4*d^-1*sin(c+d*x)^6+6//7*a^4*d^-1*sin(c+d*x)^7)
@test integrate((a+a*sin(c+d*x))^4*sin(c+d*x)^3*cos(c+d*x), x) == :(a^4*d^-1*sin(c+d*x)^6+1//4*a^4*d^-1*sin(c+d*x)^4+1//8*a^4*d^-1*sin(c+d*x)^8+4//5*a^4*d^-1*sin(c+d*x)^5+4//7*a^4*d^-1*sin(c+d*x)^7)
@test integrate((a+a*sin(c+d*x))^4*sin(c+d*x)^2*cos(c+d*x), x) == :(-1//3*a^-2*d^-1*(a+a*sin(c+d*x))^6+1//5*a^-1*d^-1*(a+a*sin(c+d*x))^5+1//7*a^-3*d^-1*(a+a*sin(c+d*x))^7)
@test integrate((a+a*sin(c+d*x))^4*cos(c+d*x)*sin(c+d*x), x) == :(-1//5*a^-1*d^-1*(a+a*sin(c+d*x))^5+1//6*a^-2*d^-1*(a+a*sin(c+d*x))^6)
@test integrate((a+a*sin(c+d*x))^4*cos(c+d*x)*csc(c+d*x), x) == :(a^4*d^-1*log(sin(c+d*x))+3*a^4*d^-1*sin(c+d*x)^2+4*a^4*d^-1*sin(c+d*x)+1//4*a^4*d^-1*sin(c+d*x)^4+4//3*a^4*d^-1*sin(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^4*csc(c+d*x)^2*cos(c+d*x), x) == :(-1*a^4*d^-1*csc(c+d*x)+2*a^4*d^-1*sin(c+d*x)^2+4*a^4*d^-1*log(sin(c+d*x))+6*a^4*d^-1*sin(c+d*x)+1//3*a^4*d^-1*sin(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^4*csc(c+d*x)^3*cos(c+d*x), x) == :((1/2)*a^4*d^-1*sin(c+d*x)^2+-4*a^4*d^-1*csc(c+d*x)+4*a^4*d^-1*sin(c+d*x)+6*a^4*d^-1*log(sin(c+d*x))+-1//2*a^4*d^-1*csc(c+d*x)^2)
@test integrate((a+a*sin(c+d*x))^-1*sin(c+d*x)^4*cos(c+d*x), x) == :(a^-1*d^-1*log(1+sin(c+d*x))+(1/2)*a^-1*d^-1*sin(c+d*x)^2+-1*a^-1*d^-1*sin(c+d*x)+-1//3*a^-1*d^-1*sin(c+d*x)^3+1//4*a^-1*d^-1*sin(c+d*x)^4)
@test integrate((a+a*sin(c+d*x))^-1*sin(c+d*x)^3*cos(c+d*x), x) == :(a^-1*d^-1*sin(c+d*x)+-1*a^-1*d^-1*log(1+sin(c+d*x))+-1//2*a^-1*d^-1*sin(c+d*x)^2+1//3*a^-1*d^-1*sin(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-1*sin(c+d*x)^2*cos(c+d*x), x) == :(a^-1*d^-1*log(1+sin(c+d*x))+(1/2)*a^-1*d^-1*sin(c+d*x)^2+-1*a^-1*d^-1*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)*sin(c+d*x), x) == :(a^-1*d^-1*sin(c+d*x)+-1*a^-1*d^-1*log(1+sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)*csc(c+d*x), x) == :(a^-1*d^-1*log(sin(c+d*x))+-1*a^-1*d^-1*log(1+sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-1*csc(c+d*x)^2*cos(c+d*x), x) == :(a^-1*d^-1*log(1+sin(c+d*x))+-1*a^-1*d^-1*csc(c+d*x)+-1*a^-1*d^-1*log(sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-1*csc(c+d*x)^3*cos(c+d*x), x) == :(a^-1*d^-1*csc(c+d*x)+a^-1*d^-1*log(sin(c+d*x))+-1*a^-1*d^-1*log(1+sin(c+d*x))+-1//2*a^-1*d^-1*csc(c+d*x)^2)
@test integrate((a+a*sin(c+d*x))^-1*csc(c+d*x)^4*cos(c+d*x), x) == :(a^-1*d^-1*log(1+sin(c+d*x))+(1/2)*a^-1*d^-1*csc(c+d*x)^2+-1*a^-1*d^-1*csc(c+d*x)+-1*a^-1*d^-1*log(sin(c+d*x))+-1//3*a^-1*d^-1*csc(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-2*sin(c+d*x)^4*cos(c+d*x), x) == :(-1*d^-1*(a^2+a^2*sin(c+d*x))^-1+-1*a^-2*d^-1*sin(c+d*x)^2+-4*a^-2*d^-1*log(1+sin(c+d*x))+3*a^-2*d^-1*sin(c+d*x)+1//3*a^-2*d^-1*sin(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-2*sin(c+d*x)^3*cos(c+d*x), x) == :(d^-1*(a^2+a^2*sin(c+d*x))^-1+(1/2)*a^-2*d^-1*sin(c+d*x)^2+-2*a^-2*d^-1*sin(c+d*x)+3*a^-2*d^-1*log(1+sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-2*sin(c+d*x)^2*cos(c+d*x), x) == :(-1*d^-1*(a^2+a^2*sin(c+d*x))^-1+a^-2*d^-1*sin(c+d*x)+-2*a^-2*d^-1*log(1+sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)*sin(c+d*x), x) == :(d^-1*(a^2+a^2*sin(c+d*x))^-1+a^-2*d^-1*log(1+sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)*csc(c+d*x), x) == :(d^-1*(a^2+a^2*sin(c+d*x))^-1+a^-2*d^-1*log(sin(c+d*x))+-1*a^-2*d^-1*log(1+sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-2*csc(c+d*x)^2*cos(c+d*x), x) == :(-1*d^-1*(a^2+a^2*sin(c+d*x))^-1+-1*a^-2*d^-1*csc(c+d*x)+-2*a^-2*d^-1*log(sin(c+d*x))+2*a^-2*d^-1*log(1+sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-2*csc(c+d*x)^3*cos(c+d*x), x) == :(d^-1*(a^2+a^2*sin(c+d*x))^-1+-3*a^-2*d^-1*log(1+sin(c+d*x))+2*a^-2*d^-1*csc(c+d*x)+3*a^-2*d^-1*log(sin(c+d*x))+-1//2*a^-2*d^-1*csc(c+d*x)^2)
@test integrate((a+a*sin(c+d*x))^-2*csc(c+d*x)^4*cos(c+d*x), x) == :(-1*d^-1*(a^2+a^2*sin(c+d*x))^-1+a^-2*d^-1*csc(c+d*x)^2+-4*a^-2*d^-1*log(sin(c+d*x))+-3*a^-2*d^-1*csc(c+d*x)+4*a^-2*d^-1*log(1+sin(c+d*x))+-1//3*a^-2*d^-1*csc(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-3*sin(c+d*x)^5*cos(c+d*x), x) == :(-5*d^-1*(a^3+a^3*sin(c+d*x))^-1+(1/2)*a^-1*d^-1*(a+a*sin(c+d*x))^-2+-10*a^-3*d^-1*log(1+sin(c+d*x))+6*a^-3*d^-1*sin(c+d*x)+-3//2*a^-3*d^-1*sin(c+d*x)^2+1//3*a^-3*d^-1*sin(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-3*sin(c+d*x)^4*cos(c+d*x), x) == :(4*d^-1*(a^3+a^3*sin(c+d*x))^-1+(1/2)*a^-3*d^-1*sin(c+d*x)^2+-3*a^-3*d^-1*sin(c+d*x)+6*a^-3*d^-1*log(1+sin(c+d*x))+-1//2*a^-1*d^-1*(a+a*sin(c+d*x))^-2)
@test integrate((a+a*sin(c+d*x))^-3*sin(c+d*x)^3*cos(c+d*x), x) == :(-3*d^-1*(a^3+a^3*sin(c+d*x))^-1+a^-3*d^-1*sin(c+d*x)+(1/2)*a^-1*d^-1*(a+a*sin(c+d*x))^-2+-3*a^-3*d^-1*log(1+sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-3*sin(c+d*x)^2*cos(c+d*x), x) == :(2*d^-1*(a^3+a^3*sin(c+d*x))^-1+a^-3*d^-1*log(1+sin(c+d*x))+-1//2*a^-1*d^-1*(a+a*sin(c+d*x))^-2)
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)*sin(c+d*x), x) == :((1/2)*a^-1*d^-1*(a+a*sin(c+d*x))^-2*sin(c+d*x)^2)
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)*csc(c+d*x), x) == :(d^-1*(a^3+a^3*sin(c+d*x))^-1+a^-3*d^-1*log(sin(c+d*x))+(1/2)*a^-1*d^-1*(a+a*sin(c+d*x))^-2+-1*a^-3*d^-1*log(1+sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-3*csc(c+d*x)^2*cos(c+d*x), x) == :(-2*d^-1*(a^3+a^3*sin(c+d*x))^-1+-1*a^-3*d^-1*csc(c+d*x)+-3*a^-3*d^-1*log(sin(c+d*x))+3*a^-3*d^-1*log(1+sin(c+d*x))+-1//2*a^-1*d^-1*(a+a*sin(c+d*x))^-2)
@test integrate((a+a*sin(c+d*x))^-3*csc(c+d*x)^3*cos(c+d*x), x) == :(3*d^-1*(a^3+a^3*sin(c+d*x))^-1+(1/2)*a^-1*d^-1*(a+a*sin(c+d*x))^-2+-6*a^-3*d^-1*log(1+sin(c+d*x))+3*a^-3*d^-1*csc(c+d*x)+6*a^-3*d^-1*log(sin(c+d*x))+-1//2*a^-3*d^-1*csc(c+d*x)^2)
@test integrate((a+a*sin(c+d*x))^-3*csc(c+d*x)^4*cos(c+d*x), x) == :(-4*d^-1*(a^3+a^3*sin(c+d*x))^-1+-10*a^-3*d^-1*log(sin(c+d*x))+-6*a^-3*d^-1*csc(c+d*x)+10*a^-3*d^-1*log(1+sin(c+d*x))+-1//2*a^-1*d^-1*(a+a*sin(c+d*x))^-2+-1//3*a^-3*d^-1*csc(c+d*x)^3+3//2*a^-3*d^-1*csc(c+d*x)^2)
@test integrate((a+a*sin(c+d*x))^-4*sin(c+d*x)^5*cos(c+d*x), x) == :(10*d^-1*(a^4+a^4*sin(c+d*x))^-1+-5//2*d^-1*(a^2+a^2*sin(c+d*x))^-2+(1/2)*a^-4*d^-1*sin(c+d*x)^2+-4*a^-4*d^-1*sin(c+d*x)+10*a^-4*d^-1*log(1+sin(c+d*x))+1//3*a^-1*d^-1*(a+a*sin(c+d*x))^-3)
@test integrate((a+a*sin(c+d*x))^-4*sin(c+d*x)^4*cos(c+d*x), x) == :(-6*d^-1*(a^4+a^4*sin(c+d*x))^-1+2*d^-1*(a^2+a^2*sin(c+d*x))^-2+a^-4*d^-1*sin(c+d*x)+-4*a^-4*d^-1*log(1+sin(c+d*x))+-1//3*a^-1*d^-1*(a+a*sin(c+d*x))^-3)
@test integrate((a+a*sin(c+d*x))^-4*sin(c+d*x)^3*cos(c+d*x), x) == :(3*d^-1*(a^4+a^4*sin(c+d*x))^-1+-3//2*d^-1*(a^2+a^2*sin(c+d*x))^-2+a^-4*d^-1*log(1+sin(c+d*x))+1//3*a^-1*d^-1*(a+a*sin(c+d*x))^-3)
@test integrate((a+a*sin(c+d*x))^-4*sin(c+d*x)^2*cos(c+d*x), x) == :(1//3*a^-1*d^-1*(a+a*sin(c+d*x))^-3*sin(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-4*cos(c+d*x)*sin(c+d*x), x) == :(-1//2*d^-1*(a^2+a^2*sin(c+d*x))^-2+1//3*a^-1*d^-1*(a+a*sin(c+d*x))^-3)
@test integrate((a+a*sin(c+d*x))^-4*cos(c+d*x)*csc(c+d*x), x) == :(d^-1*(a^4+a^4*sin(c+d*x))^-1+(1/2)*d^-1*(a^2+a^2*sin(c+d*x))^-2+a^-4*d^-1*log(sin(c+d*x))+-1*a^-4*d^-1*log(1+sin(c+d*x))+1//3*a^-1*d^-1*(a+a*sin(c+d*x))^-3)
@test integrate((a+a*sin(c+d*x))^-4*csc(c+d*x)^2*cos(c+d*x), x) == :(-1*d^-1*(a^2+a^2*sin(c+d*x))^-2+-3*d^-1*(a^4+a^4*sin(c+d*x))^-1+-1*a^-4*d^-1*csc(c+d*x)+-4*a^-4*d^-1*log(sin(c+d*x))+4*a^-4*d^-1*log(1+sin(c+d*x))+-1//3*a^-1*d^-1*(a+a*sin(c+d*x))^-3)
@test integrate((a+a*sin(c+d*x))^-4*csc(c+d*x)^3*cos(c+d*x), x) == :(6*d^-1*(a^4+a^4*sin(c+d*x))^-1+3//2*d^-1*(a^2+a^2*sin(c+d*x))^-2+-10*a^-4*d^-1*log(1+sin(c+d*x))+4*a^-4*d^-1*csc(c+d*x)+10*a^-4*d^-1*log(sin(c+d*x))+-1//2*a^-4*d^-1*csc(c+d*x)^2+1//3*a^-1*d^-1*(a+a*sin(c+d*x))^-3)
@test integrate((a+a*sin(c+d*x))^(1/2)*cos(c+d*x)*csc(c+d*x), x) == :(2*d^-1*(a+a*sin(c+d*x))^(1/2)+-2*a^(1/2)*d^-1*arctanh(a^-1//2*(a+a*sin(c+d*x))^(1/2)))
@test integrate((a+a*sin(c+d*x))^4*sin(c+d*x)^n*cos(c+d*x), x) == :(a^4*d^-1*(1+n)^-1*sin(c+d*x)^(1+n)+a^4*d^-1*(5+n)^-1*sin(c+d*x)^(5+n)+4*a^4*d^-1*(2+n)^-1*sin(c+d*x)^(2+n)+4*a^4*d^-1*(4+n)^-1*sin(c+d*x)^(4+n)+6*a^4*d^-1*(3+n)^-1*sin(c+d*x)^(3+n))
@test integrate((a+a*sin(c+d*x))^3*sin(c+d*x)^n*cos(c+d*x), x) == :(a^3*d^-1*(1+n)^-1*sin(c+d*x)^(1+n)+a^3*d^-1*(4+n)^-1*sin(c+d*x)^(4+n)+3*a^3*d^-1*(2+n)^-1*sin(c+d*x)^(2+n)+3*a^3*d^-1*(3+n)^-1*sin(c+d*x)^(3+n))
@test integrate((a+a*sin(c+d*x))^2*sin(c+d*x)^n*cos(c+d*x), x) == :(a^2*d^-1*(1+n)^-1*sin(c+d*x)^(1+n)+a^2*d^-1*(3+n)^-1*sin(c+d*x)^(3+n)+2*a^2*d^-1*(2+n)^-1*sin(c+d*x)^(2+n))
@test integrate(sin(c+d*x)^n*(a+a*sin(c+d*x))*cos(c+d*x), x) == :(a*d^-1*(1+n)^-1*sin(c+d*x)^(1+n)+a*d^-1*(2+n)^-1*sin(c+d*x)^(2+n))
@test integrate(cos(c+d*x)^2*sin(c+d*x)^3*(a+a*sin(c+d*x)), x) == :(1//16*a*x+-1//3*a*d^-1*cos(c+d*x)^3+1//5*a*d^-1*cos(c+d*x)^5+-1//6*a*d^-1*cos(c+d*x)^3*sin(c+d*x)^3+-1//8*a*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//16*a*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^2*sin(c+d*x)^2*(a+a*sin(c+d*x)), x) == :(1//8*a*x+-1//3*a*d^-1*cos(c+d*x)^3+1//5*a*d^-1*cos(c+d*x)^5+-1//4*a*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//8*a*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^2*(a+a*sin(c+d*x))*sin(c+d*x), x) == :(1//8*a*x+-1//3*a*d^-1*cos(c+d*x)^3+-1//4*a*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//8*a*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^2*(a+a*sin(c+d*x))*csc(c+d*x), x) == :((1/2)*a*x+a*d^-1*cos(c+d*x)+-1*a*d^-1*arctanh(cos(c+d*x))+(1/2)*a*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^2*csc(c+d*x)^2*(a+a*sin(c+d*x)), x) == :(-1*a*x+a*d^-1*cos(c+d*x)+-1*a*d^-1*arctanh(cos(c+d*x))+-1*a*d^-1*cot(c+d*x))
@test integrate(cos(c+d*x)^2*csc(c+d*x)^3*(a+a*sin(c+d*x)), x) == :(-1*a*x+(1/2)*a*d^-1*arctanh(cos(c+d*x))+-1*a*d^-1*cot(c+d*x)+-1//2*a*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate(cos(c+d*x)^2*csc(c+d*x)^4*(a+a*sin(c+d*x)), x) == :((1/2)*a*d^-1*arctanh(cos(c+d*x))+-1//3*a*d^-1*cot(c+d*x)^3+-1//2*a*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate(cos(c+d*x)^2*csc(c+d*x)^5*(a+a*sin(c+d*x)), x) == :(-1//3*a*d^-1*cot(c+d*x)^3+1//8*a*d^-1*arctanh(cos(c+d*x))+-1//4*a*d^-1*csc(c+d*x)^3*cot(c+d*x)+1//8*a*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate(cos(c+d*x)^2*csc(c+d*x)^6*(a+a*sin(c+d*x)), x) == :(-1//3*a*d^-1*cot(c+d*x)^3+-1//5*a*d^-1*cot(c+d*x)^5+1//8*a*d^-1*arctanh(cos(c+d*x))+-1//4*a*d^-1*csc(c+d*x)^3*cot(c+d*x)+1//8*a*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^2*sin(c+d*x)^3, x) == :(1//8*x*a^2+-2//3*a^2*d^-1*cos(c+d*x)^3+-1//7*a^2*d^-1*cos(c+d*x)^7+3//5*a^2*d^-1*cos(c+d*x)^5+-1//3*a^2*d^-1*cos(c+d*x)^3*sin(c+d*x)^3+-1//4*a^2*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//8*a^2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^2*sin(c+d*x)^2, x) == :(3//16*x*a^2+-1//10*a^2*d^-1*cos(c+d*x)^5+-1//6*a^-1*d^-1*(a+a*sin(c+d*x))^3*cos(c+d*x)^3+1//8*a^2*d^-1*cos(c+d*x)^3*sin(c+d*x)+3//16*a^2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^2*csc(c+d*x), x) == :(x*a^2+a^2*d^-1*cos(c+d*x)+-1*a^2*d^-1*arctanh(cos(c+d*x))+-1//3*a^2*d^-1*cos(c+d*x)^3+a^2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^2*csc(c+d*x)^2, x) == :(-1//2*x*a^2+-1*a^2*d^-1*cot(c+d*x)+-2*a^2*d^-1*arctanh(cos(c+d*x))+2*a^2*d^-1*cos(c+d*x)+(1/2)*a^2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^2*csc(c+d*x)^3, x) == :(-2*x*a^2+a^2*d^-1*cos(c+d*x)+-2*a^2*d^-1*cot(c+d*x)+-1//2*a^2*d^-1*arctanh(cos(c+d*x))+-1//2*a^2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^2*csc(c+d*x)^4, x) == :(-1*x*a^2+a^2*d^-1*arctanh(cos(c+d*x))+-1*a^2*d^-1*cot(c+d*x)+-1//3*a^2*d^-1*cot(c+d*x)^3+-1*a^2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^2*csc(c+d*x)^5, x) == :(-2//3*a^2*d^-1*cot(c+d*x)^3+5//8*a^2*d^-1*arctanh(cos(c+d*x))+-3//8*a^2*d^-1*cot(c+d*x)*csc(c+d*x)+-1//4*a^2*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^2*csc(c+d*x)^6, x) == :(-2//3*a^2*d^-1*cot(c+d*x)^3+-1//5*a^2*d^-1*cot(c+d*x)^5+1//4*a^2*d^-1*arctanh(cos(c+d*x))+-1//2*a^2*d^-1*csc(c+d*x)^3*cot(c+d*x)+1//4*a^2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^2*csc(c+d*x)^7, x) == :(-2//3*a^2*d^-1*cot(c+d*x)^3+-2//5*a^2*d^-1*cot(c+d*x)^5+3//16*a^2*d^-1*arctanh(cos(c+d*x))+-5//24*a^2*d^-1*csc(c+d*x)^3*cot(c+d*x)+-1//6*a^2*d^-1*csc(c+d*x)^5*cot(c+d*x)+3//16*a^2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^2*sin(c+d*x)^2, x) == :(5//16*x*a^3+a^3*d^-1*cos(c+d*x)^5+-4//3*a^3*d^-1*cos(c+d*x)^3+-1//7*a^3*d^-1*cos(c+d*x)^7+-5//8*a^3*d^-1*cos(c+d*x)^3*sin(c+d*x)+-1//2*a^3*d^-1*cos(c+d*x)^3*sin(c+d*x)^3+5//16*a^3*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^2*csc(c+d*x), x) == :(13//8*x*a^3+a^3*d^-1*cos(c+d*x)+-1*a^3*d^-1*cos(c+d*x)^3+-1*a^3*d^-1*arctanh(cos(c+d*x))+-1//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*sin(c+d*x))^3*cos(c+d*x)^2*csc(c+d*x)^2, x) == :((1/2)*x*a^3+-1*a^3*d^-1*cot(c+d*x)+-3*a^3*d^-1*arctanh(cos(c+d*x))+3*a^3*d^-1*cos(c+d*x)+-1//3*a^3*d^-1*cos(c+d*x)^3+3//2*a^3*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^2*csc(c+d*x)^3, x) == :(-5//2*x*a^3+-3*a^3*d^-1*cot(c+d*x)+3*a^3*d^-1*cos(c+d*x)+-5//2*a^3*d^-1*arctanh(cos(c+d*x))+(1/2)*a^3*d^-1*cos(c+d*x)*sin(c+d*x)+-1//2*a^3*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^2*csc(c+d*x)^4, x) == :(-3*x*a^3+a^3*d^-1*cos(c+d*x)+(1/2)*a^3*d^-1*arctanh(cos(c+d*x))+-3*a^3*d^-1*cot(c+d*x)+-1//3*a^3*d^-1*cot(c+d*x)^3+-3//2*a^3*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^2*csc(c+d*x)^5, x) == :(-1*x*a^3+-1*a^3*d^-1*cot(c+d*x)^3+-1*a^3*d^-1*cot(c+d*x)+13//8*a^3*d^-1*arctanh(cos(c+d*x))+-11//8*a^3*d^-1*cot(c+d*x)*csc(c+d*x)+-1//4*a^3*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^2*csc(c+d*x)^6, x) == :(-4//3*a^3*d^-1*cot(c+d*x)^3+-1//5*a^3*d^-1*cot(c+d*x)^5+7//8*a^3*d^-1*arctanh(cos(c+d*x))+-3//4*a^3*d^-1*csc(c+d*x)^3*cot(c+d*x)+-1//8*a^3*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^2*csc(c+d*x)^7, x) == :(-4//3*a^3*d^-1*cot(c+d*x)^3+-3//5*a^3*d^-1*cot(c+d*x)^5+7//16*a^3*d^-1*arctanh(cos(c+d*x))+-17//24*a^3*d^-1*csc(c+d*x)^3*cot(c+d*x)+-1//6*a^3*d^-1*csc(c+d*x)^5*cot(c+d*x)+7//16*a^3*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^4*cos(c+d*x)^2, x) == :(21//16*x*a^4+-21//40*d^-1*cos(c+d*x)^3*(a^4+a^4*sin(c+d*x))+-7//8*a^4*d^-1*cos(c+d*x)^3+-3//10*d^-1*(a^2+a^2*sin(c+d*x))^2*cos(c+d*x)^3+-1//6*a*d^-1*(a+a*sin(c+d*x))^3*cos(c+d*x)^3+21//16*a^4*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^4*cos(c+d*x)^2*csc(c+d*x), x) == :(5//2*x*a^4+a^4*d^-1*cos(c+d*x)+-1*a^4*d^-1*arctanh(cos(c+d*x))+-7//3*a^4*d^-1*cos(c+d*x)^3+1//5*a^4*d^-1*cos(c+d*x)^5+-1*a^4*d^-1*cos(c+d*x)^3*sin(c+d*x)+5//2*a^4*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^4*cos(c+d*x)^2*csc(c+d*x)^2, x) == :(17//8*x*a^4+-1*a^4*d^-1*cot(c+d*x)+-4*a^4*d^-1*arctanh(cos(c+d*x))+4*a^4*d^-1*cos(c+d*x)+-4//3*a^4*d^-1*cos(c+d*x)^3+1//4*a^4*d^-1*sin(c+d*x)^3*cos(c+d*x)+23//8*a^4*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^2*sin(c+d*x)^4, x) == :(3//8*x*a^-1+a^-1*d^-1*cos(c+d*x)+-2//3*a^-1*d^-1*cos(c+d*x)^3+1//5*a^-1*d^-1*cos(c+d*x)^5+-3//8*a^-1*d^-1*cos(c+d*x)*sin(c+d*x)+-1//4*a^-1*d^-1*sin(c+d*x)^3*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^2*sin(c+d*x)^3, x) == :(-3//8*x*a^-1+-1*a^-1*d^-1*cos(c+d*x)+1//3*a^-1*d^-1*cos(c+d*x)^3+1//4*a^-1*d^-1*sin(c+d*x)^3*cos(c+d*x)+3//8*a^-1*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^2*sin(c+d*x)^2, x) == :((1/2)*x*a^-1+a^-1*d^-1*cos(c+d*x)+-1//3*a^-1*d^-1*cos(c+d*x)^3+-1//2*a^-1*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^2*sin(c+d*x), x) == :(-1//2*x*a^-1+-1*a^-1*d^-1*cos(c+d*x)+(1/2)*a^-1*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^2*csc(c+d*x), x) == :(-1*x*a^-1+-1*a^-1*d^-1*arctanh(cos(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^2*csc(c+d*x)^2, x) == :(a^-1*d^-1*arctanh(cos(c+d*x))+-1*a^-1*d^-1*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^2*csc(c+d*x)^3, x) == :(a^-1*d^-1*cot(c+d*x)+-1//2*a^-1*d^-1*arctanh(cos(c+d*x))+-1//2*a^-1*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^2*csc(c+d*x)^4, x) == :((1/2)*a^-1*d^-1*arctanh(cos(c+d*x))+-1*a^-1*d^-1*cot(c+d*x)+-1//3*a^-1*d^-1*cot(c+d*x)^3+(1/2)*a^-1*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^2*csc(c+d*x)^5, x) == :(a^-1*d^-1*cot(c+d*x)+-3//8*a^-1*d^-1*arctanh(cos(c+d*x))+1//3*a^-1*d^-1*cot(c+d*x)^3+-3//8*a^-1*d^-1*cot(c+d*x)*csc(c+d*x)+-1//4*a^-1*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^2*csc(c+d*x)^6, x) == :(-1*a^-1*d^-1*cot(c+d*x)+-2//3*a^-1*d^-1*cot(c+d*x)^3+-1//5*a^-1*d^-1*cot(c+d*x)^5+3//8*a^-1*d^-1*arctanh(cos(c+d*x))+1//4*a^-1*d^-1*csc(c+d*x)^3*cot(c+d*x)+3//8*a^-1*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^2*sin(c+d*x)^4, x) == :(-27//8*x*a^-2+-4*a^-2*d^-1*cos(c+d*x)+2//3*a^-2*d^-1*cos(c+d*x)^3+-2*a^-2*d^-1*(1+sin(c+d*x))^-1*cos(c+d*x)+1//4*a^-2*d^-1*sin(c+d*x)^3*cos(c+d*x)+11//8*a^-2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^2*sin(c+d*x)^3, x) == :(3*x*a^-2+3*a^-2*d^-1*cos(c+d*x)+-1//3*a^-2*d^-1*cos(c+d*x)^3+-1*a^-2*d^-1*cos(c+d*x)*sin(c+d*x)+2*a^-2*d^-1*(1+sin(c+d*x))^-1*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^2*sin(c+d*x)^2, x) == :(-5//2*x*a^-2+-2*a^-2*d^-1*cos(c+d*x)+(1/2)*a^-2*d^-1*cos(c+d*x)*sin(c+d*x)+-2*a^-2*d^-1*(1+sin(c+d*x))^-1*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^2*sin(c+d*x), x) == :(2*x*a^-2+a^-2*d^-1*cos(c+d*x)+2*d^-1*(a^2+a^2*sin(c+d*x))^-1*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^2*csc(c+d*x), x) == :(-1*a^-2*d^-1*arctanh(cos(c+d*x))+2*a^-2*d^-1*(1+sin(c+d*x))^-1*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^2*csc(c+d*x)^3, x) == :(2*a^-2*d^-1*cot(c+d*x)+-5//2*a^-2*d^-1*arctanh(cos(c+d*x))+2*a^-2*d^-1*(1+sin(c+d*x))^-1*cos(c+d*x)+-1//2*a^-2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^2*csc(c+d*x)^4, x) == :(-3*a^-2*d^-1*cot(c+d*x)+3*a^-2*d^-1*arctanh(cos(c+d*x))+-1//3*a^-2*d^-1*cot(c+d*x)^3+a^-2*d^-1*cot(c+d*x)*csc(c+d*x)+-2*a^-2*d^-1*(1+sin(c+d*x))^-1*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^2*sin(c+d*x)^3, x) == :(-11//2*x*a^-3+-3*a^-3*d^-1*cos(c+d*x)+(1/2)*a^-3*d^-1*cos(c+d*x)*sin(c+d*x)+-19//3*a^-3*d^-1*(1+sin(c+d*x))^-1*cos(c+d*x)+2//3*a^-3*d^-1*(1+sin(c+d*x))^-2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^2*sin(c+d*x)^2, x) == :(3*x*a^-3+3*a^-3*d^-1*cos(c+d*x)+-1//3*d^-1*(a+a*sin(c+d*x))^-3*cos(c+d*x)^3+2*a^-1*d^-1*(a+a*sin(c+d*x))^-2*cos(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^2*sin(c+d*x), x) == :(-1*x*a^-3+-7//3*a^-3*d^-1*(1+sin(c+d*x))^-1*cos(c+d*x)+2//3*a^-1*d^-1*(a+a*sin(c+d*x))^-2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^2*csc(c+d*x), x) == :(-1*a^-3*d^-1*arctanh(cos(c+d*x))+2//3*a^-3*d^-1*(1+sin(c+d*x))^-2*cos(c+d*x)+5//3*a^-3*d^-1*(1+sin(c+d*x))^-1*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^2*csc(c+d*x)^3, x) == :(3*a^-3*d^-1*cot(c+d*x)+-11//2*a^-3*d^-1*arctanh(cos(c+d*x))+-1//2*a^-3*d^-1*cot(c+d*x)*csc(c+d*x)+2//3*a^-3*d^-1*(1+sin(c+d*x))^-2*cos(c+d*x)+17//3*a^-3*d^-1*(1+sin(c+d*x))^-1*cos(c+d*x))
@test integrate((a+a*sin(e+f*x))^-6*cos(e+f*x)^2*sin(e+f*x), x) == :(2//105*f^-1*(a^2+a^2*sin(e+f*x))^-3*cos(e+f*x)+4//315*f^-1*(a^3+a^3*sin(e+f*x))^-2*cos(e+f*x)+4//315*f^-1*(a^6+a^6*sin(e+f*x))^-1*cos(e+f*x)+-19//63*a^-2*f^-1*(a+a*sin(e+f*x))^-4*cos(e+f*x)+2//9*a^-1*f^-1*(a+a*sin(e+f*x))^-5*cos(e+f*x))
@test integrate((a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^2*sin(c+d*x)^3, x) == :(152//3465*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)+-76//495*a*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+-76//1155*a^-1*d^-1*(a+a*sin(c+d*x))^3//2*cos(c+d*x)+2//11*d^-1*(a+a*sin(c+d*x))^(1/2)*sin(c+d*x)^4*cos(c+d*x)+-38//693*a*d^-1*(a+a*sin(c+d*x))^-1//2*sin(c+d*x)^3*cos(c+d*x)+2//99*a*d^-1*(a+a*sin(c+d*x))^-1//2*sin(c+d*x)^4*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^2*sin(c+d*x)^2, x) == :(4//21*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^3+-8//63*a^2*d^-1*(a+a*sin(c+d*x))^-3//2*cos(c+d*x)^3+-2//9*a^-1*d^-1*(a+a*sin(c+d*x))^3//2*cos(c+d*x)^3+-2//21*a*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^2*sin(c+d*x), x) == :(-2//7*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^3+-8//105*a^2*d^-1*(a+a*sin(c+d*x))^-3//2*cos(c+d*x)^3+-2//35*a*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^2*csc(c+d*x), x) == :(-2*a^(1/2)*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+2//3*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)+2//3*a*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^2*csc(c+d*x)^2, x) == :(-1*a^(1/2)*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-1*d^-1*(a+a*sin(c+d*x))^(1/2)*cot(c+d*x)+3*a*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^2*csc(c+d*x)^3, x) == :(5//4*a^(1/2)*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-1//2*d^-1*(a+a*sin(c+d*x))^(1/2)*cot(c+d*x)*csc(c+d*x)+-1//4*a*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^2*csc(c+d*x)^4, x) == :(3//8*a^(1/2)*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-1//3*d^-1*(a+a*sin(c+d*x))^(1/2)*csc(c+d*x)^2*cot(c+d*x)+3//8*a*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//12*a*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^3//2*cos(c+d*x)^2*sin(c+d*x)^3, x) == :(-1724//15015*d^-1*(a+a*sin(c+d*x))^3//2*cos(c+d*x)+-1724//6435*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+2//13*d^-1*(a+a*sin(c+d*x))^3//2*sin(c+d*x)^4*cos(c+d*x)+3448//45045*a*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)+-862//9009*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*sin(c+d*x)^3*cos(c+d*x)+-38//1287*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*sin(c+d*x)^4*cos(c+d*x)+6//143*a*d^-1*(a+a*sin(c+d*x))^(1/2)*sin(c+d*x)^4*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^3//2*cos(c+d*x)^2*sin(c+d*x)^2, x) == :(4//33*d^-1*(a+a*sin(c+d*x))^3//2*cos(c+d*x)^3+-64//385*a^3*d^-1*(a+a*sin(c+d*x))^-3//2*cos(c+d*x)^3+-48//385*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)^3+-6//77*a*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^3+-2//11*a^-1*d^-1*(a+a*sin(c+d*x))^5//2*cos(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^3//2*cos(c+d*x)^2*sin(c+d*x), x) == :(-2//9*d^-1*(a+a*sin(c+d*x))^3//2*cos(c+d*x)^3+-64//315*a^3*d^-1*(a+a*sin(c+d*x))^-3//2*cos(c+d*x)^3+-16//105*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)^3+-2//21*a*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^3//2*cos(c+d*x)^2*csc(c+d*x), x) == :(-2*a^3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+2//5*d^-1*(a+a*sin(c+d*x))^3//2*cos(c+d*x)+-2//5*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+2//5*a*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^3//2*cos(c+d*x)^2*csc(c+d*x)^2, x) == :(-1*d^-1*(a+a*sin(c+d*x))^3//2*cot(c+d*x)+-3*a^3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+5//3*a*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)+11//3*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^3//2*cos(c+d*x)^2*csc(c+d*x)^3, x) == :(1//4*a^3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-3//4*a*d^-1*(a+a*sin(c+d*x))^(1/2)*cot(c+d*x)+-1//2*d^-1*(a+a*sin(c+d*x))^3//2*cot(c+d*x)*csc(c+d*x)+13//4*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^3//2*cos(c+d*x)^2*csc(c+d*x)^4, x) == :(13//8*a^3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-1//3*d^-1*(a+a*sin(c+d*x))^3//2*csc(c+d*x)^2*cot(c+d*x)+5//24*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//4*a*d^-1*(a+a*sin(c+d*x))^(1/2)*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1//2*cos(c+d*x)^2*sin(c+d*x)^3, x) == :(-4//45*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+-4//105*a^-2*d^-1*(a+a*sin(c+d*x))^3//2*cos(c+d*x)+-2//63*d^-1*(a+a*sin(c+d*x))^-1//2*sin(c+d*x)^3*cos(c+d*x)+2//9*d^-1*(a+a*sin(c+d*x))^-1//2*sin(c+d*x)^4*cos(c+d*x)+8//315*a^-1*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1//2*cos(c+d*x)^2*sin(c+d*x)^2, x) == :(12//35*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)^3+-22//105*a*d^-1*(a+a*sin(c+d*x))^-3//2*cos(c+d*x)^3+-2//7*a^-1*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-1//2*cos(c+d*x)^2*sin(c+d*x), x) == :(-2//5*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)^3+2//15*a*d^-1*(a+a*sin(c+d*x))^-3//2*cos(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-1//2*cos(c+d*x)^2*csc(c+d*x), x) == :(-2*a^-1//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1//2*cos(c+d*x)^2*csc(c+d*x)^2, x) == :(a^-1//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-1*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1//2*cos(c+d*x)^2*csc(c+d*x)^3, x) == :(1//4*a^-1//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+1//4*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//2*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1//2*cos(c+d*x)^2*csc(c+d*x)^4, x) == :(1//8*a^-1//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+1//8*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//3*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^2*cot(c+d*x)+1//12*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3//2*cos(c+d*x)^2*sin(c+d*x)^3, x) == :(2*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-344//105*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+76//105*a^-2*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)+-16//35*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*sin(c+d*x)^2*cos(c+d*x)+2//7*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*sin(c+d*x)^3*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3//2*cos(c+d*x)^2*sin(c+d*x)^2, x) == :(-2*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-4//5*a^-2*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)+-2//5*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)^3+18//5*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3//2*cos(c+d*x)^2*sin(c+d*x), x) == :(2*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-10//3*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+2//3*a^-2*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3//2*cos(c+d*x)^2*csc(c+d*x), x) == :(-2*a^-3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+2*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-3//2*cos(c+d*x)^2*csc(c+d*x)^2, x) == :(3*a^-3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-1*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-2*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-3//2*cos(c+d*x)^2*csc(c+d*x)^3, x) == :(-11//4*a^-3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+2*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+5//4*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//2*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3//2*cos(c+d*x)^2*csc(c+d*x)^4, x) == :(23//8*a^-3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-2*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-9//8*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//3*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^2*cot(c+d*x)+7//12*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x))
@test integrate(cos(c+d*x)^3*sin(c+d*x)^3*(a+a*sin(c+d*x)), x) == :(-1//6*a*d^-1*sin(c+d*x)^6+-1//7*a*d^-1*sin(c+d*x)^7+1//4*a*d^-1*sin(c+d*x)^4+1//5*a*d^-1*sin(c+d*x)^5)
@test integrate(cos(c+d*x)^3*sin(c+d*x)^2*(a+a*sin(c+d*x)), x) == :(-1//5*a*d^-1*sin(c+d*x)^5+-1//6*a*d^-1*sin(c+d*x)^6+1//3*a*d^-1*sin(c+d*x)^3+1//4*a*d^-1*sin(c+d*x)^4)
@test integrate(cos(c+d*x)^3*(a+a*sin(c+d*x))*sin(c+d*x), x) == :(-1//4*a*d^-1*cos(c+d*x)^4+-1//5*a*d^-1*sin(c+d*x)^5+1//3*a*d^-1*sin(c+d*x)^3)
@test integrate(cos(c+d*x)^3*(a+a*sin(c+d*x)), x) == :(-1//4*a^-3*d^-1*(a+a*sin(c+d*x))^4+2//3*a^-2*d^-1*(a+a*sin(c+d*x))^3)
@test integrate(cos(c+d*x)^3*(a+a*sin(c+d*x))*csc(c+d*x), x) == :(a*d^-1*log(sin(c+d*x))+a*d^-1*sin(c+d*x)+-1//2*a*d^-1*sin(c+d*x)^2+-1//3*a*d^-1*sin(c+d*x)^3)
@test integrate(cos(c+d*x)^3*csc(c+d*x)^2*(a+a*sin(c+d*x)), x) == :(a*d^-1*log(sin(c+d*x))+-1*a*d^-1*csc(c+d*x)+-1*a*d^-1*sin(c+d*x)+-1//2*a*d^-1*sin(c+d*x)^2)
@test integrate(cos(c+d*x)^3*csc(c+d*x)^3*(a+a*sin(c+d*x)), x) == :(-1*a*d^-1*csc(c+d*x)+-1*a*d^-1*log(sin(c+d*x))+-1*a*d^-1*sin(c+d*x)+-1//2*a*d^-1*csc(c+d*x)^2)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^3*sin(c+d*x)^2, x) == :(-1//4*a^-1*d^-1*sin(c+d*x)^4+1//3*a^-1*d^-1*sin(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^3*sin(c+d*x), x) == :((1/2)*a^-1*d^-1*sin(c+d*x)^2+-1//3*a^-1*d^-1*sin(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^3, x) == :(a^-1*d^-1*sin(c+d*x)+-1//2*a^-1*d^-1*sin(c+d*x)^2)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^3*csc(c+d*x), x) == :(a^-1*d^-1*log(sin(c+d*x))+-1*a^-1*d^-1*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^3*csc(c+d*x)^2, x) == :(-1*a^-1*d^-1*csc(c+d*x)+-1*a^-1*d^-1*log(sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^3*csc(c+d*x)^3, x) == :(a^-1*d^-1*csc(c+d*x)+-1//2*a^-1*d^-1*csc(c+d*x)^2)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^3*csc(c+d*x)^4, x) == :((1/2)*a^-1*d^-1*csc(c+d*x)^2+-1//3*a^-1*d^-1*csc(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^3*csc(c+d*x)^5, x) == :(-1//4*a^-1*d^-1*csc(c+d*x)^4+1//3*a^-1*d^-1*csc(c+d*x)^3)
@test integrate(cos(c+d*x)^4*sin(c+d*x)^4*(a+a*sin(c+d*x)), x) == :(3//128*a*x+-1//5*a*d^-1*cos(c+d*x)^5+-1//9*a*d^-1*cos(c+d*x)^9+2//7*a*d^-1*cos(c+d*x)^7+-1//8*a*d^-1*cos(c+d*x)^5*sin(c+d*x)^3+-1//16*a*d^-1*cos(c+d*x)^5*sin(c+d*x)+1//64*a*d^-1*cos(c+d*x)^3*sin(c+d*x)+3//128*a*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^4*sin(c+d*x)^3*(a+a*sin(c+d*x)), x) == :(3//128*a*x+-1//5*a*d^-1*cos(c+d*x)^5+1//7*a*d^-1*cos(c+d*x)^7+-1//8*a*d^-1*cos(c+d*x)^5*sin(c+d*x)^3+-1//16*a*d^-1*cos(c+d*x)^5*sin(c+d*x)+1//64*a*d^-1*cos(c+d*x)^3*sin(c+d*x)+3//128*a*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^4*sin(c+d*x)^2*(a+a*sin(c+d*x)), x) == :(1//16*a*x+-1//5*a*d^-1*cos(c+d*x)^5+1//7*a*d^-1*cos(c+d*x)^7+-1//6*a*d^-1*cos(c+d*x)^5*sin(c+d*x)+1//16*a*d^-1*cos(c+d*x)*sin(c+d*x)+1//24*a*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate(cos(c+d*x)^4*(a+a*sin(c+d*x))*sin(c+d*x), x) == :(1//16*a*x+-1//5*a*d^-1*cos(c+d*x)^5+-1//6*a*d^-1*cos(c+d*x)^5*sin(c+d*x)+1//16*a*d^-1*cos(c+d*x)*sin(c+d*x)+1//24*a*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate(cos(c+d*x)^4*(a+a*sin(c+d*x))*csc(c+d*x), x) == :(3//8*a*x+a*d^-1*cos(c+d*x)+-1*a*d^-1*arctanh(cos(c+d*x))+1//3*a*d^-1*cos(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)^4*csc(c+d*x)^2*(a+a*sin(c+d*x)), x) == :(-3//2*a*x+a*d^-1*cos(c+d*x)+-1*a*d^-1*arctanh(cos(c+d*x))+-3//2*a*d^-1*cot(c+d*x)+1//3*a*d^-1*cos(c+d*x)^3+(1/2)*a*d^-1*cos(c+d*x)^2*cot(c+d*x))
@test integrate(cos(c+d*x)^4*csc(c+d*x)^3*(a+a*sin(c+d*x)), x) == :(-3//2*a*x+-3//2*a*d^-1*cos(c+d*x)+-3//2*a*d^-1*cot(c+d*x)+3//2*a*d^-1*arctanh(cos(c+d*x))+(1/2)*a*d^-1*cos(c+d*x)^2*cot(c+d*x)+-1//2*a*d^-1*cot(c+d*x)^2*cos(c+d*x))
@test integrate(cos(c+d*x)^4*csc(c+d*x)^4*(a+a*sin(c+d*x)), x) == :(a*x+a*d^-1*cot(c+d*x)+-3//2*a*d^-1*cos(c+d*x)+-1//3*a*d^-1*cot(c+d*x)^3+3//2*a*d^-1*arctanh(cos(c+d*x))+-1//2*a*d^-1*cot(c+d*x)^2*cos(c+d*x))
@test integrate(cos(c+d*x)^4*csc(c+d*x)^5*(a+a*sin(c+d*x)), x) == :(a*x+a*d^-1*cot(c+d*x)+-3//8*a*d^-1*arctanh(cos(c+d*x))+-1//3*a*d^-1*cot(c+d*x)^3+-1//4*a*d^-1*cot(c+d*x)^3*csc(c+d*x)+3//8*a*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate(cos(c+d*x)^4*csc(c+d*x)^6*(a+a*sin(c+d*x)), x) == :(-3//8*a*d^-1*arctanh(cos(c+d*x))+-1//5*a*d^-1*cot(c+d*x)^5+-1//4*a*d^-1*cot(c+d*x)^3*csc(c+d*x)+3//8*a*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate(cos(c+d*x)^4*csc(c+d*x)^7*(a+a*sin(c+d*x)), x) == :(-1//5*a*d^-1*cot(c+d*x)^5+-1//16*a*d^-1*arctanh(cos(c+d*x))+-1//6*a*d^-1*cot(c+d*x)^3*csc(c+d*x)^3+-1//16*a*d^-1*cot(c+d*x)*csc(c+d*x)+1//8*a*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate(cos(c+d*x)^4*csc(c+d*x)^8*(a+a*sin(c+d*x)), x) == :(-1//5*a*d^-1*cot(c+d*x)^5+-1//7*a*d^-1*cot(c+d*x)^7+-1//16*a*d^-1*arctanh(cos(c+d*x))+-1//6*a*d^-1*cot(c+d*x)^3*csc(c+d*x)^3+-1//16*a*d^-1*cot(c+d*x)*csc(c+d*x)+1//8*a*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate(cos(c+d*x)^4*csc(c+d*x)^9*(a+a*sin(c+d*x)), x) == :(-3//128*a*d^-1*arctanh(cos(c+d*x))+-1//5*a*d^-1*cot(c+d*x)^5+-1//7*a*d^-1*cot(c+d*x)^7+-3//128*a*d^-1*cot(c+d*x)*csc(c+d*x)+-1//8*a*d^-1*cot(c+d*x)^3*csc(c+d*x)^5+-1//64*a*d^-1*csc(c+d*x)^3*cot(c+d*x)+1//16*a*d^-1*csc(c+d*x)^5*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^4*sin(c+d*x)^4, x) == :(9//256*x*a^2+-2//5*a^2*d^-1*cos(c+d*x)^5+-2//9*a^2*d^-1*cos(c+d*x)^9+4//7*a^2*d^-1*cos(c+d*x)^7+-3//16*a^2*d^-1*cos(c+d*x)^5*sin(c+d*x)^3+-3//32*a^2*d^-1*cos(c+d*x)^5*sin(c+d*x)+-1//10*a^2*d^-1*cos(c+d*x)^5*sin(c+d*x)^5+3//128*a^2*d^-1*cos(c+d*x)^3*sin(c+d*x)+9//256*a^2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^4*sin(c+d*x)^3, x) == :(3//64*x*a^2+-2//5*a^2*d^-1*cos(c+d*x)^5+-1//9*a^2*d^-1*cos(c+d*x)^9+3//7*a^2*d^-1*cos(c+d*x)^7+-1//4*a^2*d^-1*cos(c+d*x)^5*sin(c+d*x)^3+-1//8*a^2*d^-1*cos(c+d*x)^5*sin(c+d*x)+1//32*a^2*d^-1*cos(c+d*x)^3*sin(c+d*x)+3//64*a^2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^4*sin(c+d*x)^2, x) == :(11//128*x*a^2+-2//5*a^2*d^-1*cos(c+d*x)^5+2//7*a^2*d^-1*cos(c+d*x)^7+-11//48*a^2*d^-1*cos(c+d*x)^5*sin(c+d*x)+-1//8*a^2*d^-1*cos(c+d*x)^5*sin(c+d*x)^3+11//128*a^2*d^-1*cos(c+d*x)*sin(c+d*x)+11//192*a^2*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^4*sin(c+d*x), x) == :(1//8*x*a^2+-1//7*d^-1*(a+a*sin(c+d*x))^2*cos(c+d*x)^5+-1//15*a^2*d^-1*cos(c+d*x)^5+-1//21*d^-1*cos(c+d*x)^5*(a^2+a^2*sin(c+d*x))+1//8*a^2*d^-1*cos(c+d*x)*sin(c+d*x)+1//12*a^2*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^4*csc(c+d*x), x) == :(3//4*x*a^2+a^2*d^-1*cos(c+d*x)+-1*a^2*d^-1*arctanh(cos(c+d*x))+-1//5*a^2*d^-1*cos(c+d*x)^5+1//3*a^2*d^-1*cos(c+d*x)^3+(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*sin(c+d*x))^2*cos(c+d*x)^4*csc(c+d*x)^2, x) == :(-9//8*x*a^2+-1*a^2*d^-1*cot(c+d*x)+-2*a^2*d^-1*arctanh(cos(c+d*x))+2*a^2*d^-1*cos(c+d*x)+2//3*a^2*d^-1*cos(c+d*x)^3+-1//4*a^2*d^-1*sin(c+d*x)^3*cos(c+d*x)+1//8*a^2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^4*csc(c+d*x)^3, x) == :(-3*x*a^2+(1/2)*a^2*d^-1*arctanh(cos(c+d*x))+-2*a^2*d^-1*cot(c+d*x)+1//3*a^2*d^-1*cos(c+d*x)^3+-1*a^2*d^-1*cos(c+d*x)*sin(c+d*x)+-1//2*a^2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^4*csc(c+d*x)^4, x) == :(-1//2*x*a^2+-2*a^2*d^-1*cos(c+d*x)+3*a^2*d^-1*arctanh(cos(c+d*x))+-1//3*a^2*d^-1*cot(c+d*x)^3+-1*a^2*d^-1*cot(c+d*x)*csc(c+d*x)+-1//2*a^2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^4*csc(c+d*x)^5, x) == :(2*x*a^2+-1*a^2*d^-1*cos(c+d*x)+2*a^2*d^-1*cot(c+d*x)+-2//3*a^2*d^-1*cot(c+d*x)^3+9//8*a^2*d^-1*arctanh(cos(c+d*x))+-1//4*a^2*d^-1*csc(c+d*x)^3*cot(c+d*x)+1//8*a^2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^4*csc(c+d*x)^6, x) == :(x*a^2+a^2*d^-1*cot(c+d*x)+-3//4*a^2*d^-1*arctanh(cos(c+d*x))+-1//3*a^2*d^-1*cot(c+d*x)^3+-1//5*a^2*d^-1*cot(c+d*x)^5+-1//2*a^2*d^-1*cot(c+d*x)^3*csc(c+d*x)+3//4*a^2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^4*csc(c+d*x)^7, x) == :(-7//16*a^2*d^-1*arctanh(cos(c+d*x))+-2//5*a^2*d^-1*cot(c+d*x)^5+-1//4*a^2*d^-1*cot(c+d*x)^3*csc(c+d*x)+-1//6*a^2*d^-1*cot(c+d*x)^3*csc(c+d*x)^3+1//8*a^2*d^-1*csc(c+d*x)^3*cot(c+d*x)+5//16*a^2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^4*csc(c+d*x)^9, x) == :(-11//128*a^2*d^-1*arctanh(cos(c+d*x))+-2//5*a^2*d^-1*cot(c+d*x)^5+-2//7*a^2*d^-1*cot(c+d*x)^7+-11//128*a^2*d^-1*cot(c+d*x)*csc(c+d*x)+-1//6*a^2*d^-1*cot(c+d*x)^3*csc(c+d*x)^3+-1//8*a^2*d^-1*cot(c+d*x)^3*csc(c+d*x)^5+1//16*a^2*d^-1*csc(c+d*x)^5*cot(c+d*x)+7//64*a^2*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^4*csc(c+d*x)^10, x) == :(-3//7*a^2*d^-1*cot(c+d*x)^7+-3//64*a^2*d^-1*arctanh(cos(c+d*x))+-2//5*a^2*d^-1*cot(c+d*x)^5+-1//9*a^2*d^-1*cot(c+d*x)^9+-3//64*a^2*d^-1*cot(c+d*x)*csc(c+d*x)+-1//4*a^2*d^-1*cot(c+d*x)^3*csc(c+d*x)^5+-1//32*a^2*d^-1*csc(c+d*x)^3*cot(c+d*x)+1//8*a^2*d^-1*csc(c+d*x)^5*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^4*csc(c+d*x)^11, x) == :(-9//256*a^2*d^-1*arctanh(cos(c+d*x))+-4//7*a^2*d^-1*cot(c+d*x)^7+-2//5*a^2*d^-1*cot(c+d*x)^5+-2//9*a^2*d^-1*cot(c+d*x)^9+-9//256*a^2*d^-1*cot(c+d*x)*csc(c+d*x)+-3//128*a^2*d^-1*csc(c+d*x)^3*cot(c+d*x)+-1//8*a^2*d^-1*cot(c+d*x)^3*csc(c+d*x)^5+-1//10*a^2*d^-1*cot(c+d*x)^3*csc(c+d*x)^7+3//80*a^2*d^-1*csc(c+d*x)^7*cot(c+d*x)+9//160*a^2*d^-1*csc(c+d*x)^5*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^4*sin(c+d*x)^4, x) == :(15//256*x*a^3+-4//5*a^3*d^-1*cos(c+d*x)^5+-2//3*a^3*d^-1*cos(c+d*x)^9+1//11*a^3*d^-1*cos(c+d*x)^11+9//7*a^3*d^-1*cos(c+d*x)^7+-5//16*a^3*d^-1*cos(c+d*x)^5*sin(c+d*x)^3+-5//32*a^3*d^-1*cos(c+d*x)^5*sin(c+d*x)+-3//10*a^3*d^-1*cos(c+d*x)^5*sin(c+d*x)^5+5//128*a^3*d^-1*cos(c+d*x)^3*sin(c+d*x)+15//256*a^3*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^4*sin(c+d*x)^3, x) == :(21//256*x*a^3+a^3*d^-1*cos(c+d*x)^7+-4//5*a^3*d^-1*cos(c+d*x)^5+-1//3*a^3*d^-1*cos(c+d*x)^9+-7//16*a^3*d^-1*cos(c+d*x)^5*sin(c+d*x)^3+-7//32*a^3*d^-1*cos(c+d*x)^5*sin(c+d*x)+-1//10*a^3*d^-1*cos(c+d*x)^5*sin(c+d*x)^5+7//128*a^3*d^-1*cos(c+d*x)^3*sin(c+d*x)+21//256*a^3*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^4*sin(c+d*x)^2, x) == :(17//128*x*a^3+-4//5*a^3*d^-1*cos(c+d*x)^5+-1//9*a^3*d^-1*cos(c+d*x)^9+5//7*a^3*d^-1*cos(c+d*x)^7+-17//48*a^3*d^-1*cos(c+d*x)^5*sin(c+d*x)+-3//8*a^3*d^-1*cos(c+d*x)^5*sin(c+d*x)^3+17//128*a^3*d^-1*cos(c+d*x)*sin(c+d*x)+17//192*a^3*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^4*sin(c+d*x), x) == :(27//128*x*a^3+-9//80*a^3*d^-1*cos(c+d*x)^5+-9//112*d^-1*cos(c+d*x)^5*(a^3+a^3*sin(c+d*x))+-1//8*d^-1*(a+a*sin(c+d*x))^3*cos(c+d*x)^5+-3//56*a*d^-1*(a+a*sin(c+d*x))^2*cos(c+d*x)^5+9//64*a^3*d^-1*cos(c+d*x)^3*sin(c+d*x)+27//128*a^3*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^4*csc(c+d*x), x) == :(19//16*x*a^3+a^3*d^-1*cos(c+d*x)+-1*a^3*d^-1*arctanh(cos(c+d*x))+-3//5*a^3*d^-1*cos(c+d*x)^5+1//3*a^3*d^-1*cos(c+d*x)^3+-1//6*a^3*d^-1*cos(c+d*x)^5*sin(c+d*x)+19//16*a^3*d^-1*cos(c+d*x)*sin(c+d*x)+19//24*a^3*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^4*csc(c+d*x)^2, x) == :(-3//8*x*a^3+a^3*d^-1*cos(c+d*x)^3+-1*a^3*d^-1*cot(c+d*x)+-3*a^3*d^-1*arctanh(cos(c+d*x))+3*a^3*d^-1*cos(c+d*x)+-1//5*a^3*d^-1*cos(c+d*x)^5+-3//4*a^3*d^-1*sin(c+d*x)^3*cos(c+d*x)+11//8*a^3*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^4*csc(c+d*x)^3, x) == :(-33//8*x*a^3+a^3*d^-1*cos(c+d*x)^3+-3*a^3*d^-1*cot(c+d*x)+2*a^3*d^-1*cos(c+d*x)+-3//2*a^3*d^-1*arctanh(cos(c+d*x))+-7//8*a^3*d^-1*cos(c+d*x)*sin(c+d*x)+-1//2*a^3*d^-1*cot(c+d*x)*csc(c+d*x)+-1//4*a^3*d^-1*sin(c+d*x)^3*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^4*csc(c+d*x)^4, x) == :(-7//2*x*a^3+-2*a^3*d^-1*cos(c+d*x)+-2*a^3*d^-1*cot(c+d*x)+-1//3*a^3*d^-1*cot(c+d*x)^3+1//3*a^3*d^-1*cos(c+d*x)^3+7//2*a^3*d^-1*arctanh(cos(c+d*x))+-3//2*a^3*d^-1*cos(c+d*x)*sin(c+d*x)+-3//2*a^3*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^4*csc(c+d*x)^5, x) == :(3//2*x*a^3+-1*a^3*d^-1*cot(c+d*x)^3+-3*a^3*d^-1*cos(c+d*x)+2*a^3*d^-1*cot(c+d*x)+33//8*a^3*d^-1*arctanh(cos(c+d*x))+-7//8*a^3*d^-1*cot(c+d*x)*csc(c+d*x)+-1//2*a^3*d^-1*cos(c+d*x)*sin(c+d*x)+-1//4*a^3*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^4*csc(c+d*x)^6, x) == :(3*x*a^3+-1*a^3*d^-1*cot(c+d*x)^3+-1*a^3*d^-1*cos(c+d*x)+3*a^3*d^-1*cot(c+d*x)+-1//5*a^3*d^-1*cot(c+d*x)^5+3//8*a^3*d^-1*arctanh(cos(c+d*x))+-3//4*a^3*d^-1*csc(c+d*x)^3*cot(c+d*x)+11//8*a^3*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^4*csc(c+d*x)^7, x) == :(x*a^3+a^3*d^-1*cot(c+d*x)+-19//16*a^3*d^-1*arctanh(cos(c+d*x))+-3//5*a^3*d^-1*cot(c+d*x)^5+-1//3*a^3*d^-1*cot(c+d*x)^3+-3//4*a^3*d^-1*cot(c+d*x)^3*csc(c+d*x)+-1//6*a^3*d^-1*cot(c+d*x)^3*csc(c+d*x)^3+1//8*a^3*d^-1*csc(c+d*x)^3*cot(c+d*x)+17//16*a^3*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^4*csc(c+d*x)^8, x) == :(-9//16*a^3*d^-1*arctanh(cos(c+d*x))+-4//5*a^3*d^-1*cot(c+d*x)^5+-1//7*a^3*d^-1*cot(c+d*x)^7+-1//2*a^3*d^-1*cot(c+d*x)^3*csc(c+d*x)^3+-1//4*a^3*d^-1*cot(c+d*x)^3*csc(c+d*x)+3//8*a^3*d^-1*csc(c+d*x)^3*cot(c+d*x)+3//16*a^3*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^4*csc(c+d*x)^9, x) == :(-27//128*a^3*d^-1*arctanh(cos(c+d*x))+-4//5*a^3*d^-1*cot(c+d*x)^5+-3//7*a^3*d^-1*cot(c+d*x)^7+-27//128*a^3*d^-1*cot(c+d*x)*csc(c+d*x)+-1//2*a^3*d^-1*cot(c+d*x)^3*csc(c+d*x)^3+-1//8*a^3*d^-1*cot(c+d*x)^3*csc(c+d*x)^5+1//16*a^3*d^-1*csc(c+d*x)^5*cot(c+d*x)+23//64*a^3*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^4*csc(c+d*x)^10, x) == :(-17//128*a^3*d^-1*arctanh(cos(c+d*x))+-5//7*a^3*d^-1*cot(c+d*x)^7+-4//5*a^3*d^-1*cot(c+d*x)^5+-1//9*a^3*d^-1*cot(c+d*x)^9+-17//128*a^3*d^-1*cot(c+d*x)*csc(c+d*x)+-3//8*a^3*d^-1*cot(c+d*x)^3*csc(c+d*x)^5+-1//6*a^3*d^-1*cot(c+d*x)^3*csc(c+d*x)^3+3//16*a^3*d^-1*csc(c+d*x)^5*cot(c+d*x)+5//64*a^3*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^4*csc(c+d*x)^11, x) == :(-1*a^3*d^-1*cot(c+d*x)^7+-21//256*a^3*d^-1*arctanh(cos(c+d*x))+-4//5*a^3*d^-1*cot(c+d*x)^5+-1//3*a^3*d^-1*cot(c+d*x)^9+-21//256*a^3*d^-1*cot(c+d*x)*csc(c+d*x)+-7//128*a^3*d^-1*csc(c+d*x)^3*cot(c+d*x)+-3//8*a^3*d^-1*cot(c+d*x)^3*csc(c+d*x)^5+-1//10*a^3*d^-1*cot(c+d*x)^3*csc(c+d*x)^7+3//80*a^3*d^-1*csc(c+d*x)^7*cot(c+d*x)+29//160*a^3*d^-1*csc(c+d*x)^5*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^4*cos(c+d*x)^4*sin(c+d*x)^2, x) == :(55//256*x*a^4+-11//112*a^4*d^-1*cos(c+d*x)^7+-11//144*d^-1*cos(c+d*x)^7*(a^4+a^4*sin(c+d*x))+-1//18*d^-1*(a^2+a^2*sin(c+d*x))^2*cos(c+d*x)^7+-1//10*a^-1*d^-1*(a+a*sin(c+d*x))^5*cos(c+d*x)^5+11//96*a^4*d^-1*cos(c+d*x)^5*sin(c+d*x)+55//256*a^4*d^-1*cos(c+d*x)*sin(c+d*x)+55//384*a^4*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^4*cos(c+d*x)^4*csc(c+d*x)^4, x) == :(-61//8*x*a^4+-5*a^4*d^-1*cot(c+d*x)+2*a^4*d^-1*arctanh(cos(c+d*x))+-1//3*a^4*d^-1*cot(c+d*x)^3+4//3*a^4*d^-1*cos(c+d*x)^3+-2*a^4*d^-1*cot(c+d*x)*csc(c+d*x)+-19//8*a^4*d^-1*cos(c+d*x)*sin(c+d*x)+-1//4*a^4*d^-1*sin(c+d*x)^3*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^4*sin(c+d*x)^4, x) == :(1//16*x*a^-1+-2//5*a^-1*d^-1*cos(c+d*x)^5+1//3*a^-1*d^-1*cos(c+d*x)^3+1//7*a^-1*d^-1*cos(c+d*x)^7+-1//6*a^-1*d^-1*cos(c+d*x)^3*sin(c+d*x)^3+-1//8*a^-1*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//16*a^-1*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^4*sin(c+d*x)^3, x) == :(-1//16*x*a^-1+-1//3*a^-1*d^-1*cos(c+d*x)^3+1//5*a^-1*d^-1*cos(c+d*x)^5+-1//16*a^-1*d^-1*cos(c+d*x)*sin(c+d*x)+1//6*a^-1*d^-1*cos(c+d*x)^3*sin(c+d*x)^3+1//8*a^-1*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^4*sin(c+d*x)^2, x) == :(1//8*x*a^-1+-1//5*a^-1*d^-1*cos(c+d*x)^5+1//3*a^-1*d^-1*cos(c+d*x)^3+-1//4*a^-1*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//8*a^-1*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^4*sin(c+d*x), x) == :(-1//8*x*a^-1+-1//3*a^-1*d^-1*cos(c+d*x)^3+-1//8*a^-1*d^-1*cos(c+d*x)*sin(c+d*x)+1//4*a^-1*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^4*csc(c+d*x), x) == :(-1//2*x*a^-1+a^-1*d^-1*cos(c+d*x)+-1*a^-1*d^-1*arctanh(cos(c+d*x))+-1//2*a^-1*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^4*csc(c+d*x)^2, x) == :(-1*x*a^-1+a^-1*d^-1*arctanh(cos(c+d*x))+-1*a^-1*d^-1*cos(c+d*x)+-1*a^-1*d^-1*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^4*csc(c+d*x)^3, x) == :(x*a^-1+a^-1*d^-1*cot(c+d*x)+(1/2)*a^-1*d^-1*arctanh(cos(c+d*x))+-1//2*a^-1*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^4*csc(c+d*x)^4, x) == :(-1//2*a^-1*d^-1*arctanh(cos(c+d*x))+-1//3*a^-1*d^-1*cot(c+d*x)^3+(1/2)*a^-1*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^4*csc(c+d*x)^5, x) == :(1//3*a^-1*d^-1*cot(c+d*x)^3+1//8*a^-1*d^-1*arctanh(cos(c+d*x))+-1//4*a^-1*d^-1*csc(c+d*x)^3*cot(c+d*x)+1//8*a^-1*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^4*csc(c+d*x)^6, x) == :(-1//3*a^-1*d^-1*cot(c+d*x)^3+-1//5*a^-1*d^-1*cot(c+d*x)^5+-1//8*a^-1*d^-1*arctanh(cos(c+d*x))+-1//8*a^-1*d^-1*cot(c+d*x)*csc(c+d*x)+1//4*a^-1*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^4*csc(c+d*x)^7, x) == :(1//3*a^-1*d^-1*cot(c+d*x)^3+1//5*a^-1*d^-1*cot(c+d*x)^5+1//16*a^-1*d^-1*arctanh(cos(c+d*x))+-1//6*a^-1*d^-1*csc(c+d*x)^5*cot(c+d*x)+1//16*a^-1*d^-1*cot(c+d*x)*csc(c+d*x)+1//24*a^-1*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^4*sin(c+d*x)^5, x) == :(-5//8*x*a^-2+-2*a^-2*d^-1*cos(c+d*x)+-4//5*a^-2*d^-1*cos(c+d*x)^5+1//7*a^-2*d^-1*cos(c+d*x)^7+5//3*a^-2*d^-1*cos(c+d*x)^3+1//3*a^-2*d^-1*sin(c+d*x)^5*cos(c+d*x)+5//8*a^-2*d^-1*cos(c+d*x)*sin(c+d*x)+5//12*a^-2*d^-1*sin(c+d*x)^3*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^4*sin(c+d*x)^4, x) == :(11//16*x*a^-2+2*a^-2*d^-1*cos(c+d*x)+-4//3*a^-2*d^-1*cos(c+d*x)^3+2//5*a^-2*d^-1*cos(c+d*x)^5+-11//16*a^-2*d^-1*cos(c+d*x)*sin(c+d*x)+-11//24*a^-2*d^-1*sin(c+d*x)^3*cos(c+d*x)+-1//6*a^-2*d^-1*sin(c+d*x)^5*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^4*sin(c+d*x)^3, x) == :(-3//4*x*a^-2+a^-2*d^-1*cos(c+d*x)^3+-2*a^-2*d^-1*cos(c+d*x)+-1//5*a^-2*d^-1*cos(c+d*x)^5+(1/2)*a^-2*d^-1*sin(c+d*x)^3*cos(c+d*x)+3//4*a^-2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^4*sin(c+d*x)^2, x) == :(7//8*x*a^-2+2*a^-2*d^-1*cos(c+d*x)+-2//3*a^-2*d^-1*cos(c+d*x)^3+-7//8*a^-2*d^-1*cos(c+d*x)*sin(c+d*x)+-1//4*a^-2*d^-1*sin(c+d*x)^3*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^4*sin(c+d*x), x) == :(-1*x*a^-2+-1*d^-1*(a+a*sin(c+d*x))^-2*cos(c+d*x)^5+-2//3*a^-2*d^-1*cos(c+d*x)^3+-1*a^-2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^4*csc(c+d*x), x) == :(-2*x*a^-2+-1*a^-2*d^-1*arctanh(cos(c+d*x))+-1*a^-2*d^-1*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^4*csc(c+d*x)^2, x) == :(x*a^-2+-1*a^-2*d^-1*cot(c+d*x)+2*a^-2*d^-1*arctanh(cos(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^4*csc(c+d*x)^3, x) == :(2*a^-2*d^-1*cot(c+d*x)+-3//2*a^-2*d^-1*arctanh(cos(c+d*x))+-1//2*a^-2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^4*csc(c+d*x)^4, x) == :(a^-2*d^-1*arctanh(cos(c+d*x))+-2*a^-2*d^-1*cot(c+d*x)+-1//3*a^-2*d^-1*cot(c+d*x)^3+a^-2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^4*csc(c+d*x)^5, x) == :(2*a^-2*d^-1*cot(c+d*x)+-7//8*a^-2*d^-1*arctanh(cos(c+d*x))+2//3*a^-2*d^-1*cot(c+d*x)^3+-7//8*a^-2*d^-1*cot(c+d*x)*csc(c+d*x)+-1//4*a^-2*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^4*csc(c+d*x)^6, x) == :(-1*a^-2*d^-1*cot(c+d*x)^3+-2*a^-2*d^-1*cot(c+d*x)+-1//5*a^-2*d^-1*cot(c+d*x)^5+3//4*a^-2*d^-1*arctanh(cos(c+d*x))+(1/2)*a^-2*d^-1*csc(c+d*x)^3*cot(c+d*x)+3//4*a^-2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^4*csc(c+d*x)^7, x) == :(2*a^-2*d^-1*cot(c+d*x)+-11//16*a^-2*d^-1*arctanh(cos(c+d*x))+2//5*a^-2*d^-1*cot(c+d*x)^5+4//3*a^-2*d^-1*cot(c+d*x)^3+-11//16*a^-2*d^-1*cot(c+d*x)*csc(c+d*x)+-11//24*a^-2*d^-1*csc(c+d*x)^3*cot(c+d*x)+-1//6*a^-2*d^-1*csc(c+d*x)^5*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^4*sin(c+d*x)^3, x) == :(51//8*x*a^-3+-1*a^-3*d^-1*cos(c+d*x)^3+7*a^-3*d^-1*cos(c+d*x)+4*a^-3*d^-1*(1+sin(c+d*x))^-1*cos(c+d*x)+-19//8*a^-3*d^-1*cos(c+d*x)*sin(c+d*x)+-1//4*a^-3*d^-1*sin(c+d*x)^3*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^4*sin(c+d*x)^2, x) == :(-11//2*x*a^-3+-5*a^-3*d^-1*cos(c+d*x)+1//3*a^-3*d^-1*cos(c+d*x)^3+-4*a^-3*d^-1*(1+sin(c+d*x))^-1*cos(c+d*x)+3//2*a^-3*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^4*sin(c+d*x), x) == :(9//2*x*a^-3+d^-1*(a+a*sin(c+d*x))^-3*cos(c+d*x)^5+3//2*d^-1*(a^3+a^3*sin(c+d*x))^-1*cos(c+d*x)^3+9//2*a^-3*d^-1*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^4*csc(c+d*x), x) == :(x*a^-3+-1*a^-3*d^-1*arctanh(cos(c+d*x))+4*a^-3*d^-1*(1+sin(c+d*x))^-1*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^4*csc(c+d*x)^2, x) == :(-1*a^-3*d^-1*cot(c+d*x)+3*a^-3*d^-1*arctanh(cos(c+d*x))+-4*a^-3*d^-1*(1+sin(c+d*x))^-1*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^4*csc(c+d*x)^3, x) == :(3*a^-3*d^-1*cot(c+d*x)+-9//2*a^-3*d^-1*arctanh(cos(c+d*x))+4*a^-3*d^-1*(1+sin(c+d*x))^-1*cos(c+d*x)+-1//2*a^-3*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^4*csc(c+d*x)^5, x) == :(a^-3*d^-1*cot(c+d*x)^3+7*a^-3*d^-1*cot(c+d*x)+-51//8*a^-3*d^-1*arctanh(cos(c+d*x))+4*a^-3*d^-1*(1+sin(c+d*x))^-1*cos(c+d*x)+-19//8*a^-3*d^-1*cot(c+d*x)*csc(c+d*x)+-1//4*a^-3*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(e+f*x))^-6*cos(e+f*x)^4*sin(e+f*x), x) == :(1//7*f^-1*(a+a*sin(e+f*x))^-6*cos(e+f*x)^5+-6//35*a^-1*f^-1*(a+a*sin(e+f*x))^-5*cos(e+f*x)^5)
@test integrate((a+a*sin(e+f*x))^-8*cos(e+f*x)^4*sin(e+f*x)^3, x) == :(-846//385*a^-8*f^-1*(1+sin(e+f*x))^-3*cos(e+f*x)+-152//1155*a^-8*f^-1*(1+sin(e+f*x))^-1*cos(e+f*x)+-52//33*a^-8*f^-1*(1+sin(e+f*x))^-5*cos(e+f*x)+4//11*a^-8*f^-1*(1+sin(e+f*x))^-6*cos(e+f*x)+617//231*a^-8*f^-1*(1+sin(e+f*x))^-4*cos(e+f*x)+1003//1155*a^-8*f^-1*(1+sin(e+f*x))^-2*cos(e+f*x))
@test integrate((a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^4*sin(c+d*x)^2, x) == :(20//143*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^5+-1472//45045*a^3*d^-1*(a+a*sin(c+d*x))^-5//2*cos(c+d*x)^5+-368//9009*a^2*d^-1*(a+a*sin(c+d*x))^-3//2*cos(c+d*x)^5+-46//1287*a*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)^5+-2//13*a^-1*d^-1*(a+a*sin(c+d*x))^3//2*cos(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^4*sin(c+d*x), x) == :(-2//11*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^5+-64//3465*a^3*d^-1*(a+a*sin(c+d*x))^-5//2*cos(c+d*x)^5+-16//693*a^2*d^-1*(a+a*sin(c+d*x))^-3//2*cos(c+d*x)^5+-2//99*a*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^4*csc(c+d*x), x) == :(-2*a^(1/2)*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+164//105*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)+-12//35*a^-1*d^-1*(a+a*sin(c+d*x))^3//2*cos(c+d*x)+8//15*a*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+-2//7*a*d^-1*(a+a*sin(c+d*x))^-1//2*sin(c+d*x)^3*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^4*csc(c+d*x)^2, x) == :(-1*a^(1/2)*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-1*d^-1*(a+a*sin(c+d*x))^(1/2)*cot(c+d*x)+4//15*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)+-2//5*a^-1*d^-1*(a+a*sin(c+d*x))^3//2*cos(c+d*x)+61//15*a*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^4*csc(c+d*x)^3, x) == :(-2//3*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)+13//4*a^(1/2)*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-2//3*a*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+-1//2*d^-1*(a+a*sin(c+d*x))^(1/2)*cot(c+d*x)*csc(c+d*x)+-1//4*a*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^4*csc(c+d*x)^4, x) == :(11//8*a^(1/2)*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-2*a*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+-1//3*d^-1*(a+a*sin(c+d*x))^(1/2)*csc(c+d*x)^2*cot(c+d*x)+11//8*a*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//12*a*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^4*csc(c+d*x)^5, x) == :(-67//64*a^(1/2)*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-1//4*d^-1*(a+a*sin(c+d*x))^(1/2)*csc(c+d*x)^3*cot(c+d*x)+61//64*a*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//24*a*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^2*cot(c+d*x)+61//96*a*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^4*csc(c+d*x)^6, x) == :(-31//128*a^(1/2)*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-31//128*a*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//5*d^-1*(a+a*sin(c+d*x))^(1/2)*csc(c+d*x)^4*cot(c+d*x)+-1//40*a*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^3*cot(c+d*x)+97//192*a*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x)+97//240*a*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^2*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^4*csc(c+d*x)^7, x) == :(-55//512*a^(1/2)*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-55//512*a*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//6*d^-1*(a+a*sin(c+d*x))^(1/2)*csc(c+d*x)^5*cot(c+d*x)+-55//768*a*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x)+-1//60*a*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^4*cot(c+d*x)+47//160*a*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^3*cot(c+d*x)+329//960*a*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^2*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^4*csc(c+d*x)^8, x) == :(-61//1024*a^(1/2)*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-61//1024*a*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//7*d^-1*(a+a*sin(c+d*x))^(1/2)*csc(c+d*x)^6*cot(c+d*x)+-61//1536*a*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x)+-61//1920*a*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^2*cot(c+d*x)+-1//84*a*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^5*cot(c+d*x)+193//840*a*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^4*cot(c+d*x)+579//2240*a*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^3//2*cos(c+d*x)^4*sin(c+d*x)^2, x) == :(4//39*d^-1*(a+a*sin(c+d*x))^3//2*cos(c+d*x)^5+-256//6435*a^4*d^-1*(a+a*sin(c+d*x))^-5//2*cos(c+d*x)^5+-64//1287*a^3*d^-1*(a+a*sin(c+d*x))^-3//2*cos(c+d*x)^5+-56//1287*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)^5+-14//429*a*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^5+-2//15*a^-1*d^-1*(a+a*sin(c+d*x))^5//2*cos(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^3//2*cos(c+d*x)^4*sin(c+d*x), x) == :(-2//13*d^-1*(a+a*sin(c+d*x))^3//2*cos(c+d*x)^5+-256//5005*a^4*d^-1*(a+a*sin(c+d*x))^-5//2*cos(c+d*x)^5+-64//1001*a^3*d^-1*(a+a*sin(c+d*x))^-3//2*cos(c+d*x)^5+-8//143*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)^5+-6//143*a*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^3//2*cos(c+d*x)^4*csc(c+d*x), x) == :(-2*a^3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+16//105*d^-1*(a+a*sin(c+d*x))^3//2*cos(c+d*x)+-14//45*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+388//315*a*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)+-34//63*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*sin(c+d*x)^3*cos(c+d*x)+-2//9*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*sin(c+d*x)^4*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^3//2*cos(c+d*x)^4*csc(c+d*x)^2, x) == :(-1*d^-1*(a+a*sin(c+d*x))^3//2*cot(c+d*x)+-3*a^3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+4//35*d^-1*(a+a*sin(c+d*x))^3//2*cos(c+d*x)+-2//7*a^-1*d^-1*(a+a*sin(c+d*x))^5//2*cos(c+d*x)+69//35*a*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)+171//35*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^3//2*cos(c+d*x)^4*csc(c+d*x)^3, x) == :(-2//5*d^-1*(a+a*sin(c+d*x))^3//2*cos(c+d*x)+9//4*a^3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-3//4*a*d^-1*(a+a*sin(c+d*x))^(1/2)*cot(c+d*x)+-2//5*a*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)+-1//2*d^-1*(a+a*sin(c+d*x))^3//2*cot(c+d*x)*csc(c+d*x)+73//20*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^3//2*cos(c+d*x)^4*csc(c+d*x)^4, x) == :(37//8*a^3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-8//3*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+-2//3*a*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)+-1//3*d^-1*(a+a*sin(c+d*x))^3//2*csc(c+d*x)^2*cot(c+d*x)+29//24*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//4*a*d^-1*(a+a*sin(c+d*x))^(1/2)*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^3//2*cos(c+d*x)^4*csc(c+d*x)^5, x) == :(21//64*a^3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-2*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+-1//4*d^-1*(a+a*sin(c+d*x))^3//2*csc(c+d*x)^3*cot(c+d*x)+149//64*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//8*a*d^-1*(a+a*sin(c+d*x))^(1/2)*csc(c+d*x)^2*cot(c+d*x)+19//32*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^3//2*cos(c+d*x)^4*csc(c+d*x)^6, x) == :(-165//128*a^3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-1//5*d^-1*(a+a*sin(c+d*x))^3//2*csc(c+d*x)^4*cot(c+d*x)+91//128*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-3//40*a*d^-1*(a+a*sin(c+d*x))^(1/2)*csc(c+d*x)^3*cot(c+d*x)+31//80*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^2*cot(c+d*x)+73//64*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^3//2*cos(c+d*x)^4*csc(c+d*x)^7, x) == :(-179//512*a^3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-179//512*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//6*d^-1*(a+a*sin(c+d*x))^3//2*csc(c+d*x)^5*cot(c+d*x)+-1//20*a*d^-1*(a+a*sin(c+d*x))^(1/2)*csc(c+d*x)^4*cot(c+d*x)+111//256*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x)+137//480*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^3*cot(c+d*x)+239//320*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^2*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^3//2*cos(c+d*x)^4*csc(c+d*x)^8, x) == :(-171//1024*a^3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-171//1024*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//7*d^-1*(a+a*sin(c+d*x))^3//2*csc(c+d*x)^6*cot(c+d*x)+-57//512*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x)+-1//28*a*d^-1*(a+a*sin(c+d*x))^(1/2)*csc(c+d*x)^5*cot(c+d*x)+9//40*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^4*cot(c+d*x)+199//640*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^2*cot(c+d*x)+1237//2240*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^3//2*cos(c+d*x)^4*csc(c+d*x)^9, x) == :(-1587//16384*a^3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-1587//16384*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//8*d^-1*(a+a*sin(c+d*x))^3//2*csc(c+d*x)^7*cot(c+d*x)+-529//8192*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x)+-529//10240*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^2*cot(c+d*x)+-3//112*a*d^-1*(a+a*sin(c+d*x))^(1/2)*csc(c+d*x)^6*cot(c+d*x)+83//448*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^5*cot(c+d*x)+1957//4480*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^4*cot(c+d*x)+8653//35840*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1//2*cos(c+d*x)^4*sin(c+d*x)^2, x) == :(20//99*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)^5+-152//3465*a^2*d^-1*(a+a*sin(c+d*x))^-5//2*cos(c+d*x)^5+-38//693*a*d^-1*(a+a*sin(c+d*x))^-3//2*cos(c+d*x)^5+-2//11*a^-1*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-1//2*cos(c+d*x)^4*sin(c+d*x), x) == :(-2//9*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)^5+2//63*a*d^-1*(a+a*sin(c+d*x))^-3//2*cos(c+d*x)^5+8//315*a^2*d^-1*(a+a*sin(c+d*x))^-5//2*cos(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-1//2*cos(c+d*x)^4*csc(c+d*x), x) == :(-2*a^-1//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+32//15*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+-2//5*d^-1*(a+a*sin(c+d*x))^-1//2*sin(c+d*x)^2*cos(c+d*x)+2//15*a^-1*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1//2*cos(c+d*x)^4*csc(c+d*x)^2, x) == :(a^-1//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-1*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+4//3*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+-2//3*a^-1*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1//2*cos(c+d*x)^4*csc(c+d*x)^3, x) == :(-2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+1//4*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+9//4*a^-1//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-1//2*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1//2*cos(c+d*x)^4*csc(c+d*x)^4, x) == :(-7//8*a^-1//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+9//8*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//3*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^2*cot(c+d*x)+1//12*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1//2*cos(c+d*x)^4*csc(c+d*x)^5, x) == :(-11//64*a^-1//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-11//64*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//4*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^3*cot(c+d*x)+1//24*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^2*cot(c+d*x)+53//96*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1//2*cos(c+d*x)^4*csc(c+d*x)^6, x) == :(-9//128*a^-1//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-9//128*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-3//64*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x)+-1//5*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^4*cot(c+d*x)+1//40*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^3*cot(c+d*x)+29//80*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^2*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3//2*cos(c+d*x)^4*sin(c+d*x)^3, x) == :(-4//165*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+-4//385*a^-3*d^-1*(a+a*sin(c+d*x))^3//2*cos(c+d*x)+8//1155*a^-2*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)+-2//11*a^-2*d^-1*(a+a*sin(c+d*x))^(1/2)*sin(c+d*x)^4*cos(c+d*x)+-2//231*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*sin(c+d*x)^3*cos(c+d*x)+14//33*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*sin(c+d*x)^4*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3//2*cos(c+d*x)^4*sin(c+d*x)^2, x) == :(20//63*d^-1*(a+a*sin(c+d*x))^-3//2*cos(c+d*x)^5+-46//315*a*d^-1*(a+a*sin(c+d*x))^-5//2*cos(c+d*x)^5+-2//9*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-3//2*cos(c+d*x)^4*sin(c+d*x), x) == :(-2//7*d^-1*(a+a*sin(c+d*x))^-3//2*cos(c+d*x)^5+6//35*a*d^-1*(a+a*sin(c+d*x))^-5//2*cos(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-3//2*cos(c+d*x)^4*csc(c+d*x), x) == :(-2*a^-3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-2//3*a^-2*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)+10//3*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3//2*cos(c+d*x)^4*csc(c+d*x)^2, x) == :(3*a^-3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-1*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+-1*a^-2*d^-1*(a+a*sin(c+d*x))^(1/2)*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3//2*cos(c+d*x)^4*csc(c+d*x)^3, x) == :(-3//4*a^-3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+7//4*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//2*a^-2*d^-1*(a+a*sin(c+d*x))^(1/2)*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3//2*cos(c+d*x)^4*csc(c+d*x)^4, x) == :(-1//8*a^-3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-1//8*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//3*a^-2*d^-1*(a+a*sin(c+d*x))^(1/2)*csc(c+d*x)^2*cot(c+d*x)+11//12*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3//2*cos(c+d*x)^4*csc(c+d*x)^5, x) == :(-3//64*a^-3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-3//64*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//4*a^-2*d^-1*(a+a*sin(c+d*x))^(1/2)*csc(c+d*x)^3*cot(c+d*x)+-1//32*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x)+5//8*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^2*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3//2*cos(c+d*x)^4*csc(c+d*x)^6, x) == :(-3//128*a^-3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-3//128*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//5*a^-2*d^-1*(a+a*sin(c+d*x))^(1/2)*csc(c+d*x)^4*cot(c+d*x)+-1//64*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x)+-1//80*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^2*cot(c+d*x)+19//40*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-5//2*cos(c+d*x)^4*sin(c+d*x)^4, x) == :(-4*2^(1/2)*a^-5//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-1048//693*a^-3*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)+4496//693*a^-2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+-424//693*a^-2*d^-1*(a+a*sin(c+d*x))^-1//2*sin(c+d*x)^3*cos(c+d*x)+-2//11*a^-2*d^-1*(a+a*sin(c+d*x))^-1//2*sin(c+d*x)^5*cos(c+d*x)+46//99*a^-2*d^-1*(a+a*sin(c+d*x))^-1//2*sin(c+d*x)^4*cos(c+d*x)+200//231*a^-2*d^-1*(a+a*sin(c+d*x))^-1//2*sin(c+d*x)^2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-5//2*cos(c+d*x)^4*sin(c+d*x)^3, x) == :(4*2^(1/2)*a^-5//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-2048//315*a^-2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+472//315*a^-3*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)+-92//105*a^-2*d^-1*(a+a*sin(c+d*x))^-1//2*sin(c+d*x)^2*cos(c+d*x)+-2//9*a^-2*d^-1*(a+a*sin(c+d*x))^-1//2*sin(c+d*x)^4*cos(c+d*x)+38//63*a^-2*d^-1*(a+a*sin(c+d*x))^-1//2*sin(c+d*x)^3*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-5//2*cos(c+d*x)^4*sin(c+d*x)^2, x) == :(4//7*d^-1*(a+a*sin(c+d*x))^-5//2*cos(c+d*x)^5+-4*2^(1/2)*a^-5//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+4*a^-2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+-2//7*a^-1*d^-1*(a+a*sin(c+d*x))^-3//2*cos(c+d*x)^5+2//3*a^-1*d^-1*(a+a*sin(c+d*x))^-3//2*cos(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-5//2*cos(c+d*x)^4*sin(c+d*x), x) == :(-2//5*d^-1*(a+a*sin(c+d*x))^-5//2*cos(c+d*x)^5+-4*a^-2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+4*2^(1/2)*a^-5//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-2//3*a^-1*d^-1*(a+a*sin(c+d*x))^-3//2*cos(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-5//2*cos(c+d*x)^4*csc(c+d*x), x) == :(-2*a^-5//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-2*a^-2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+4*2^(1/2)*a^-5//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-5//2*cos(c+d*x)^4*csc(c+d*x)^2, x) == :(5*a^-5//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-1*a^-2*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-4*2^(1/2)*a^-5//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-5//2*cos(c+d*x)^4*csc(c+d*x)^3, x) == :(-23//4*a^-5//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+4*2^(1/2)*a^-5//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+9//4*a^-2*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//2*a^-2*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-5//2*cos(c+d*x)^4*csc(c+d*x)^4, x) == :(45//8*a^-5//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-4*2^(1/2)*a^-5//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-19//8*a^-2*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//3*a^-2*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^2*cot(c+d*x)+13//12*a^-2*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-5//2*cos(c+d*x)^4*csc(c+d*x)^5, x) == :(-363//64*a^-5//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+4*2^(1/2)*a^-5//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+149//64*a^-2*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-107//96*a^-2*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x)+-1//4*a^-2*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^3*cot(c+d*x)+17//24*a^-2*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^2*cot(c+d*x))
@test integrate(cos(c+d*x)^5*sin(c+d*x)^5*(a+a*sin(c+d*x)), x) == :(-2//9*a*d^-1*sin(c+d*x)^9+-1//4*a*d^-1*sin(c+d*x)^8+1//6*a*d^-1*sin(c+d*x)^6+1//7*a*d^-1*sin(c+d*x)^7+1//10*a*d^-1*sin(c+d*x)^10+1//11*a*d^-1*sin(c+d*x)^11)
@test integrate(cos(c+d*x)^5*sin(c+d*x)^4*(a+a*sin(c+d*x)), x) == :(-2//7*a*d^-1*sin(c+d*x)^7+-1//4*a*d^-1*sin(c+d*x)^8+1//5*a*d^-1*sin(c+d*x)^5+1//6*a*d^-1*sin(c+d*x)^6+1//9*a*d^-1*sin(c+d*x)^9+1//10*a*d^-1*sin(c+d*x)^10)
@test integrate(cos(c+d*x)^5*sin(c+d*x)^3*(a+a*sin(c+d*x)), x) == :(-2//7*a*d^-1*sin(c+d*x)^7+-1//6*a*d^-1*cos(c+d*x)^6+1//5*a*d^-1*sin(c+d*x)^5+1//8*a*d^-1*cos(c+d*x)^8+1//9*a*d^-1*sin(c+d*x)^9)
@test integrate(cos(c+d*x)^5*sin(c+d*x)^2*(a+a*sin(c+d*x)), x) == :(-2//5*a*d^-1*sin(c+d*x)^5+-1//6*a*d^-1*cos(c+d*x)^6+1//3*a*d^-1*sin(c+d*x)^3+1//7*a*d^-1*sin(c+d*x)^7+1//8*a*d^-1*cos(c+d*x)^8)
@test integrate(cos(c+d*x)^5*(a+a*sin(c+d*x))*sin(c+d*x), x) == :(-2//5*a*d^-1*sin(c+d*x)^5+-1//6*a*d^-1*cos(c+d*x)^6+1//3*a*d^-1*sin(c+d*x)^3+1//7*a*d^-1*sin(c+d*x)^7)
@test integrate(cos(c+d*x)^5*(a+a*sin(c+d*x))*csc(c+d*x), x) == :(a*d^-1*log(sin(c+d*x))+a*d^-1*sin(c+d*x)+-1*a*d^-1*sin(c+d*x)^2+-2//3*a*d^-1*sin(c+d*x)^3+1//4*a*d^-1*sin(c+d*x)^4+1//5*a*d^-1*sin(c+d*x)^5)
@test integrate(cos(c+d*x)^5*csc(c+d*x)^2*(a+a*sin(c+d*x)), x) == :(a*d^-1*log(sin(c+d*x))+-1*a*d^-1*sin(c+d*x)^2+-1*a*d^-1*csc(c+d*x)+-2*a*d^-1*sin(c+d*x)+1//3*a*d^-1*sin(c+d*x)^3+1//4*a*d^-1*sin(c+d*x)^4)
@test integrate(cos(c+d*x)^5*csc(c+d*x)^3*(a+a*sin(c+d*x)), x) == :((1/2)*a*d^-1*sin(c+d*x)^2+-1*a*d^-1*csc(c+d*x)+-2*a*d^-1*log(sin(c+d*x))+-2*a*d^-1*sin(c+d*x)+-1//2*a*d^-1*csc(c+d*x)^2+1//3*a*d^-1*sin(c+d*x)^3)
@test integrate(cos(c+d*x)^5*csc(c+d*x)^4*(a+a*sin(c+d*x)), x) == :(a*d^-1*sin(c+d*x)+(1/2)*a*d^-1*sin(c+d*x)^2+-2*a*d^-1*log(sin(c+d*x))+2*a*d^-1*csc(c+d*x)+-1//2*a*d^-1*csc(c+d*x)^2+-1//3*a*d^-1*csc(c+d*x)^3)
@test integrate(cos(c+d*x)^5*csc(c+d*x)^5*(a+a*sin(c+d*x)), x) == :(a*d^-1*csc(c+d*x)^2+a*d^-1*log(sin(c+d*x))+a*d^-1*sin(c+d*x)+2*a*d^-1*csc(c+d*x)+-1//3*a*d^-1*csc(c+d*x)^3+-1//4*a*d^-1*csc(c+d*x)^4)
@test integrate(cos(c+d*x)^5*csc(c+d*x)^6*(a+a*sin(c+d*x)), x) == :(a*d^-1*csc(c+d*x)^2+a*d^-1*log(sin(c+d*x))+-1*a*d^-1*csc(c+d*x)+-1//4*a*d^-1*csc(c+d*x)^4+-1//5*a*d^-1*csc(c+d*x)^5+2//3*a*d^-1*csc(c+d*x)^3)
@test integrate(cos(c+d*x)^5*csc(c+d*x)^7*(a+a*sin(c+d*x)), x) == :(-1*a*d^-1*csc(c+d*x)+-1//5*a*d^-1*csc(c+d*x)^5+-1//6*a*d^-1*cot(c+d*x)^6+2//3*a*d^-1*csc(c+d*x)^3)
@test integrate(cos(c+d*x)^5*csc(c+d*x)^8*(a+a*sin(c+d*x)), x) == :(-1//3*a*d^-1*csc(c+d*x)^3+-1//6*a*d^-1*cot(c+d*x)^6+-1//7*a*d^-1*csc(c+d*x)^7+2//5*a*d^-1*csc(c+d*x)^5)
@test integrate(cos(c+d*x)^5*csc(c+d*x)^9*(a+a*sin(c+d*x)), x) == :(-1//3*a*d^-1*csc(c+d*x)^3+-1//6*a*d^-1*cot(c+d*x)^6+-1//7*a*d^-1*csc(c+d*x)^7+-1//8*a*d^-1*cot(c+d*x)^8+2//5*a*d^-1*csc(c+d*x)^5)
@test integrate(cos(c+d*x)^5*csc(c+d*x)^10*(a+a*sin(c+d*x)), x) == :(-1//5*a*d^-1*csc(c+d*x)^5+-1//6*a*d^-1*cot(c+d*x)^6+-1//8*a*d^-1*cot(c+d*x)^8+-1//9*a*d^-1*csc(c+d*x)^9+2//7*a*d^-1*csc(c+d*x)^7)
@test integrate(cos(c+d*x)^5*csc(c+d*x)^11*(a+a*sin(c+d*x)), x) == :(-1//5*a*d^-1*csc(c+d*x)^5+-1//6*a*d^-1*csc(c+d*x)^6+-1//9*a*d^-1*csc(c+d*x)^9+-1//10*a*d^-1*csc(c+d*x)^10+1//4*a*d^-1*csc(c+d*x)^8+2//7*a*d^-1*csc(c+d*x)^7)
@test integrate(cos(c+d*x)^5*csc(c+d*x)^12*(a+a*sin(c+d*x)), x) == :(-1//6*a*d^-1*csc(c+d*x)^6+-1//7*a*d^-1*csc(c+d*x)^7+-1//10*a*d^-1*csc(c+d*x)^10+-1//11*a*d^-1*csc(c+d*x)^11+1//4*a*d^-1*csc(c+d*x)^8+2//9*a*d^-1*csc(c+d*x)^9)
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^5*sin(c+d*x)^3, x) == :(-4//7*a^2*d^-1*sin(c+d*x)^7+-1//6*a^2*d^-1*sin(c+d*x)^6+-1//8*a^2*d^-1*sin(c+d*x)^8+1//4*a^2*d^-1*sin(c+d*x)^4+1//10*a^2*d^-1*sin(c+d*x)^10+2//5*a^2*d^-1*sin(c+d*x)^5+2//9*a^2*d^-1*sin(c+d*x)^9)
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^5*sin(c+d*x)^2, x) == :(-2*a^-4*d^-1*(a+a*sin(c+d*x))^6+-3//4*a^-6*d^-1*(a+a*sin(c+d*x))^8+1//9*a^-7*d^-1*(a+a*sin(c+d*x))^9+4//5*a^-3*d^-1*(a+a*sin(c+d*x))^5+13//7*a^-5*d^-1*(a+a*sin(c+d*x))^7)
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^5*sin(c+d*x), x) == :(-5//7*a^-5*d^-1*(a+a*sin(c+d*x))^7+-4//5*a^-3*d^-1*(a+a*sin(c+d*x))^5+1//8*a^-6*d^-1*(a+a*sin(c+d*x))^8+4//3*a^-4*d^-1*(a+a*sin(c+d*x))^6)
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^5*csc(c+d*x), x) == :(a^2*d^-1*log(sin(c+d*x))+2*a^2*d^-1*sin(c+d*x)+-4//3*a^2*d^-1*sin(c+d*x)^3+-1//2*a^2*d^-1*sin(c+d*x)^2+-1//4*a^2*d^-1*sin(c+d*x)^4+1//6*a^2*d^-1*sin(c+d*x)^6+2//5*a^2*d^-1*sin(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^5*csc(c+d*x)^2, x) == :((1/2)*a^2*d^-1*sin(c+d*x)^4+-1*a^2*d^-1*csc(c+d*x)+-1*a^2*d^-1*sin(c+d*x)+-2*a^2*d^-1*sin(c+d*x)^2+2*a^2*d^-1*log(sin(c+d*x))+-1//3*a^2*d^-1*sin(c+d*x)^3+1//5*a^2*d^-1*sin(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^5*csc(c+d*x)^3, x) == :(-1*a^2*d^-1*log(sin(c+d*x))+-4*a^2*d^-1*sin(c+d*x)+-2*a^2*d^-1*csc(c+d*x)+-1//2*a^2*d^-1*csc(c+d*x)^2+-1//2*a^2*d^-1*sin(c+d*x)^2+1//4*a^2*d^-1*sin(c+d*x)^4+2//3*a^2*d^-1*sin(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^5*csc(c+d*x)^4, x) == :(a^2*d^-1*sin(c+d*x)^2+a^2*d^-1*csc(c+d*x)+-1*a^2*d^-1*csc(c+d*x)^2+-1*a^2*d^-1*sin(c+d*x)+-4*a^2*d^-1*log(sin(c+d*x))+-1//3*a^2*d^-1*csc(c+d*x)^3+1//3*a^2*d^-1*sin(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^5*csc(c+d*x)^5, x) == :((1/2)*a^2*d^-1*csc(c+d*x)^2+(1/2)*a^2*d^-1*sin(c+d*x)^2+-1*a^2*d^-1*log(sin(c+d*x))+2*a^2*d^-1*sin(c+d*x)+4*a^2*d^-1*csc(c+d*x)+-2//3*a^2*d^-1*csc(c+d*x)^3+-1//4*a^2*d^-1*csc(c+d*x)^4)
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^5*csc(c+d*x)^6, x) == :(a^2*d^-1*csc(c+d*x)+a^2*d^-1*sin(c+d*x)+2*a^2*d^-1*csc(c+d*x)^2+2*a^2*d^-1*log(sin(c+d*x))+-1//2*a^2*d^-1*csc(c+d*x)^4+-1//5*a^2*d^-1*csc(c+d*x)^5+1//3*a^2*d^-1*csc(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^5*csc(c+d*x)^7, x) == :(a^2*d^-1*log(sin(c+d*x))+(1/2)*a^2*d^-1*csc(c+d*x)^2+-2*a^2*d^-1*csc(c+d*x)+-2//5*a^2*d^-1*csc(c+d*x)^5+-1//6*a^2*d^-1*csc(c+d*x)^6+1//4*a^2*d^-1*csc(c+d*x)^4+4//3*a^2*d^-1*csc(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^5*sin(c+d*x)^2, x) == :(-12//7*a^-4*d^-1*(a+a*sin(c+d*x))^7+-2//3*a^-6*d^-1*(a+a*sin(c+d*x))^9+1//10*a^-7*d^-1*(a+a*sin(c+d*x))^10+2//3*a^-3*d^-1*(a+a*sin(c+d*x))^6+13//8*a^-5*d^-1*(a+a*sin(c+d*x))^8)
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^5*sin(c+d*x), x) == :(-5//8*a^-5*d^-1*(a+a*sin(c+d*x))^8+-2//3*a^-3*d^-1*(a+a*sin(c+d*x))^6+1//9*a^-6*d^-1*(a+a*sin(c+d*x))^9+8//7*a^-4*d^-1*(a+a*sin(c+d*x))^7)
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^5*csc(c+d*x), x) == :(a^3*d^-1*log(sin(c+d*x))+(1/2)*a^3*d^-1*sin(c+d*x)^2+(1/2)*a^3*d^-1*sin(c+d*x)^6+3*a^3*d^-1*sin(c+d*x)+-5//3*a^3*d^-1*sin(c+d*x)^3+-5//4*a^3*d^-1*sin(c+d*x)^4+1//5*a^3*d^-1*sin(c+d*x)^5+1//7*a^3*d^-1*sin(c+d*x)^7)
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^5*csc(c+d*x)^2, x) == :(a^3*d^-1*sin(c+d*x)+-1*a^3*d^-1*csc(c+d*x)+3*a^3*d^-1*log(sin(c+d*x))+-5//2*a^3*d^-1*sin(c+d*x)^2+-5//3*a^3*d^-1*sin(c+d*x)^3+1//4*a^3*d^-1*sin(c+d*x)^4+1//6*a^3*d^-1*sin(c+d*x)^6+3//5*a^3*d^-1*sin(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^5*csc(c+d*x)^3, x) == :(a^3*d^-1*log(sin(c+d*x))+-5*a^3*d^-1*sin(c+d*x)+-3*a^3*d^-1*csc(c+d*x)+-5//2*a^3*d^-1*sin(c+d*x)^2+-1//2*a^3*d^-1*csc(c+d*x)^2+1//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*sin(c+d*x)^4)
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^5*csc(c+d*x)^4, x) == :(a^3*d^-1*sin(c+d*x)^3+(1/2)*a^3*d^-1*sin(c+d*x)^2+-1*a^3*d^-1*csc(c+d*x)+-5*a^3*d^-1*log(sin(c+d*x))+-5*a^3*d^-1*sin(c+d*x)+-3//2*a^3*d^-1*csc(c+d*x)^2+-1//3*a^3*d^-1*csc(c+d*x)^3+1//4*a^3*d^-1*sin(c+d*x)^4)
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^5*csc(c+d*x)^5, x) == :(a^3*d^-1*sin(c+d*x)+-1*a^3*d^-1*csc(c+d*x)^3+-5*a^3*d^-1*log(sin(c+d*x))+5*a^3*d^-1*csc(c+d*x)+-1//2*a^3*d^-1*csc(c+d*x)^2+-1//4*a^3*d^-1*csc(c+d*x)^4+1//3*a^3*d^-1*sin(c+d*x)^3+3//2*a^3*d^-1*sin(c+d*x)^2)
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^5*csc(c+d*x)^6, x) == :(a^3*d^-1*log(sin(c+d*x))+(1/2)*a^3*d^-1*sin(c+d*x)^2+3*a^3*d^-1*sin(c+d*x)+5*a^3*d^-1*csc(c+d*x)+-3//4*a^3*d^-1*csc(c+d*x)^4+-1//3*a^3*d^-1*csc(c+d*x)^3+-1//5*a^3*d^-1*csc(c+d*x)^5+5//2*a^3*d^-1*csc(c+d*x)^2)
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^5*csc(c+d*x)^7, x) == :(a^3*d^-1*sin(c+d*x)+-1*a^3*d^-1*csc(c+d*x)+3*a^3*d^-1*log(sin(c+d*x))+-3//5*a^3*d^-1*csc(c+d*x)^5+-1//4*a^3*d^-1*csc(c+d*x)^4+-1//6*a^3*d^-1*csc(c+d*x)^6+5//2*a^3*d^-1*csc(c+d*x)^2+5//3*a^3*d^-1*csc(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^4*cos(c+d*x)^5*csc(c+d*x)^4, x) == :(a^4*d^-1*sin(c+d*x)^4+-10*a^4*d^-1*sin(c+d*x)+-4*a^4*d^-1*csc(c+d*x)+-4*a^4*d^-1*log(sin(c+d*x))+-2*a^4*d^-1*csc(c+d*x)^2+-2*a^4*d^-1*sin(c+d*x)^2+-1//3*a^4*d^-1*csc(c+d*x)^3+1//5*a^4*d^-1*sin(c+d*x)^5+4//3*a^4*d^-1*sin(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^4*cos(c+d*x)^5*csc(c+d*x)^5, x) == :(-10*a^4*d^-1*log(sin(c+d*x))+-4*a^4*d^-1*sin(c+d*x)+-2*a^4*d^-1*csc(c+d*x)^2+2*a^4*d^-1*sin(c+d*x)^2+4*a^4*d^-1*csc(c+d*x)+-4//3*a^4*d^-1*csc(c+d*x)^3+-1//4*a^4*d^-1*csc(c+d*x)^4+1//4*a^4*d^-1*sin(c+d*x)^4+4//3*a^4*d^-1*sin(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^4*cos(c+d*x)^5*csc(c+d*x)^6, x) == :(-1*a^4*d^-1*csc(c+d*x)^4+-4*a^4*d^-1*log(sin(c+d*x))+2*a^4*d^-1*csc(c+d*x)^2+2*a^4*d^-1*sin(c+d*x)^2+4*a^4*d^-1*sin(c+d*x)+10*a^4*d^-1*csc(c+d*x)+-4//3*a^4*d^-1*csc(c+d*x)^3+-1//5*a^4*d^-1*csc(c+d*x)^5+1//3*a^4*d^-1*sin(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^5*sin(c+d*x)^3, x) == :(-1//5*a^-1*d^-1*sin(c+d*x)^5+-1//6*a^-1*d^-1*sin(c+d*x)^6+1//4*a^-1*d^-1*sin(c+d*x)^4+1//7*a^-1*d^-1*sin(c+d*x)^7)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^5*sin(c+d*x)^2, x) == :(-1//4*a^-1*d^-1*sin(c+d*x)^4+-1//5*a^-1*d^-1*sin(c+d*x)^5+1//3*a^-1*d^-1*sin(c+d*x)^3+1//6*a^-1*d^-1*sin(c+d*x)^6)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^5*sin(c+d*x), x) == :(-1//3*a^-1*d^-1*sin(c+d*x)^3+-1//4*a^-1*d^-1*cos(c+d*x)^4+1//5*a^-1*d^-1*sin(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^5*csc(c+d*x), x) == :(a^-1*d^-1*log(sin(c+d*x))+-1*a^-1*d^-1*sin(c+d*x)+-1//2*a^-1*d^-1*sin(c+d*x)^2+1//3*a^-1*d^-1*sin(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^5*csc(c+d*x)^2, x) == :((1/2)*a^-1*d^-1*sin(c+d*x)^2+-1*a^-1*d^-1*csc(c+d*x)+-1*a^-1*d^-1*log(sin(c+d*x))+-1*a^-1*d^-1*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^5*csc(c+d*x)^3, x) == :(a^-1*d^-1*csc(c+d*x)+a^-1*d^-1*sin(c+d*x)+-1*a^-1*d^-1*log(sin(c+d*x))+-1//2*a^-1*d^-1*csc(c+d*x)^2)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^5*csc(c+d*x)^4, x) == :(a^-1*d^-1*csc(c+d*x)+a^-1*d^-1*log(sin(c+d*x))+(1/2)*a^-1*d^-1*csc(c+d*x)^2+-1//3*a^-1*d^-1*csc(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^5*csc(c+d*x)^5, x) == :(-1*a^-1*d^-1*csc(c+d*x)+-1//4*a^-1*d^-1*cot(c+d*x)^4+1//3*a^-1*d^-1*csc(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^5*csc(c+d*x)^6, x) == :(-1//5*a^-1*d^-1*csc(c+d*x)^5+1//3*a^-1*d^-1*csc(c+d*x)^3+1//4*a^-1*d^-1*cot(c+d*x)^4)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^5*csc(c+d*x)^7, x) == :(-1//3*a^-1*d^-1*csc(c+d*x)^3+-1//6*a^-1*d^-1*csc(c+d*x)^6+1//4*a^-1*d^-1*csc(c+d*x)^4+1//5*a^-1*d^-1*csc(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^5*csc(c+d*x)^8, x) == :(-1//4*a^-1*d^-1*csc(c+d*x)^4+-1//7*a^-1*d^-1*csc(c+d*x)^7+1//5*a^-1*d^-1*csc(c+d*x)^5+1//6*a^-1*d^-1*csc(c+d*x)^6)
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^5*sin(c+d*x)^3, x) == :(-2//5*a^-2*d^-1*sin(c+d*x)^5+1//4*a^-2*d^-1*sin(c+d*x)^4+1//6*a^-2*d^-1*sin(c+d*x)^6)
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^5*sin(c+d*x)^2, x) == :(-1//2*a^-2*d^-1*sin(c+d*x)^4+1//3*a^-2*d^-1*sin(c+d*x)^3+1//5*a^-2*d^-1*sin(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^5*sin(c+d*x), x) == :((1/2)*a^-2*d^-1*sin(c+d*x)^2+-2//3*a^-2*d^-1*sin(c+d*x)^3+1//4*a^-2*d^-1*sin(c+d*x)^4)
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^5*csc(c+d*x), x) == :(a^-2*d^-1*log(sin(c+d*x))+(1/2)*a^-2*d^-1*sin(c+d*x)^2+-2*a^-2*d^-1*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^5*csc(c+d*x)^2, x) == :(a^-2*d^-1*sin(c+d*x)+-1*a^-2*d^-1*csc(c+d*x)+-2*a^-2*d^-1*log(sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^5*csc(c+d*x)^3, x) == :(a^-2*d^-1*log(sin(c+d*x))+2*a^-2*d^-1*csc(c+d*x)+-1//2*a^-2*d^-1*csc(c+d*x)^2)
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^5*csc(c+d*x)^4, x) == :(-1//3*a^-5*d^-1*(a+-1*a*sin(c+d*x))^3*csc(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^5*csc(c+d*x)^5, x) == :(-1//2*a^-2*d^-1*csc(c+d*x)^2+-1//4*a^-2*d^-1*csc(c+d*x)^4+2//3*a^-2*d^-1*csc(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^5*csc(c+d*x)^6, x) == :((1/2)*a^-2*d^-1*csc(c+d*x)^4+-1//3*a^-2*d^-1*csc(c+d*x)^3+-1//5*a^-2*d^-1*csc(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^5*csc(c+d*x)^7, x) == :(-1//4*a^-2*d^-1*csc(c+d*x)^4+-1//6*a^-2*d^-1*csc(c+d*x)^6+2//5*a^-2*d^-1*csc(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^5*sin(c+d*x)^3, x) == :(-4*a^-3*d^-1*log(1+sin(c+d*x))+-2*a^-3*d^-1*sin(c+d*x)^2+4*a^-3*d^-1*sin(c+d*x)+-3//4*a^-3*d^-1*sin(c+d*x)^4+1//5*a^-3*d^-1*sin(c+d*x)^5+4//3*a^-3*d^-1*sin(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^5*sin(c+d*x)^2, x) == :(-1*a^-3*d^-1*sin(c+d*x)^3+-4*a^-3*d^-1*sin(c+d*x)+2*a^-3*d^-1*sin(c+d*x)^2+4*a^-3*d^-1*log(1+sin(c+d*x))+1//4*a^-3*d^-1*sin(c+d*x)^4)
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^5*sin(c+d*x), x) == :(-4*a^-3*d^-1*log(1+sin(c+d*x))+4*a^-3*d^-1*sin(c+d*x)+-3//2*a^-3*d^-1*sin(c+d*x)^2+1//3*a^-3*d^-1*sin(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^5*csc(c+d*x), x) == :(a^-3*d^-1*log(sin(c+d*x))+a^-3*d^-1*sin(c+d*x)+-4*a^-3*d^-1*log(1+sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^5*csc(c+d*x)^2, x) == :(-1*a^-3*d^-1*csc(c+d*x)+-3*a^-3*d^-1*log(sin(c+d*x))+4*a^-3*d^-1*log(1+sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^5*csc(c+d*x)^3, x) == :(-4*a^-3*d^-1*log(1+sin(c+d*x))+3*a^-3*d^-1*csc(c+d*x)+4*a^-3*d^-1*log(sin(c+d*x))+-1//2*a^-3*d^-1*csc(c+d*x)^2)
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^5*csc(c+d*x)^4, x) == :(-4*a^-3*d^-1*csc(c+d*x)+-4*a^-3*d^-1*log(sin(c+d*x))+4*a^-3*d^-1*log(1+sin(c+d*x))+-1//3*a^-3*d^-1*csc(c+d*x)^3+3//2*a^-3*d^-1*csc(c+d*x)^2)
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^5*csc(c+d*x)^5, x) == :(a^-3*d^-1*csc(c+d*x)^3+-4*a^-3*d^-1*log(1+sin(c+d*x))+-2*a^-3*d^-1*csc(c+d*x)^2+4*a^-3*d^-1*csc(c+d*x)+4*a^-3*d^-1*log(sin(c+d*x))+-1//4*a^-3*d^-1*csc(c+d*x)^4)
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^5*csc(c+d*x)^6, x) == :(-4*a^-3*d^-1*csc(c+d*x)+-4*a^-3*d^-1*log(sin(c+d*x))+2*a^-3*d^-1*csc(c+d*x)^2+4*a^-3*d^-1*log(1+sin(c+d*x))+-4//3*a^-3*d^-1*csc(c+d*x)^3+-1//5*a^-3*d^-1*csc(c+d*x)^5+3//4*a^-3*d^-1*csc(c+d*x)^4)
@test integrate((a+a*sin(c+d*x))^-4*cos(c+d*x)^5*csc(c+d*x)^5, x) == :(4*d^-1*(a^4+a^4*sin(c+d*x))^-1+-16*a^-4*d^-1*log(1+sin(c+d*x))+-4*a^-4*d^-1*csc(c+d*x)^2+12*a^-4*d^-1*csc(c+d*x)+16*a^-4*d^-1*log(sin(c+d*x))+-1//4*a^-4*d^-1*csc(c+d*x)^4+4//3*a^-4*d^-1*csc(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-4*cos(c+d*x)^5*csc(c+d*x)^6, x) == :(-4*d^-1*(a^4+a^4*sin(c+d*x))^-1+a^-4*d^-1*csc(c+d*x)^4+-20*a^-4*d^-1*log(sin(c+d*x))+-16*a^-4*d^-1*csc(c+d*x)+6*a^-4*d^-1*csc(c+d*x)^2+20*a^-4*d^-1*log(1+sin(c+d*x))+-8//3*a^-4*d^-1*csc(c+d*x)^3+-1//5*a^-4*d^-1*csc(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^5*sin(c+d*x)^n, x) == :(a^3*d^-1*(1+n)^-1*sin(c+d*x)^(1+n)+a^3*d^-1*(3+n)^-1*sin(c+d*x)^(3+n)+a^3*d^-1*(6+n)^-1*sin(c+d*x)^(6+n)+a^3*d^-1*(8+n)^-1*sin(c+d*x)^(8+n)+-5*a^3*d^-1*(4+n)^-1*sin(c+d*x)^(4+n)+-5*a^3*d^-1*(5+n)^-1*sin(c+d*x)^(5+n)+3*a^3*d^-1*(2+n)^-1*sin(c+d*x)^(2+n)+3*a^3*d^-1*(7+n)^-1*sin(c+d*x)^(7+n))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^5*sin(c+d*x)^n, x) == :(a^2*d^-1*(1+n)^-1*sin(c+d*x)^(1+n)+a^2*d^-1*(7+n)^-1*sin(c+d*x)^(7+n)+-1*a^2*d^-1*(3+n)^-1*sin(c+d*x)^(3+n)+-1*a^2*d^-1*(5+n)^-1*sin(c+d*x)^(5+n)+-4*a^2*d^-1*(4+n)^-1*sin(c+d*x)^(4+n)+2*a^2*d^-1*(2+n)^-1*sin(c+d*x)^(2+n)+2*a^2*d^-1*(6+n)^-1*sin(c+d*x)^(6+n))
@test integrate(cos(c+d*x)^5*sin(c+d*x)^n*(a+a*sin(c+d*x)), x) == :(a*d^-1*(1+n)^-1*sin(c+d*x)^(1+n)+a*d^-1*(2+n)^-1*sin(c+d*x)^(2+n)+a*d^-1*(5+n)^-1*sin(c+d*x)^(5+n)+a*d^-1*(6+n)^-1*sin(c+d*x)^(6+n)+-2*a*d^-1*(3+n)^-1*sin(c+d*x)^(3+n)+-2*a*d^-1*(4+n)^-1*sin(c+d*x)^(4+n))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^5*sin(c+d*x)^n, x) == :(a^-1*d^-1*(1+n)^-1*sin(c+d*x)^(1+n)+a^-1*d^-1*(4+n)^-1*sin(c+d*x)^(4+n)+-1*a^-1*d^-1*(2+n)^-1*sin(c+d*x)^(2+n)+-1*a^-1*d^-1*(3+n)^-1*sin(c+d*x)^(3+n))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^5*sin(c+d*x)^n, x) == :(a^-2*d^-1*(1+n)^-1*sin(c+d*x)^(1+n)+a^-2*d^-1*(3+n)^-1*sin(c+d*x)^(3+n)+-2*a^-2*d^-1*(2+n)^-1*sin(c+d*x)^(2+n))
@test integrate(cos(c+d*x)^6*sin(c+d*x)^4*(a+a*sin(c+d*x)), x) == :(3//256*a*x+-1//7*a*d^-1*cos(c+d*x)^7+-1//11*a*d^-1*cos(c+d*x)^11+2//9*a*d^-1*cos(c+d*x)^9+-3//80*a*d^-1*cos(c+d*x)^7*sin(c+d*x)+-1//10*a*d^-1*cos(c+d*x)^7*sin(c+d*x)^3+1//128*a*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//160*a*d^-1*cos(c+d*x)^5*sin(c+d*x)+3//256*a*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^6*sin(c+d*x)^3*(a+a*sin(c+d*x)), x) == :(3//256*a*x+-1//7*a*d^-1*cos(c+d*x)^7+1//9*a*d^-1*cos(c+d*x)^9+-3//80*a*d^-1*cos(c+d*x)^7*sin(c+d*x)+-1//10*a*d^-1*cos(c+d*x)^7*sin(c+d*x)^3+1//128*a*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//160*a*d^-1*cos(c+d*x)^5*sin(c+d*x)+3//256*a*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^6*sin(c+d*x)^2*(a+a*sin(c+d*x)), x) == :(5//128*a*x+-1//7*a*d^-1*cos(c+d*x)^7+1//9*a*d^-1*cos(c+d*x)^9+-1//8*a*d^-1*cos(c+d*x)^7*sin(c+d*x)+1//48*a*d^-1*cos(c+d*x)^5*sin(c+d*x)+5//128*a*d^-1*cos(c+d*x)*sin(c+d*x)+5//192*a*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate(cos(c+d*x)^6*(a+a*sin(c+d*x))*sin(c+d*x), x) == :(5//128*a*x+-1//7*a*d^-1*cos(c+d*x)^7+-1//8*a*d^-1*cos(c+d*x)^7*sin(c+d*x)+1//48*a*d^-1*cos(c+d*x)^5*sin(c+d*x)+5//128*a*d^-1*cos(c+d*x)*sin(c+d*x)+5//192*a*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate(cos(c+d*x)^6*(a+a*sin(c+d*x))*csc(c+d*x), x) == :(5//16*a*x+a*d^-1*cos(c+d*x)+-1*a*d^-1*arctanh(cos(c+d*x))+1//3*a*d^-1*cos(c+d*x)^3+1//5*a*d^-1*cos(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)^6*csc(c+d*x)^2*(a+a*sin(c+d*x)), x) == :(-15//8*a*x+a*d^-1*cos(c+d*x)+-1*a*d^-1*arctanh(cos(c+d*x))+-15//8*a*d^-1*cot(c+d*x)+1//3*a*d^-1*cos(c+d*x)^3+1//5*a*d^-1*cos(c+d*x)^5+1//4*a*d^-1*cos(c+d*x)^4*cot(c+d*x)+5//8*a*d^-1*cos(c+d*x)^2*cot(c+d*x))
@test integrate(cos(c+d*x)^6*csc(c+d*x)^3*(a+a*sin(c+d*x)), x) == :(-15//8*a*x+-15//8*a*d^-1*cot(c+d*x)+-5//2*a*d^-1*cos(c+d*x)+-5//6*a*d^-1*cos(c+d*x)^3+5//2*a*d^-1*arctanh(cos(c+d*x))+-1//2*a*d^-1*cos(c+d*x)^3*cot(c+d*x)^2+1//4*a*d^-1*cos(c+d*x)^4*cot(c+d*x)+5//8*a*d^-1*cos(c+d*x)^2*cot(c+d*x))
@test integrate(cos(c+d*x)^6*csc(c+d*x)^4*(a+a*sin(c+d*x)), x) == :(5//2*a*x+-5//2*a*d^-1*cos(c+d*x)+-5//6*a*d^-1*cos(c+d*x)^3+-5//6*a*d^-1*cot(c+d*x)^3+5//2*a*d^-1*arctanh(cos(c+d*x))+5//2*a*d^-1*cot(c+d*x)+(1/2)*a*d^-1*cos(c+d*x)^2*cot(c+d*x)^3+-1//2*a*d^-1*cos(c+d*x)^3*cot(c+d*x)^2)
@test integrate(cos(c+d*x)^6*csc(c+d*x)^5*(a+a*sin(c+d*x)), x) == :(5//2*a*x+-15//8*a*d^-1*arctanh(cos(c+d*x))+-5//6*a*d^-1*cot(c+d*x)^3+5//2*a*d^-1*cot(c+d*x)+15//8*a*d^-1*cos(c+d*x)+(1/2)*a*d^-1*cos(c+d*x)^2*cot(c+d*x)^3+-1//4*a*d^-1*cot(c+d*x)^4*cos(c+d*x)+5//8*a*d^-1*cot(c+d*x)^2*cos(c+d*x))
@test integrate(cos(c+d*x)^6*csc(c+d*x)^6*(a+a*sin(c+d*x)), x) == :(-1*a*x+-1*a*d^-1*cot(c+d*x)+-15//8*a*d^-1*arctanh(cos(c+d*x))+-1//5*a*d^-1*cot(c+d*x)^5+1//3*a*d^-1*cot(c+d*x)^3+15//8*a*d^-1*cos(c+d*x)+-1//4*a*d^-1*cot(c+d*x)^4*cos(c+d*x)+5//8*a*d^-1*cot(c+d*x)^2*cos(c+d*x))
@test integrate(cos(c+d*x)^6*csc(c+d*x)^7*(a+a*sin(c+d*x)), x) == :(-1*a*x+-1*a*d^-1*cot(c+d*x)+-1//5*a*d^-1*cot(c+d*x)^5+1//3*a*d^-1*cot(c+d*x)^3+5//16*a*d^-1*arctanh(cos(c+d*x))+-5//16*a*d^-1*cot(c+d*x)*csc(c+d*x)+-1//6*a*d^-1*cot(c+d*x)^5*csc(c+d*x)+5//24*a*d^-1*cot(c+d*x)^3*csc(c+d*x))
@test integrate(cos(c+d*x)^6*csc(c+d*x)^8*(a+a*sin(c+d*x)), x) == :(-1//7*a*d^-1*cot(c+d*x)^7+5//16*a*d^-1*arctanh(cos(c+d*x))+-5//16*a*d^-1*cot(c+d*x)*csc(c+d*x)+-1//6*a*d^-1*cot(c+d*x)^5*csc(c+d*x)+5//24*a*d^-1*cot(c+d*x)^3*csc(c+d*x))
@test integrate(cos(c+d*x)^6*csc(c+d*x)^9*(a+a*sin(c+d*x)), x) == :(-1//7*a*d^-1*cot(c+d*x)^7+5//128*a*d^-1*arctanh(cos(c+d*x))+-5//64*a*d^-1*csc(c+d*x)^3*cot(c+d*x)+-1//8*a*d^-1*cot(c+d*x)^5*csc(c+d*x)^3+5//48*a*d^-1*cot(c+d*x)^3*csc(c+d*x)^3+5//128*a*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate(cos(c+d*x)^6*csc(c+d*x)^10*(a+a*sin(c+d*x)), x) == :(-1//7*a*d^-1*cot(c+d*x)^7+-1//9*a*d^-1*cot(c+d*x)^9+5//128*a*d^-1*arctanh(cos(c+d*x))+-5//64*a*d^-1*csc(c+d*x)^3*cot(c+d*x)+-1//8*a*d^-1*cot(c+d*x)^5*csc(c+d*x)^3+5//48*a*d^-1*cot(c+d*x)^3*csc(c+d*x)^3+5//128*a*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate(cos(c+d*x)^6*csc(c+d*x)^11*(a+a*sin(c+d*x)), x) == :(-1//7*a*d^-1*cot(c+d*x)^7+-1//9*a*d^-1*cot(c+d*x)^9+3//256*a*d^-1*arctanh(cos(c+d*x))+-1//10*a*d^-1*cot(c+d*x)^5*csc(c+d*x)^5+-1//32*a*d^-1*csc(c+d*x)^5*cot(c+d*x)+1//16*a*d^-1*cot(c+d*x)^3*csc(c+d*x)^5+1//128*a*d^-1*csc(c+d*x)^3*cot(c+d*x)+3//256*a*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate(cos(c+d*x)^6*csc(c+d*x)^12*(a+a*sin(c+d*x)), x) == :(-2//9*a*d^-1*cot(c+d*x)^9+-1//7*a*d^-1*cot(c+d*x)^7+-1//11*a*d^-1*cot(c+d*x)^11+3//256*a*d^-1*arctanh(cos(c+d*x))+-1//10*a*d^-1*cot(c+d*x)^5*csc(c+d*x)^5+-1//32*a*d^-1*csc(c+d*x)^5*cot(c+d*x)+1//16*a*d^-1*cot(c+d*x)^3*csc(c+d*x)^5+1//128*a*d^-1*csc(c+d*x)^3*cot(c+d*x)+3//256*a*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^6*sin(c+d*x)^4, x) == :(17//1024*x*a^2+-2//7*a^2*d^-1*cos(c+d*x)^7+-2//11*a^2*d^-1*cos(c+d*x)^11+4//9*a^2*d^-1*cos(c+d*x)^9+-17//120*a^2*d^-1*cos(c+d*x)^7*sin(c+d*x)^3+-17//320*a^2*d^-1*cos(c+d*x)^7*sin(c+d*x)+-1//12*a^2*d^-1*cos(c+d*x)^7*sin(c+d*x)^5+17//1024*a^2*d^-1*cos(c+d*x)*sin(c+d*x)+17//1536*a^2*d^-1*cos(c+d*x)^3*sin(c+d*x)+17//1920*a^2*d^-1*cos(c+d*x)^5*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^6*sin(c+d*x)^3, x) == :(3//128*x*a^2+-2//7*a^2*d^-1*cos(c+d*x)^7+-1//11*a^2*d^-1*cos(c+d*x)^11+1//3*a^2*d^-1*cos(c+d*x)^9+-3//40*a^2*d^-1*cos(c+d*x)^7*sin(c+d*x)+-1//5*a^2*d^-1*cos(c+d*x)^7*sin(c+d*x)^3+1//64*a^2*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//80*a^2*d^-1*cos(c+d*x)^5*sin(c+d*x)+3//128*a^2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^6*sin(c+d*x)^2, x) == :(13//256*x*a^2+-2//7*a^2*d^-1*cos(c+d*x)^7+2//9*a^2*d^-1*cos(c+d*x)^9+-13//80*a^2*d^-1*cos(c+d*x)^7*sin(c+d*x)+-1//10*a^2*d^-1*cos(c+d*x)^7*sin(c+d*x)^3+13//256*a^2*d^-1*cos(c+d*x)*sin(c+d*x)+13//384*a^2*d^-1*cos(c+d*x)^3*sin(c+d*x)+13//480*a^2*d^-1*cos(c+d*x)^5*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^6*sin(c+d*x), x) == :(5//64*x*a^2+-1//9*d^-1*(a+a*sin(c+d*x))^2*cos(c+d*x)^7+-1//28*a^2*d^-1*cos(c+d*x)^7+-1//36*d^-1*cos(c+d*x)^7*(a^2+a^2*sin(c+d*x))+1//24*a^2*d^-1*cos(c+d*x)^5*sin(c+d*x)+5//64*a^2*d^-1*cos(c+d*x)*sin(c+d*x)+5//96*a^2*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^6*csc(c+d*x), x) == :(5//8*x*a^2+a^2*d^-1*cos(c+d*x)+-1*a^2*d^-1*arctanh(cos(c+d*x))+-1//7*a^2*d^-1*cos(c+d*x)^7+1//3*a^2*d^-1*cos(c+d*x)^3+1//5*a^2*d^-1*cos(c+d*x)^5+1//3*a^2*d^-1*cos(c+d*x)^5*sin(c+d*x)+5//8*a^2*d^-1*cos(c+d*x)*sin(c+d*x)+5//12*a^2*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^6*csc(c+d*x)^2, x) == :(-25//16*x*a^2+-1*a^2*d^-1*cot(c+d*x)+-2*a^2*d^-1*arctanh(cos(c+d*x))+2*a^2*d^-1*cos(c+d*x)+2//3*a^2*d^-1*cos(c+d*x)^3+2//5*a^2*d^-1*cos(c+d*x)^5+-7//16*a^2*d^-1*cos(c+d*x)*sin(c+d*x)+-7//24*a^2*d^-1*sin(c+d*x)^3*cos(c+d*x)+1//6*a^2*d^-1*sin(c+d*x)^5*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^6*csc(c+d*x)^3, x) == :(-15//4*x*a^2+-1*a^2*d^-1*cos(c+d*x)+-2*a^2*d^-1*cot(c+d*x)+1//5*a^2*d^-1*cos(c+d*x)^5+3//2*a^2*d^-1*arctanh(cos(c+d*x))+(1/2)*a^2*d^-1*sin(c+d*x)^3*cos(c+d*x)+-9//4*a^2*d^-1*cos(c+d*x)*sin(c+d*x)+-1//2*a^2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^6*csc(c+d*x)^4, x) == :(5//8*x*a^2+a^2*d^-1*cot(c+d*x)+-4*a^2*d^-1*cos(c+d*x)+5*a^2*d^-1*arctanh(cos(c+d*x))+-2//3*a^2*d^-1*cos(c+d*x)^3+-1//3*a^2*d^-1*cot(c+d*x)^3+-1*a^2*d^-1*cot(c+d*x)*csc(c+d*x)+-5//8*a^2*d^-1*cos(c+d*x)*sin(c+d*x)+1//4*a^2*d^-1*sin(c+d*x)^3*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^6*csc(c+d*x)^5, x) == :(5*x*a^2+-1*a^2*d^-1*cos(c+d*x)+4*a^2*d^-1*cot(c+d*x)+-2//3*a^2*d^-1*cot(c+d*x)^3+-1//3*a^2*d^-1*cos(c+d*x)^3+5//8*a^2*d^-1*arctanh(cos(c+d*x))+a^2*d^-1*cos(c+d*x)*sin(c+d*x)+-1//4*a^2*d^-1*csc(c+d*x)^3*cot(c+d*x)+5//8*a^2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^6*csc(c+d*x)^6, x) == :(3//2*x*a^2+a^2*d^-1*cot(c+d*x)+2*a^2*d^-1*cos(c+d*x)+-15//4*a^2*d^-1*arctanh(cos(c+d*x))+-1//5*a^2*d^-1*cot(c+d*x)^5+(1/2)*a^2*d^-1*cos(c+d*x)*sin(c+d*x)+-1//2*a^2*d^-1*csc(c+d*x)^3*cot(c+d*x)+9//4*a^2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^6*csc(c+d*x)^7, x) == :(-2*x*a^2+a^2*d^-1*cos(c+d*x)+-2*a^2*d^-1*cot(c+d*x)+-25//16*a^2*d^-1*arctanh(cos(c+d*x))+-2//5*a^2*d^-1*cot(c+d*x)^5+2//3*a^2*d^-1*cot(c+d*x)^3+-1//6*a^2*d^-1*csc(c+d*x)^5*cot(c+d*x)+7//16*a^2*d^-1*cot(c+d*x)*csc(c+d*x)+7//24*a^2*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^6*csc(c+d*x)^8, x) == :(-1*x*a^2+-1*a^2*d^-1*cot(c+d*x)+-1//5*a^2*d^-1*cot(c+d*x)^5+-1//7*a^2*d^-1*cot(c+d*x)^7+1//3*a^2*d^-1*cot(c+d*x)^3+5//8*a^2*d^-1*arctanh(cos(c+d*x))+-5//8*a^2*d^-1*cot(c+d*x)*csc(c+d*x)+-1//3*a^2*d^-1*cot(c+d*x)^5*csc(c+d*x)+5//12*a^2*d^-1*cot(c+d*x)^3*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^6*csc(c+d*x)^9, x) == :(-2//7*a^2*d^-1*cot(c+d*x)^7+45//128*a^2*d^-1*arctanh(cos(c+d*x))+-35//128*a^2*d^-1*cot(c+d*x)*csc(c+d*x)+-5//64*a^2*d^-1*csc(c+d*x)^3*cot(c+d*x)+-1//6*a^2*d^-1*cot(c+d*x)^5*csc(c+d*x)+-1//8*a^2*d^-1*cot(c+d*x)^5*csc(c+d*x)^3+5//24*a^2*d^-1*cot(c+d*x)^3*csc(c+d*x)+5//48*a^2*d^-1*cot(c+d*x)^3*csc(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^6*csc(c+d*x)^10, x) == :(-2//7*a^2*d^-1*cot(c+d*x)^7+-1//9*a^2*d^-1*cot(c+d*x)^9+5//64*a^2*d^-1*arctanh(cos(c+d*x))+-5//32*a^2*d^-1*csc(c+d*x)^3*cot(c+d*x)+-1//4*a^2*d^-1*cot(c+d*x)^5*csc(c+d*x)^3+5//24*a^2*d^-1*cot(c+d*x)^3*csc(c+d*x)^3+5//64*a^2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^6*csc(c+d*x)^11, x) == :(-2//7*a^2*d^-1*cot(c+d*x)^7+-2//9*a^2*d^-1*cot(c+d*x)^9+13//256*a^2*d^-1*arctanh(cos(c+d*x))+-9//128*a^2*d^-1*csc(c+d*x)^3*cot(c+d*x)+-1//8*a^2*d^-1*cot(c+d*x)^5*csc(c+d*x)^3+-1//10*a^2*d^-1*cot(c+d*x)^5*csc(c+d*x)^5+-1//32*a^2*d^-1*csc(c+d*x)^5*cot(c+d*x)+1//16*a^2*d^-1*cot(c+d*x)^3*csc(c+d*x)^5+5//48*a^2*d^-1*cot(c+d*x)^3*csc(c+d*x)^3+13//256*a^2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^6*csc(c+d*x)^12, x) == :(-2//7*a^2*d^-1*cot(c+d*x)^7+-1//3*a^2*d^-1*cot(c+d*x)^9+-1//11*a^2*d^-1*cot(c+d*x)^11+3//128*a^2*d^-1*arctanh(cos(c+d*x))+-1//5*a^2*d^-1*cot(c+d*x)^5*csc(c+d*x)^5+-1//16*a^2*d^-1*csc(c+d*x)^5*cot(c+d*x)+1//8*a^2*d^-1*cot(c+d*x)^3*csc(c+d*x)^5+1//64*a^2*d^-1*csc(c+d*x)^3*cot(c+d*x)+3//128*a^2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^6*csc(c+d*x)^13, x) == :(-4//9*a^2*d^-1*cot(c+d*x)^9+-2//7*a^2*d^-1*cot(c+d*x)^7+-2//11*a^2*d^-1*cot(c+d*x)^11+17//1024*a^2*d^-1*arctanh(cos(c+d*x))+-11//384*a^2*d^-1*csc(c+d*x)^5*cot(c+d*x)+-1//10*a^2*d^-1*cot(c+d*x)^5*csc(c+d*x)^5+-1//12*a^2*d^-1*cot(c+d*x)^5*csc(c+d*x)^7+-1//64*a^2*d^-1*csc(c+d*x)^7*cot(c+d*x)+1//16*a^2*d^-1*cot(c+d*x)^3*csc(c+d*x)^5+1//24*a^2*d^-1*cot(c+d*x)^3*csc(c+d*x)^7+17//1024*a^2*d^-1*cot(c+d*x)*csc(c+d*x)+17//1536*a^2*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^6*sin(c+d*x)^4, x) == :(27//1024*x*a^3+a^3*d^-1*cos(c+d*x)^9+-6//11*a^3*d^-1*cos(c+d*x)^11+-4//7*a^3*d^-1*cos(c+d*x)^7+1//13*a^3*d^-1*cos(c+d*x)^13+-27//320*a^3*d^-1*cos(c+d*x)^7*sin(c+d*x)+-9//40*a^3*d^-1*cos(c+d*x)^7*sin(c+d*x)^3+-1//4*a^3*d^-1*cos(c+d*x)^7*sin(c+d*x)^5+9//512*a^3*d^-1*cos(c+d*x)^3*sin(c+d*x)+9//640*a^3*d^-1*cos(c+d*x)^5*sin(c+d*x)+27//1024*a^3*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^6*sin(c+d*x)^3, x) == :(41//1024*x*a^3+-4//7*a^3*d^-1*cos(c+d*x)^7+-3//11*a^3*d^-1*cos(c+d*x)^11+7//9*a^3*d^-1*cos(c+d*x)^9+-41//120*a^3*d^-1*cos(c+d*x)^7*sin(c+d*x)^3+-41//320*a^3*d^-1*cos(c+d*x)^7*sin(c+d*x)+-1//12*a^3*d^-1*cos(c+d*x)^7*sin(c+d*x)^5+41//1024*a^3*d^-1*cos(c+d*x)*sin(c+d*x)+41//1536*a^3*d^-1*cos(c+d*x)^3*sin(c+d*x)+41//1920*a^3*d^-1*cos(c+d*x)^5*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^6*sin(c+d*x)^2, x) == :(19//256*x*a^3+-4//7*a^3*d^-1*cos(c+d*x)^7+-1//11*a^3*d^-1*cos(c+d*x)^11+5//9*a^3*d^-1*cos(c+d*x)^9+-19//80*a^3*d^-1*cos(c+d*x)^7*sin(c+d*x)+-3//10*a^3*d^-1*cos(c+d*x)^7*sin(c+d*x)^3+19//256*a^3*d^-1*cos(c+d*x)*sin(c+d*x)+19//384*a^3*d^-1*cos(c+d*x)^3*sin(c+d*x)+19//480*a^3*d^-1*cos(c+d*x)^5*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^6*sin(c+d*x), x) == :(33//256*x*a^3+-33//560*a^3*d^-1*cos(c+d*x)^7+-11//240*d^-1*cos(c+d*x)^7*(a^3+a^3*sin(c+d*x))+-1//10*d^-1*(a+a*sin(c+d*x))^3*cos(c+d*x)^7+-1//30*a*d^-1*(a+a*sin(c+d*x))^2*cos(c+d*x)^7+11//128*a^3*d^-1*cos(c+d*x)^3*sin(c+d*x)+11//160*a^3*d^-1*cos(c+d*x)^5*sin(c+d*x)+33//256*a^3*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^6*csc(c+d*x), x) == :(125//128*x*a^3+a^3*d^-1*cos(c+d*x)+-1*a^3*d^-1*arctanh(cos(c+d*x))+-3//7*a^3*d^-1*cos(c+d*x)^7+1//3*a^3*d^-1*cos(c+d*x)^3+1//5*a^3*d^-1*cos(c+d*x)^5+-1//8*a^3*d^-1*cos(c+d*x)^7*sin(c+d*x)+25//48*a^3*d^-1*cos(c+d*x)^5*sin(c+d*x)+125//128*a^3*d^-1*cos(c+d*x)*sin(c+d*x)+125//192*a^3*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^6*csc(c+d*x)^2, x) == :(-15//16*x*a^3+a^3*d^-1*cos(c+d*x)^3+-1*a^3*d^-1*cot(c+d*x)+-3*a^3*d^-1*arctanh(cos(c+d*x))+3*a^3*d^-1*cos(c+d*x)+-1//7*a^3*d^-1*cos(c+d*x)^7+3//5*a^3*d^-1*cos(c+d*x)^5+(1/2)*a^3*d^-1*sin(c+d*x)^5*cos(c+d*x)+-11//8*a^3*d^-1*sin(c+d*x)^3*cos(c+d*x)+15//16*a^3*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^6*csc(c+d*x)^3, x) == :(-85//16*x*a^3+a^3*d^-1*cos(c+d*x)+-3*a^3*d^-1*cot(c+d*x)+-1//2*a^3*d^-1*arctanh(cos(c+d*x))+2//3*a^3*d^-1*cos(c+d*x)^3+3//5*a^3*d^-1*cos(c+d*x)^5+-43//16*a^3*d^-1*cos(c+d*x)*sin(c+d*x)+-1//2*a^3*d^-1*cot(c+d*x)*csc(c+d*x)+1//6*a^3*d^-1*sin(c+d*x)^5*cos(c+d*x)+5//24*a^3*d^-1*sin(c+d*x)^3*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^6*csc(c+d*x)^4, x) == :(-25//8*x*a^3+-1*a^3*d^-1*cot(c+d*x)+-5*a^3*d^-1*cos(c+d*x)+-2//3*a^3*d^-1*cos(c+d*x)^3+-1//3*a^3*d^-1*cot(c+d*x)^3+1//5*a^3*d^-1*cos(c+d*x)^5+13//2*a^3*d^-1*arctanh(cos(c+d*x))+-23//8*a^3*d^-1*cos(c+d*x)*sin(c+d*x)+-3//2*a^3*d^-1*cot(c+d*x)*csc(c+d*x)+3//4*a^3*d^-1*sin(c+d*x)^3*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^6*csc(c+d*x)^5, x) == :(45//8*x*a^3+-1*a^3*d^-1*cos(c+d*x)^3+-1*a^3*d^-1*cot(c+d*x)^3+-5*a^3*d^-1*cos(c+d*x)+5*a^3*d^-1*cot(c+d*x)+45//8*a^3*d^-1*arctanh(cos(c+d*x))+-3//8*a^3*d^-1*cot(c+d*x)*csc(c+d*x)+-1//4*a^3*d^-1*csc(c+d*x)^3*cot(c+d*x)+1//4*a^3*d^-1*sin(c+d*x)^3*cos(c+d*x)+3//8*a^3*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^6*csc(c+d*x)^6, x) == :(13//2*x*a^3+a^3*d^-1*cos(c+d*x)+5*a^3*d^-1*cot(c+d*x)+-25//8*a^3*d^-1*arctanh(cos(c+d*x))+-2//3*a^3*d^-1*cot(c+d*x)^3+-1//3*a^3*d^-1*cos(c+d*x)^3+-1//5*a^3*d^-1*cot(c+d*x)^5+-3//4*a^3*d^-1*csc(c+d*x)^3*cot(c+d*x)+3//2*a^3*d^-1*cos(c+d*x)*sin(c+d*x)+23//8*a^3*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^6*csc(c+d*x)^7, x) == :(-1//2*x*a^3+-1*a^3*d^-1*cot(c+d*x)+3*a^3*d^-1*cos(c+d*x)+-85//16*a^3*d^-1*arctanh(cos(c+d*x))+-3//5*a^3*d^-1*cot(c+d*x)^5+2//3*a^3*d^-1*cot(c+d*x)^3+(1/2)*a^3*d^-1*cos(c+d*x)*sin(c+d*x)+-5//24*a^3*d^-1*csc(c+d*x)^3*cot(c+d*x)+-1//6*a^3*d^-1*csc(c+d*x)^5*cot(c+d*x)+43//16*a^3*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^6*csc(c+d*x)^8, x) == :(-3*x*a^3+a^3*d^-1*cot(c+d*x)^3+a^3*d^-1*cos(c+d*x)+-3*a^3*d^-1*cot(c+d*x)+-15//16*a^3*d^-1*arctanh(cos(c+d*x))+-3//5*a^3*d^-1*cot(c+d*x)^5+-1//7*a^3*d^-1*cot(c+d*x)^7+-15//16*a^3*d^-1*cot(c+d*x)*csc(c+d*x)+-1//2*a^3*d^-1*csc(c+d*x)^5*cot(c+d*x)+11//8*a^3*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^6*csc(c+d*x)^9, x) == :(-1*x*a^3+-1*a^3*d^-1*cot(c+d*x)+-3//7*a^3*d^-1*cot(c+d*x)^7+-1//5*a^3*d^-1*cot(c+d*x)^5+1//3*a^3*d^-1*cot(c+d*x)^3+125//128*a^3*d^-1*arctanh(cos(c+d*x))+-115//128*a^3*d^-1*cot(c+d*x)*csc(c+d*x)+-5//64*a^3*d^-1*csc(c+d*x)^3*cot(c+d*x)+-1//2*a^3*d^-1*cot(c+d*x)^5*csc(c+d*x)+-1//8*a^3*d^-1*cot(c+d*x)^5*csc(c+d*x)^3+5//8*a^3*d^-1*cot(c+d*x)^3*csc(c+d*x)+5//48*a^3*d^-1*cot(c+d*x)^3*csc(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^6*csc(c+d*x)^10, x) == :(-4//7*a^3*d^-1*cot(c+d*x)^7+-1//9*a^3*d^-1*cot(c+d*x)^9+55//128*a^3*d^-1*arctanh(cos(c+d*x))+-25//128*a^3*d^-1*cot(c+d*x)*csc(c+d*x)+-15//64*a^3*d^-1*csc(c+d*x)^3*cot(c+d*x)+-3//8*a^3*d^-1*cot(c+d*x)^5*csc(c+d*x)^3+-1//6*a^3*d^-1*cot(c+d*x)^5*csc(c+d*x)+5//16*a^3*d^-1*cot(c+d*x)^3*csc(c+d*x)^3+5//24*a^3*d^-1*cot(c+d*x)^3*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^6*csc(c+d*x)^11, x) == :(-4//7*a^3*d^-1*cot(c+d*x)^7+-1//3*a^3*d^-1*cot(c+d*x)^9+33//256*a^3*d^-1*arctanh(cos(c+d*x))+-29//128*a^3*d^-1*csc(c+d*x)^3*cot(c+d*x)+-3//8*a^3*d^-1*cot(c+d*x)^5*csc(c+d*x)^3+-1//10*a^3*d^-1*cot(c+d*x)^5*csc(c+d*x)^5+-1//32*a^3*d^-1*csc(c+d*x)^5*cot(c+d*x)+1//16*a^3*d^-1*cot(c+d*x)^3*csc(c+d*x)^5+5//16*a^3*d^-1*cot(c+d*x)^3*csc(c+d*x)^3+33//256*a^3*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^6*csc(c+d*x)^12, x) == :(-5//9*a^3*d^-1*cot(c+d*x)^9+-4//7*a^3*d^-1*cot(c+d*x)^7+-1//11*a^3*d^-1*cot(c+d*x)^11+19//256*a^3*d^-1*arctanh(cos(c+d*x))+-7//128*a^3*d^-1*csc(c+d*x)^3*cot(c+d*x)+-3//10*a^3*d^-1*cot(c+d*x)^5*csc(c+d*x)^5+-3//32*a^3*d^-1*csc(c+d*x)^5*cot(c+d*x)+-1//8*a^3*d^-1*cot(c+d*x)^5*csc(c+d*x)^3+3//16*a^3*d^-1*cot(c+d*x)^3*csc(c+d*x)^5+5//48*a^3*d^-1*cot(c+d*x)^3*csc(c+d*x)^3+19//256*a^3*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^6*csc(c+d*x)^13, x) == :(-7//9*a^3*d^-1*cot(c+d*x)^9+-4//7*a^3*d^-1*cot(c+d*x)^7+-3//11*a^3*d^-1*cot(c+d*x)^11+41//1024*a^3*d^-1*arctanh(cos(c+d*x))+-35//384*a^3*d^-1*csc(c+d*x)^5*cot(c+d*x)+-3//10*a^3*d^-1*cot(c+d*x)^5*csc(c+d*x)^5+-1//12*a^3*d^-1*cot(c+d*x)^5*csc(c+d*x)^7+-1//64*a^3*d^-1*csc(c+d*x)^7*cot(c+d*x)+1//24*a^3*d^-1*cot(c+d*x)^3*csc(c+d*x)^7+3//16*a^3*d^-1*cot(c+d*x)^3*csc(c+d*x)^5+41//1024*a^3*d^-1*cot(c+d*x)*csc(c+d*x)+41//1536*a^3*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^6*csc(c+d*x)^14, x) == :(-1*a^3*d^-1*cot(c+d*x)^9+-6//11*a^3*d^-1*cot(c+d*x)^11+-4//7*a^3*d^-1*cot(c+d*x)^7+-1//13*a^3*d^-1*cot(c+d*x)^13+27//1024*a^3*d^-1*arctanh(cos(c+d*x))+-3//64*a^3*d^-1*csc(c+d*x)^7*cot(c+d*x)+-3//128*a^3*d^-1*csc(c+d*x)^5*cot(c+d*x)+-1//4*a^3*d^-1*cot(c+d*x)^5*csc(c+d*x)^7+-1//10*a^3*d^-1*cot(c+d*x)^5*csc(c+d*x)^5+1//8*a^3*d^-1*cot(c+d*x)^3*csc(c+d*x)^7+1//16*a^3*d^-1*cot(c+d*x)^3*csc(c+d*x)^5+9//512*a^3*d^-1*csc(c+d*x)^3*cot(c+d*x)+27//1024*a^3*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^4*cos(c+d*x)^6*csc(c+d*x)^4, x) == :(-135//16*x*a^4+-4*a^4*d^-1*cos(c+d*x)+-4*a^4*d^-1*cot(c+d*x)+6*a^4*d^-1*arctanh(cos(c+d*x))+-1//3*a^4*d^-1*cot(c+d*x)^3+4//5*a^4*d^-1*cos(c+d*x)^5+-2*a^4*d^-1*cot(c+d*x)*csc(c+d*x)+-89//16*a^4*d^-1*cos(c+d*x)*sin(c+d*x)+1//6*a^4*d^-1*sin(c+d*x)^5*cos(c+d*x)+23//24*a^4*d^-1*sin(c+d*x)^3*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^6*sin(c+d*x)^4, x) == :(3//128*x*a^-1+-2//7*a^-1*d^-1*cos(c+d*x)^7+1//5*a^-1*d^-1*cos(c+d*x)^5+1//9*a^-1*d^-1*cos(c+d*x)^9+-1//8*a^-1*d^-1*cos(c+d*x)^5*sin(c+d*x)^3+-1//16*a^-1*d^-1*cos(c+d*x)^5*sin(c+d*x)+1//64*a^-1*d^-1*cos(c+d*x)^3*sin(c+d*x)+3//128*a^-1*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^6*sin(c+d*x)^3, x) == :(-3//128*x*a^-1+-1//5*a^-1*d^-1*cos(c+d*x)^5+1//7*a^-1*d^-1*cos(c+d*x)^7+-3//128*a^-1*d^-1*cos(c+d*x)*sin(c+d*x)+-1//64*a^-1*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//8*a^-1*d^-1*cos(c+d*x)^5*sin(c+d*x)^3+1//16*a^-1*d^-1*cos(c+d*x)^5*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^6*sin(c+d*x)^2, x) == :(1//16*x*a^-1+-1//7*a^-1*d^-1*cos(c+d*x)^7+1//5*a^-1*d^-1*cos(c+d*x)^5+-1//6*a^-1*d^-1*cos(c+d*x)^5*sin(c+d*x)+1//16*a^-1*d^-1*cos(c+d*x)*sin(c+d*x)+1//24*a^-1*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^6*sin(c+d*x), x) == :(-1//16*x*a^-1+-1//5*a^-1*d^-1*cos(c+d*x)^5+-1//16*a^-1*d^-1*cos(c+d*x)*sin(c+d*x)+-1//24*a^-1*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//6*a^-1*d^-1*cos(c+d*x)^5*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^6*csc(c+d*x), x) == :(-3//8*x*a^-1+a^-1*d^-1*cos(c+d*x)+-1*a^-1*d^-1*arctanh(cos(c+d*x))+1//3*a^-1*d^-1*cos(c+d*x)^3+-3//8*a^-1*d^-1*cos(c+d*x)*sin(c+d*x)+-1//4*a^-1*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^6*csc(c+d*x)^2, x) == :(-3//2*x*a^-1+a^-1*d^-1*arctanh(cos(c+d*x))+-1*a^-1*d^-1*cos(c+d*x)+-3//2*a^-1*d^-1*cot(c+d*x)+-1//3*a^-1*d^-1*cos(c+d*x)^3+(1/2)*a^-1*d^-1*cos(c+d*x)^2*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^6*csc(c+d*x)^3, x) == :(3//2*x*a^-1+-3//2*a^-1*d^-1*cos(c+d*x)+3//2*a^-1*d^-1*arctanh(cos(c+d*x))+3//2*a^-1*d^-1*cot(c+d*x)+-1//2*a^-1*d^-1*cos(c+d*x)^2*cot(c+d*x)+-1//2*a^-1*d^-1*cot(c+d*x)^2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^6*csc(c+d*x)^4, x) == :(x*a^-1+a^-1*d^-1*cot(c+d*x)+-3//2*a^-1*d^-1*arctanh(cos(c+d*x))+-1//3*a^-1*d^-1*cot(c+d*x)^3+3//2*a^-1*d^-1*cos(c+d*x)+(1/2)*a^-1*d^-1*cot(c+d*x)^2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^6*csc(c+d*x)^5, x) == :(-1*x*a^-1+-1*a^-1*d^-1*cot(c+d*x)+-3//8*a^-1*d^-1*arctanh(cos(c+d*x))+1//3*a^-1*d^-1*cot(c+d*x)^3+-1//4*a^-1*d^-1*cot(c+d*x)^3*csc(c+d*x)+3//8*a^-1*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^6*csc(c+d*x)^6, x) == :(-1//5*a^-1*d^-1*cot(c+d*x)^5+3//8*a^-1*d^-1*arctanh(cos(c+d*x))+-3//8*a^-1*d^-1*cot(c+d*x)*csc(c+d*x)+1//4*a^-1*d^-1*cot(c+d*x)^3*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^6*sin(c+d*x)^3, x) == :(-1//8*x*a^-2+-2//3*a^-2*d^-1*cos(c+d*x)^3+-1//7*a^-2*d^-1*cos(c+d*x)^7+3//5*a^-2*d^-1*cos(c+d*x)^5+-1//8*a^-2*d^-1*cos(c+d*x)*sin(c+d*x)+1//3*a^-2*d^-1*cos(c+d*x)^3*sin(c+d*x)^3+1//4*a^-2*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^6*sin(c+d*x)^2, x) == :(3//16*x*a^-2+1//10*a^-2*d^-1*cos(c+d*x)^5+1//6*a^-5*d^-1*(a+-1*a*sin(c+d*x))^3*cos(c+d*x)^3+1//8*a^-2*d^-1*cos(c+d*x)^3*sin(c+d*x)+3//16*a^-2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^6*sin(c+d*x), x) == :(-1//4*x*a^-2+-2//15*a^-2*d^-1*cos(c+d*x)^5+-1//3*d^-1*(a+a*sin(c+d*x))^-2*cos(c+d*x)^7+-1//4*a^-2*d^-1*cos(c+d*x)*sin(c+d*x)+-1//6*a^-2*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^6*csc(c+d*x), x) == :(-1*x*a^-2+a^-2*d^-1*cos(c+d*x)+-1*a^-2*d^-1*arctanh(cos(c+d*x))+-1//3*a^-2*d^-1*cos(c+d*x)^3+-1*a^-2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^6*csc(c+d*x)^2, x) == :(-1//2*x*a^-2+-1*a^-2*d^-1*cot(c+d*x)+-2*a^-2*d^-1*cos(c+d*x)+2*a^-2*d^-1*arctanh(cos(c+d*x))+(1/2)*a^-2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^6*csc(c+d*x)^3, x) == :(2*x*a^-2+a^-2*d^-1*cos(c+d*x)+2*a^-2*d^-1*cot(c+d*x)+-1//2*a^-2*d^-1*arctanh(cos(c+d*x))+-1//2*a^-2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^6*csc(c+d*x)^4, x) == :(-1*x*a^-2+-1*a^-2*d^-1*arctanh(cos(c+d*x))+-1*a^-2*d^-1*cot(c+d*x)+-1//3*a^-2*d^-1*cot(c+d*x)^3+a^-2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^6*csc(c+d*x)^5, x) == :(2//3*a^-2*d^-1*cot(c+d*x)^3+5//8*a^-2*d^-1*arctanh(cos(c+d*x))+-3//8*a^-2*d^-1*cot(c+d*x)*csc(c+d*x)+-1//4*a^-2*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^6*csc(c+d*x)^6, x) == :(-2//3*a^-2*d^-1*cot(c+d*x)^3+-1//4*a^-2*d^-1*arctanh(cos(c+d*x))+-1//5*a^-2*d^-1*cot(c+d*x)^5+(1/2)*a^-2*d^-1*csc(c+d*x)^3*cot(c+d*x)+-1//4*a^-2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^6*csc(c+d*x)^7, x) == :(2//3*a^-2*d^-1*cot(c+d*x)^3+2//5*a^-2*d^-1*cot(c+d*x)^5+3//16*a^-2*d^-1*arctanh(cos(c+d*x))+-5//24*a^-2*d^-1*csc(c+d*x)^3*cot(c+d*x)+-1//6*a^-2*d^-1*csc(c+d*x)^5*cot(c+d*x)+3//16*a^-2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^6*sin(c+d*x)^3, x) == :(-23//16*x*a^-3+-4*a^-3*d^-1*cos(c+d*x)+-3//5*a^-3*d^-1*cos(c+d*x)^5+7//3*a^-3*d^-1*cos(c+d*x)^3+1//6*a^-3*d^-1*sin(c+d*x)^5*cos(c+d*x)+23//16*a^-3*d^-1*cos(c+d*x)*sin(c+d*x)+23//24*a^-3*d^-1*sin(c+d*x)^3*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^6*sin(c+d*x)^2, x) == :(13//8*x*a^-3+4*a^-3*d^-1*cos(c+d*x)+-5//3*a^-3*d^-1*cos(c+d*x)^3+1//5*a^-3*d^-1*cos(c+d*x)^5+-13//8*a^-3*d^-1*cos(c+d*x)*sin(c+d*x)+-3//4*a^-3*d^-1*sin(c+d*x)^3*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^6*csc(c+d*x), x) == :(-7//2*x*a^-3+-1*a^-3*d^-1*arctanh(cos(c+d*x))+-3*a^-3*d^-1*cos(c+d*x)+(1/2)*a^-3*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^6*csc(c+d*x)^2, x) == :(3*x*a^-3+a^-3*d^-1*cos(c+d*x)+-1*a^-3*d^-1*cot(c+d*x)+3*a^-3*d^-1*arctanh(cos(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^6*csc(c+d*x)^3, x) == :(-1*x*a^-3+3*a^-3*d^-1*cot(c+d*x)+-7//2*a^-3*d^-1*arctanh(cos(c+d*x))+-1//2*a^-3*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^6*csc(c+d*x)^4, x) == :(-4*a^-3*d^-1*cot(c+d*x)+-1//3*a^-3*d^-1*cot(c+d*x)^3+5//2*a^-3*d^-1*arctanh(cos(c+d*x))+3//2*a^-3*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^6*csc(c+d*x)^5, x) == :(a^-3*d^-1*cot(c+d*x)^3+4*a^-3*d^-1*cot(c+d*x)+-15//8*a^-3*d^-1*arctanh(cos(c+d*x))+-15//8*a^-3*d^-1*cot(c+d*x)*csc(c+d*x)+-1//4*a^-3*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^6*csc(c+d*x)^6, x) == :(-4*a^-3*d^-1*cot(c+d*x)+-5//3*a^-3*d^-1*cot(c+d*x)^3+-1//5*a^-3*d^-1*cot(c+d*x)^5+13//8*a^-3*d^-1*arctanh(cos(c+d*x))+3//4*a^-3*d^-1*csc(c+d*x)^3*cot(c+d*x)+13//8*a^-3*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate(cos(c+d*x)^7*sin(c+d*x)^6*(a+a*sin(c+d*x)), x) == :(-3//10*a*d^-1*sin(c+d*x)^10+-1//3*a*d^-1*sin(c+d*x)^9+-1//13*a*d^-1*sin(c+d*x)^13+-1//14*a*d^-1*sin(c+d*x)^14+1//4*a*d^-1*sin(c+d*x)^12+1//7*a*d^-1*sin(c+d*x)^7+1//8*a*d^-1*sin(c+d*x)^8+3//11*a*d^-1*sin(c+d*x)^11)
@test integrate(cos(c+d*x)^7*sin(c+d*x)^5*(a+a*sin(c+d*x)), x) == :(-1//3*a*d^-1*sin(c+d*x)^9+-1//8*a*d^-1*cos(c+d*x)^8+-1//12*a*d^-1*cos(c+d*x)^12+-1//13*a*d^-1*sin(c+d*x)^13+1//5*a*d^-1*cos(c+d*x)^10+1//7*a*d^-1*sin(c+d*x)^7+3//11*a*d^-1*sin(c+d*x)^11)
@test integrate(cos(c+d*x)^7*sin(c+d*x)^4*(a+a*sin(c+d*x)), x) == :(-3//7*a*d^-1*sin(c+d*x)^7+-1//8*a*d^-1*cos(c+d*x)^8+-1//11*a*d^-1*sin(c+d*x)^11+-1//12*a*d^-1*cos(c+d*x)^12+1//3*a*d^-1*sin(c+d*x)^9+1//5*a*d^-1*cos(c+d*x)^10+1//5*a*d^-1*sin(c+d*x)^5)
@test integrate(cos(c+d*x)^7*sin(c+d*x)^3*(a+a*sin(c+d*x)), x) == :(-3//7*a*d^-1*sin(c+d*x)^7+-1//8*a*d^-1*cos(c+d*x)^8+-1//11*a*d^-1*sin(c+d*x)^11+1//3*a*d^-1*sin(c+d*x)^9+1//5*a*d^-1*sin(c+d*x)^5+1//10*a*d^-1*cos(c+d*x)^10)
@test integrate(cos(c+d*x)^7*sin(c+d*x)^2*(a+a*sin(c+d*x)), x) == :(-3//5*a*d^-1*sin(c+d*x)^5+-1//8*a*d^-1*cos(c+d*x)^8+-1//9*a*d^-1*sin(c+d*x)^9+1//3*a*d^-1*sin(c+d*x)^3+1//10*a*d^-1*cos(c+d*x)^10+3//7*a*d^-1*sin(c+d*x)^7)
@test integrate(cos(c+d*x)^7*(a+a*sin(c+d*x))*sin(c+d*x), x) == :(-3//5*a*d^-1*sin(c+d*x)^5+-1//8*a*d^-1*cos(c+d*x)^8+-1//9*a*d^-1*sin(c+d*x)^9+1//3*a*d^-1*sin(c+d*x)^3+3//7*a*d^-1*sin(c+d*x)^7)
@test integrate(cos(c+d*x)^7*(a+a*sin(c+d*x))*csc(c+d*x), x) == :(a*d^-1*log(sin(c+d*x))+a*d^-1*sin(c+d*x)+-1*a*d^-1*sin(c+d*x)^3+-3//2*a*d^-1*sin(c+d*x)^2+-1//6*a*d^-1*sin(c+d*x)^6+-1//7*a*d^-1*sin(c+d*x)^7+3//4*a*d^-1*sin(c+d*x)^4+3//5*a*d^-1*sin(c+d*x)^5)
@test integrate(cos(c+d*x)^7*csc(c+d*x)^2*(a+a*sin(c+d*x)), x) == :(a*d^-1*sin(c+d*x)^3+a*d^-1*log(sin(c+d*x))+-1*a*d^-1*csc(c+d*x)+-3*a*d^-1*sin(c+d*x)+-3//2*a*d^-1*sin(c+d*x)^2+-1//5*a*d^-1*sin(c+d*x)^5+-1//6*a*d^-1*sin(c+d*x)^6+3//4*a*d^-1*sin(c+d*x)^4)
@test integrate(cos(c+d*x)^7*csc(c+d*x)^3*(a+a*sin(c+d*x)), x) == :(a*d^-1*sin(c+d*x)^3+-1*a*d^-1*csc(c+d*x)+-3*a*d^-1*log(sin(c+d*x))+-3*a*d^-1*sin(c+d*x)+-1//2*a*d^-1*csc(c+d*x)^2+-1//4*a*d^-1*sin(c+d*x)^4+-1//5*a*d^-1*sin(c+d*x)^5+3//2*a*d^-1*sin(c+d*x)^2)
@test integrate(cos(c+d*x)^7*csc(c+d*x)^4*(a+a*sin(c+d*x)), x) == :(-3*a*d^-1*log(sin(c+d*x))+3*a*d^-1*csc(c+d*x)+3*a*d^-1*sin(c+d*x)+-1//2*a*d^-1*csc(c+d*x)^2+-1//3*a*d^-1*csc(c+d*x)^3+-1//3*a*d^-1*sin(c+d*x)^3+-1//4*a*d^-1*sin(c+d*x)^4+3//2*a*d^-1*sin(c+d*x)^2)
@test integrate(cos(c+d*x)^7*csc(c+d*x)^5*(a+a*sin(c+d*x)), x) == :(3*a*d^-1*csc(c+d*x)+3*a*d^-1*log(sin(c+d*x))+3*a*d^-1*sin(c+d*x)+-1//2*a*d^-1*sin(c+d*x)^2+-1//3*a*d^-1*csc(c+d*x)^3+-1//3*a*d^-1*sin(c+d*x)^3+-1//4*a*d^-1*csc(c+d*x)^4+3//2*a*d^-1*csc(c+d*x)^2)
@test integrate(cos(c+d*x)^7*csc(c+d*x)^6*(a+a*sin(c+d*x)), x) == :(a*d^-1*csc(c+d*x)^3+-1*a*d^-1*sin(c+d*x)+-3*a*d^-1*csc(c+d*x)+3*a*d^-1*log(sin(c+d*x))+-1//2*a*d^-1*sin(c+d*x)^2+-1//4*a*d^-1*csc(c+d*x)^4+-1//5*a*d^-1*csc(c+d*x)^5+3//2*a*d^-1*csc(c+d*x)^2)
@test integrate(cos(c+d*x)^7*csc(c+d*x)^7*(a+a*sin(c+d*x)), x) == :(a*d^-1*csc(c+d*x)^3+-1*a*d^-1*log(sin(c+d*x))+-1*a*d^-1*sin(c+d*x)+-3*a*d^-1*csc(c+d*x)+-3//2*a*d^-1*csc(c+d*x)^2+-1//5*a*d^-1*csc(c+d*x)^5+-1//6*a*d^-1*csc(c+d*x)^6+3//4*a*d^-1*csc(c+d*x)^4)
@test integrate(cos(c+d*x)^7*csc(c+d*x)^8*(a+a*sin(c+d*x)), x) == :(a*d^-1*csc(c+d*x)+-1*a*d^-1*csc(c+d*x)^3+-1*a*d^-1*log(sin(c+d*x))+-3//2*a*d^-1*csc(c+d*x)^2+-1//6*a*d^-1*csc(c+d*x)^6+-1//7*a*d^-1*csc(c+d*x)^7+3//4*a*d^-1*csc(c+d*x)^4+3//5*a*d^-1*csc(c+d*x)^5)
@test integrate(cos(c+d*x)^7*csc(c+d*x)^9*(a+a*sin(c+d*x)), x) == :(a*d^-1*csc(c+d*x)+-1*a*d^-1*csc(c+d*x)^3+-1//7*a*d^-1*csc(c+d*x)^7+-1//8*a*d^-1*cot(c+d*x)^8+3//5*a*d^-1*csc(c+d*x)^5)
@test integrate(cos(c+d*x)^7*csc(c+d*x)^10*(a+a*sin(c+d*x)), x) == :(-3//5*a*d^-1*csc(c+d*x)^5+-1//8*a*d^-1*cot(c+d*x)^8+-1//9*a*d^-1*csc(c+d*x)^9+1//3*a*d^-1*csc(c+d*x)^3+3//7*a*d^-1*csc(c+d*x)^7)
@test integrate(cos(c+d*x)^7*csc(c+d*x)^11*(a+a*sin(c+d*x)), x) == :(-3//5*a*d^-1*csc(c+d*x)^5+-1//8*a*d^-1*cot(c+d*x)^8+-1//9*a*d^-1*csc(c+d*x)^9+-1//10*a*d^-1*cot(c+d*x)^10+1//3*a*d^-1*csc(c+d*x)^3+3//7*a*d^-1*csc(c+d*x)^7)
@test integrate(cos(c+d*x)^7*csc(c+d*x)^12*(a+a*sin(c+d*x)), x) == :(-3//7*a*d^-1*csc(c+d*x)^7+-1//8*a*d^-1*cot(c+d*x)^8+-1//10*a*d^-1*cot(c+d*x)^10+-1//11*a*d^-1*csc(c+d*x)^11+1//3*a*d^-1*csc(c+d*x)^9+1//5*a*d^-1*csc(c+d*x)^5)
@test integrate(cos(c+d*x)^7*csc(c+d*x)^13*(a+a*sin(c+d*x)), x) == :(-3//7*a*d^-1*csc(c+d*x)^7+-1//5*a*d^-1*cot(c+d*x)^10+-1//8*a*d^-1*cot(c+d*x)^8+-1//11*a*d^-1*csc(c+d*x)^11+-1//12*a*d^-1*cot(c+d*x)^12+1//3*a*d^-1*csc(c+d*x)^9+1//5*a*d^-1*csc(c+d*x)^5)
@test integrate(cos(c+d*x)^7*csc(c+d*x)^14*(a+a*sin(c+d*x)), x) == :(-1//3*a*d^-1*csc(c+d*x)^9+-1//5*a*d^-1*cot(c+d*x)^10+-1//8*a*d^-1*cot(c+d*x)^8+-1//12*a*d^-1*cot(c+d*x)^12+-1//13*a*d^-1*csc(c+d*x)^13+1//7*a*d^-1*csc(c+d*x)^7+3//11*a*d^-1*csc(c+d*x)^11)
@test integrate(cos(c+d*x)^7*csc(c+d*x)^15*(a+a*sin(c+d*x)), x) == :(-3//10*a*d^-1*csc(c+d*x)^10+-1//3*a*d^-1*csc(c+d*x)^9+-1//13*a*d^-1*csc(c+d*x)^13+-1//14*a*d^-1*csc(c+d*x)^14+1//4*a*d^-1*csc(c+d*x)^12+1//7*a*d^-1*csc(c+d*x)^7+1//8*a*d^-1*csc(c+d*x)^8+3//11*a*d^-1*csc(c+d*x)^11)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^7*sin(c+d*x)^6, x) == :(-2//9*a^-1*d^-1*sin(c+d*x)^9+-1//8*a^-1*d^-1*sin(c+d*x)^8+-1//12*a^-1*d^-1*sin(c+d*x)^12+1//5*a^-1*d^-1*sin(c+d*x)^10+1//7*a^-1*d^-1*sin(c+d*x)^7+1//11*a^-1*d^-1*sin(c+d*x)^11)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^7*sin(c+d*x)^5, x) == :(-1//4*a^-1*d^-1*sin(c+d*x)^8+-1//7*a^-1*d^-1*sin(c+d*x)^7+-1//11*a^-1*d^-1*sin(c+d*x)^11+1//6*a^-1*d^-1*sin(c+d*x)^6+1//10*a^-1*d^-1*sin(c+d*x)^10+2//9*a^-1*d^-1*sin(c+d*x)^9)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^7*sin(c+d*x)^4, x) == :(-2//7*a^-1*d^-1*sin(c+d*x)^7+-1//6*a^-1*d^-1*sin(c+d*x)^6+-1//10*a^-1*d^-1*sin(c+d*x)^10+1//4*a^-1*d^-1*sin(c+d*x)^8+1//5*a^-1*d^-1*sin(c+d*x)^5+1//9*a^-1*d^-1*sin(c+d*x)^9)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^7*sin(c+d*x)^3, x) == :(-1//5*a^-1*d^-1*sin(c+d*x)^5+-1//6*a^-1*d^-1*cos(c+d*x)^6+-1//9*a^-1*d^-1*sin(c+d*x)^9+1//8*a^-1*d^-1*cos(c+d*x)^8+2//7*a^-1*d^-1*sin(c+d*x)^7)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^7*sin(c+d*x)^2, x) == :(-2//5*a^-1*d^-1*sin(c+d*x)^5+-1//8*a^-1*d^-1*cos(c+d*x)^8+1//3*a^-1*d^-1*sin(c+d*x)^3+1//6*a^-1*d^-1*cos(c+d*x)^6+1//7*a^-1*d^-1*sin(c+d*x)^7)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^7*sin(c+d*x), x) == :(-1//3*a^-1*d^-1*sin(c+d*x)^3+-1//6*a^-1*d^-1*cos(c+d*x)^6+-1//7*a^-1*d^-1*sin(c+d*x)^7+2//5*a^-1*d^-1*sin(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^7, x) == :(-1*a^-5*d^-1*(a+-1*a*sin(c+d*x))^4+-1//6*a^-7*d^-1*(a+-1*a*sin(c+d*x))^6+4//5*a^-6*d^-1*(a+-1*a*sin(c+d*x))^5)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^7*csc(c+d*x), x) == :(a^-1*d^-1*log(sin(c+d*x))+-1*a^-1*d^-1*sin(c+d*x)^2+-1*a^-1*d^-1*sin(c+d*x)+-1//5*a^-1*d^-1*sin(c+d*x)^5+1//4*a^-1*d^-1*sin(c+d*x)^4+2//3*a^-1*d^-1*sin(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^7*csc(c+d*x)^2, x) == :(a^-1*d^-1*sin(c+d*x)^2+-1*a^-1*d^-1*csc(c+d*x)+-1*a^-1*d^-1*log(sin(c+d*x))+-2*a^-1*d^-1*sin(c+d*x)+-1//4*a^-1*d^-1*sin(c+d*x)^4+1//3*a^-1*d^-1*sin(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^7*csc(c+d*x)^3, x) == :(a^-1*d^-1*csc(c+d*x)+(1/2)*a^-1*d^-1*sin(c+d*x)^2+-2*a^-1*d^-1*log(sin(c+d*x))+2*a^-1*d^-1*sin(c+d*x)+-1//2*a^-1*d^-1*csc(c+d*x)^2+-1//3*a^-1*d^-1*sin(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^7*csc(c+d*x)^4, x) == :(a^-1*d^-1*sin(c+d*x)+(1/2)*a^-1*d^-1*csc(c+d*x)^2+2*a^-1*d^-1*csc(c+d*x)+2*a^-1*d^-1*log(sin(c+d*x))+-1//2*a^-1*d^-1*sin(c+d*x)^2+-1//3*a^-1*d^-1*csc(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^7*csc(c+d*x)^5, x) == :(a^-1*d^-1*csc(c+d*x)^2+a^-1*d^-1*log(sin(c+d*x))+-1*a^-1*d^-1*sin(c+d*x)+-2*a^-1*d^-1*csc(c+d*x)+-1//4*a^-1*d^-1*csc(c+d*x)^4+1//3*a^-1*d^-1*csc(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^7*csc(c+d*x)^6, x) == :(-1*a^-1*d^-1*csc(c+d*x)^2+-1*a^-1*d^-1*csc(c+d*x)+-1*a^-1*d^-1*log(sin(c+d*x))+-1//5*a^-1*d^-1*csc(c+d*x)^5+1//4*a^-1*d^-1*csc(c+d*x)^4+2//3*a^-1*d^-1*csc(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^7*csc(c+d*x)^7, x) == :(a^-1*d^-1*csc(c+d*x)+-2//3*a^-1*d^-1*csc(c+d*x)^3+-1//6*a^-1*d^-1*cot(c+d*x)^6+1//5*a^-1*d^-1*csc(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^7*csc(c+d*x)^8, x) == :(-1//3*a^-1*d^-1*csc(c+d*x)^3+-1//7*a^-1*d^-1*csc(c+d*x)^7+1//6*a^-1*d^-1*cot(c+d*x)^6+2//5*a^-1*d^-1*csc(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^7*csc(c+d*x)^9, x) == :(-2//5*a^-1*d^-1*csc(c+d*x)^5+-1//6*a^-1*d^-1*cot(c+d*x)^6+-1//8*a^-1*d^-1*cot(c+d*x)^8+1//3*a^-1*d^-1*csc(c+d*x)^3+1//7*a^-1*d^-1*csc(c+d*x)^7)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^7*csc(c+d*x)^10, x) == :(-1//5*a^-1*d^-1*csc(c+d*x)^5+-1//9*a^-1*d^-1*csc(c+d*x)^9+1//6*a^-1*d^-1*cot(c+d*x)^6+1//8*a^-1*d^-1*cot(c+d*x)^8+2//7*a^-1*d^-1*csc(c+d*x)^7)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^7*csc(c+d*x)^11, x) == :(-2//7*a^-1*d^-1*csc(c+d*x)^7+-1//6*a^-1*d^-1*csc(c+d*x)^6+-1//10*a^-1*d^-1*csc(c+d*x)^10+1//4*a^-1*d^-1*csc(c+d*x)^8+1//5*a^-1*d^-1*csc(c+d*x)^5+1//9*a^-1*d^-1*csc(c+d*x)^9)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^7*csc(c+d*x)^12, x) == :(-1//4*a^-1*d^-1*csc(c+d*x)^8+-1//7*a^-1*d^-1*csc(c+d*x)^7+-1//11*a^-1*d^-1*csc(c+d*x)^11+1//6*a^-1*d^-1*csc(c+d*x)^6+1//10*a^-1*d^-1*csc(c+d*x)^10+2//9*a^-1*d^-1*csc(c+d*x)^9)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^7*csc(c+d*x)^13, x) == :(-2//9*a^-1*d^-1*csc(c+d*x)^9+-1//8*a^-1*d^-1*csc(c+d*x)^8+-1//12*a^-1*d^-1*csc(c+d*x)^12+1//5*a^-1*d^-1*csc(c+d*x)^10+1//7*a^-1*d^-1*csc(c+d*x)^7+1//11*a^-1*d^-1*csc(c+d*x)^11)
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^7*sin(c+d*x)^n, x) == :(a^3*d^-1*(1+n)^-1*sin(c+d*x)^(1+n)+-1*a^3*d^-1*(10+n)^-1*sin(c+d*x)^(10+n)+-8*a^3*d^-1*(4+n)^-1*sin(c+d*x)^(4+n)+-6*a^3*d^-1*(5+n)^-1*sin(c+d*x)^(5+n)+-3*a^3*d^-1*(9+n)^-1*sin(c+d*x)^(9+n)+3*a^3*d^-1*(2+n)^-1*sin(c+d*x)^(2+n)+6*a^3*d^-1*(6+n)^-1*sin(c+d*x)^(6+n)+8*a^3*d^-1*(7+n)^-1*sin(c+d*x)^(7+n))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^7*sin(c+d*x)^n, x) == :(a^2*d^-1*(1+n)^-1*sin(c+d*x)^(1+n)+-1*a^2*d^-1*(9+n)^-1*sin(c+d*x)^(9+n)+-6*a^2*d^-1*(4+n)^-1*sin(c+d*x)^(4+n)+-2*a^2*d^-1*(3+n)^-1*sin(c+d*x)^(3+n)+-2*a^2*d^-1*(8+n)^-1*sin(c+d*x)^(8+n)+2*a^2*d^-1*(2+n)^-1*sin(c+d*x)^(2+n)+2*a^2*d^-1*(7+n)^-1*sin(c+d*x)^(7+n)+6*a^2*d^-1*(6+n)^-1*sin(c+d*x)^(6+n))
@test integrate(cos(c+d*x)^7*sin(c+d*x)^n*(a+a*sin(c+d*x)), x) == :(a*d^-1*(1+n)^-1*sin(c+d*x)^(1+n)+a*d^-1*(2+n)^-1*sin(c+d*x)^(2+n)+-1*a*d^-1*(7+n)^-1*sin(c+d*x)^(7+n)+-1*a*d^-1*(8+n)^-1*sin(c+d*x)^(8+n)+-3*a*d^-1*(3+n)^-1*sin(c+d*x)^(3+n)+-3*a*d^-1*(4+n)^-1*sin(c+d*x)^(4+n)+3*a*d^-1*(5+n)^-1*sin(c+d*x)^(5+n)+3*a*d^-1*(6+n)^-1*sin(c+d*x)^(6+n))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^7*sin(c+d*x)^n, x) == :(a^-1*d^-1*(1+n)^-1*sin(c+d*x)^(1+n)+a^-1*d^-1*(5+n)^-1*sin(c+d*x)^(5+n)+-1*a^-1*d^-1*(2+n)^-1*sin(c+d*x)^(2+n)+-1*a^-1*d^-1*(6+n)^-1*sin(c+d*x)^(6+n)+-2*a^-1*d^-1*(3+n)^-1*sin(c+d*x)^(3+n)+2*a^-1*d^-1*(4+n)^-1*sin(c+d*x)^(4+n))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^7*sin(c+d*x)^n, x) == :(a^-2*d^-1*(1+n)^-1*sin(c+d*x)^(1+n)+-1*a^-2*d^-1*(5+n)^-1*sin(c+d*x)^(5+n)+-2*a^-2*d^-1*(2+n)^-1*sin(c+d*x)^(2+n)+2*a^-2*d^-1*(4+n)^-1*sin(c+d*x)^(4+n))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^7*sin(c+d*x)^n, x) == :(a^-3*d^-1*(1+n)^-1*sin(c+d*x)^(1+n)+-1*a^-3*d^-1*(4+n)^-1*sin(c+d*x)^(4+n)+-3*a^-3*d^-1*(2+n)^-1*sin(c+d*x)^(2+n)+3*a^-3*d^-1*(3+n)^-1*sin(c+d*x)^(3+n))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^8*sin(c+d*x)^5, x) == :(-5//1024*x*a^-1+-1//7*a^-1*d^-1*cos(c+d*x)^7+-1//11*a^-1*d^-1*cos(c+d*x)^11+2//9*a^-1*d^-1*cos(c+d*x)^9+-5//1024*a^-1*d^-1*cos(c+d*x)*sin(c+d*x)+-5//1536*a^-1*d^-1*cos(c+d*x)^3*sin(c+d*x)+-1//384*a^-1*d^-1*cos(c+d*x)^5*sin(c+d*x)+1//12*a^-1*d^-1*cos(c+d*x)^7*sin(c+d*x)^5+1//24*a^-1*d^-1*cos(c+d*x)^7*sin(c+d*x)^3+1//64*a^-1*d^-1*cos(c+d*x)^7*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^8*sin(c+d*x)^4, x) == :(3//256*x*a^-1+-2//9*a^-1*d^-1*cos(c+d*x)^9+1//7*a^-1*d^-1*cos(c+d*x)^7+1//11*a^-1*d^-1*cos(c+d*x)^11+-3//80*a^-1*d^-1*cos(c+d*x)^7*sin(c+d*x)+-1//10*a^-1*d^-1*cos(c+d*x)^7*sin(c+d*x)^3+1//128*a^-1*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//160*a^-1*d^-1*cos(c+d*x)^5*sin(c+d*x)+3//256*a^-1*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^8*sin(c+d*x)^3, x) == :(-3//256*x*a^-1+-1//7*a^-1*d^-1*cos(c+d*x)^7+1//9*a^-1*d^-1*cos(c+d*x)^9+-3//256*a^-1*d^-1*cos(c+d*x)*sin(c+d*x)+-1//128*a^-1*d^-1*cos(c+d*x)^3*sin(c+d*x)+-1//160*a^-1*d^-1*cos(c+d*x)^5*sin(c+d*x)+1//10*a^-1*d^-1*cos(c+d*x)^7*sin(c+d*x)^3+3//80*a^-1*d^-1*cos(c+d*x)^7*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^8*sin(c+d*x)^2, x) == :(5//128*x*a^-1+-1//9*a^-1*d^-1*cos(c+d*x)^9+1//7*a^-1*d^-1*cos(c+d*x)^7+-1//8*a^-1*d^-1*cos(c+d*x)^7*sin(c+d*x)+1//48*a^-1*d^-1*cos(c+d*x)^5*sin(c+d*x)+5//128*a^-1*d^-1*cos(c+d*x)*sin(c+d*x)+5//192*a^-1*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^8*sin(c+d*x), x) == :(-5//128*x*a^-1+-1//7*a^-1*d^-1*cos(c+d*x)^7+-5//128*a^-1*d^-1*cos(c+d*x)*sin(c+d*x)+-5//192*a^-1*d^-1*cos(c+d*x)^3*sin(c+d*x)+-1//48*a^-1*d^-1*cos(c+d*x)^5*sin(c+d*x)+1//8*a^-1*d^-1*cos(c+d*x)^7*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^8*csc(c+d*x), x) == :(-5//16*x*a^-1+a^-1*d^-1*cos(c+d*x)+-1*a^-1*d^-1*arctanh(cos(c+d*x))+1//3*a^-1*d^-1*cos(c+d*x)^3+1//5*a^-1*d^-1*cos(c+d*x)^5+-5//16*a^-1*d^-1*cos(c+d*x)*sin(c+d*x)+-5//24*a^-1*d^-1*cos(c+d*x)^3*sin(c+d*x)+-1//6*a^-1*d^-1*cos(c+d*x)^5*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^8*csc(c+d*x)^2, x) == :(-15//8*x*a^-1+a^-1*d^-1*arctanh(cos(c+d*x))+-1*a^-1*d^-1*cos(c+d*x)+-15//8*a^-1*d^-1*cot(c+d*x)+-1//3*a^-1*d^-1*cos(c+d*x)^3+-1//5*a^-1*d^-1*cos(c+d*x)^5+1//4*a^-1*d^-1*cos(c+d*x)^4*cot(c+d*x)+5//8*a^-1*d^-1*cos(c+d*x)^2*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^8*csc(c+d*x)^3, x) == :(15//8*x*a^-1+-5//2*a^-1*d^-1*cos(c+d*x)+-5//6*a^-1*d^-1*cos(c+d*x)^3+5//2*a^-1*d^-1*arctanh(cos(c+d*x))+15//8*a^-1*d^-1*cot(c+d*x)+-5//8*a^-1*d^-1*cos(c+d*x)^2*cot(c+d*x)+-1//2*a^-1*d^-1*cos(c+d*x)^3*cot(c+d*x)^2+-1//4*a^-1*d^-1*cos(c+d*x)^4*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^8*csc(c+d*x)^4, x) == :(5//2*x*a^-1+-5//2*a^-1*d^-1*arctanh(cos(c+d*x))+-5//6*a^-1*d^-1*cot(c+d*x)^3+5//2*a^-1*d^-1*cos(c+d*x)+5//2*a^-1*d^-1*cot(c+d*x)+5//6*a^-1*d^-1*cos(c+d*x)^3+(1/2)*a^-1*d^-1*cos(c+d*x)^2*cot(c+d*x)^3+(1/2)*a^-1*d^-1*cos(c+d*x)^3*cot(c+d*x)^2)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^8*csc(c+d*x)^5, x) == :(-5//2*x*a^-1+-15//8*a^-1*d^-1*arctanh(cos(c+d*x))+-5//2*a^-1*d^-1*cot(c+d*x)+5//6*a^-1*d^-1*cot(c+d*x)^3+15//8*a^-1*d^-1*cos(c+d*x)+-1//2*a^-1*d^-1*cos(c+d*x)^2*cot(c+d*x)^3+-1//4*a^-1*d^-1*cot(c+d*x)^4*cos(c+d*x)+5//8*a^-1*d^-1*cot(c+d*x)^2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^8*csc(c+d*x)^6, x) == :(-1*x*a^-1+-1*a^-1*d^-1*cot(c+d*x)+-15//8*a^-1*d^-1*cos(c+d*x)+-1//5*a^-1*d^-1*cot(c+d*x)^5+1//3*a^-1*d^-1*cot(c+d*x)^3+15//8*a^-1*d^-1*arctanh(cos(c+d*x))+-5//8*a^-1*d^-1*cot(c+d*x)^2*cos(c+d*x)+1//4*a^-1*d^-1*cot(c+d*x)^4*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^8*csc(c+d*x)^7, x) == :(x*a^-1+a^-1*d^-1*cot(c+d*x)+-1//3*a^-1*d^-1*cot(c+d*x)^3+1//5*a^-1*d^-1*cot(c+d*x)^5+5//16*a^-1*d^-1*arctanh(cos(c+d*x))+-5//16*a^-1*d^-1*cot(c+d*x)*csc(c+d*x)+-1//6*a^-1*d^-1*cot(c+d*x)^5*csc(c+d*x)+5//24*a^-1*d^-1*cot(c+d*x)^3*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^8*csc(c+d*x)^8, x) == :(-5//16*a^-1*d^-1*arctanh(cos(c+d*x))+-1//7*a^-1*d^-1*cot(c+d*x)^7+-5//24*a^-1*d^-1*cot(c+d*x)^3*csc(c+d*x)+1//6*a^-1*d^-1*cot(c+d*x)^5*csc(c+d*x)+5//16*a^-1*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^8*csc(c+d*x)^9, x) == :(1//7*a^-1*d^-1*cot(c+d*x)^7+5//128*a^-1*d^-1*arctanh(cos(c+d*x))+-5//64*a^-1*d^-1*csc(c+d*x)^3*cot(c+d*x)+-1//8*a^-1*d^-1*cot(c+d*x)^5*csc(c+d*x)^3+5//48*a^-1*d^-1*cot(c+d*x)^3*csc(c+d*x)^3+5//128*a^-1*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^8*csc(c+d*x)^10, x) == :(-5//128*a^-1*d^-1*arctanh(cos(c+d*x))+-1//7*a^-1*d^-1*cot(c+d*x)^7+-1//9*a^-1*d^-1*cot(c+d*x)^9+-5//48*a^-1*d^-1*cot(c+d*x)^3*csc(c+d*x)^3+-5//128*a^-1*d^-1*cot(c+d*x)*csc(c+d*x)+1//8*a^-1*d^-1*cot(c+d*x)^5*csc(c+d*x)^3+5//64*a^-1*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^8*csc(c+d*x)^11, x) == :(1//7*a^-1*d^-1*cot(c+d*x)^7+1//9*a^-1*d^-1*cot(c+d*x)^9+3//256*a^-1*d^-1*arctanh(cos(c+d*x))+-1//10*a^-1*d^-1*cot(c+d*x)^5*csc(c+d*x)^5+-1//32*a^-1*d^-1*csc(c+d*x)^5*cot(c+d*x)+1//16*a^-1*d^-1*cot(c+d*x)^3*csc(c+d*x)^5+1//128*a^-1*d^-1*csc(c+d*x)^3*cot(c+d*x)+3//256*a^-1*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^8*csc(c+d*x)^12, x) == :(-3//256*a^-1*d^-1*arctanh(cos(c+d*x))+-2//9*a^-1*d^-1*cot(c+d*x)^9+-1//7*a^-1*d^-1*cot(c+d*x)^7+-1//11*a^-1*d^-1*cot(c+d*x)^11+-3//256*a^-1*d^-1*cot(c+d*x)*csc(c+d*x)+-1//16*a^-1*d^-1*cot(c+d*x)^3*csc(c+d*x)^5+-1//128*a^-1*d^-1*csc(c+d*x)^3*cot(c+d*x)+1//10*a^-1*d^-1*cot(c+d*x)^5*csc(c+d*x)^5+1//32*a^-1*d^-1*csc(c+d*x)^5*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^8*sin(c+d*x)^5, x) == :(-3//128*x*a^-2+-4//9*a^-2*d^-1*cos(c+d*x)^9+-2//5*a^-2*d^-1*cos(c+d*x)^5+1//11*a^-2*d^-1*cos(c+d*x)^11+5//7*a^-2*d^-1*cos(c+d*x)^7+-3//128*a^-2*d^-1*cos(c+d*x)*sin(c+d*x)+-1//64*a^-2*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//5*a^-2*d^-1*cos(c+d*x)^5*sin(c+d*x)^5+1//8*a^-2*d^-1*cos(c+d*x)^5*sin(c+d*x)^3+1//16*a^-2*d^-1*cos(c+d*x)^5*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^8*sin(c+d*x)^4, x) == :(9//256*x*a^-2+-4//7*a^-2*d^-1*cos(c+d*x)^7+2//5*a^-2*d^-1*cos(c+d*x)^5+2//9*a^-2*d^-1*cos(c+d*x)^9+-3//16*a^-2*d^-1*cos(c+d*x)^5*sin(c+d*x)^3+-3//32*a^-2*d^-1*cos(c+d*x)^5*sin(c+d*x)+-1//10*a^-2*d^-1*cos(c+d*x)^5*sin(c+d*x)^5+3//128*a^-2*d^-1*cos(c+d*x)^3*sin(c+d*x)+9//256*a^-2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^8*sin(c+d*x)^3, x) == :(-3//64*x*a^-2+-2//5*a^-2*d^-1*cos(c+d*x)^5+-1//9*a^-2*d^-1*cos(c+d*x)^9+3//7*a^-2*d^-1*cos(c+d*x)^7+-3//64*a^-2*d^-1*cos(c+d*x)*sin(c+d*x)+-1//32*a^-2*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//4*a^-2*d^-1*cos(c+d*x)^5*sin(c+d*x)^3+1//8*a^-2*d^-1*cos(c+d*x)^5*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^8*sin(c+d*x)^2, x) == :(11//128*x*a^-2+-2//7*a^-2*d^-1*cos(c+d*x)^7+2//5*a^-2*d^-1*cos(c+d*x)^5+-11//48*a^-2*d^-1*cos(c+d*x)^5*sin(c+d*x)+-1//8*a^-2*d^-1*cos(c+d*x)^5*sin(c+d*x)^3+11//128*a^-2*d^-1*cos(c+d*x)*sin(c+d*x)+11//192*a^-2*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^8*sin(c+d*x), x) == :(-1//8*x*a^-2+-2//35*a^-2*d^-1*cos(c+d*x)^7+-1//5*d^-1*(a+a*sin(c+d*x))^-2*cos(c+d*x)^9+-1//8*a^-2*d^-1*cos(c+d*x)*sin(c+d*x)+-1//12*a^-2*d^-1*cos(c+d*x)^3*sin(c+d*x)+-1//15*a^-2*d^-1*cos(c+d*x)^5*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^8*csc(c+d*x), x) == :(-3//4*x*a^-2+a^-2*d^-1*cos(c+d*x)+-1*a^-2*d^-1*arctanh(cos(c+d*x))+-1//5*a^-2*d^-1*cos(c+d*x)^5+1//3*a^-2*d^-1*cos(c+d*x)^3+-3//4*a^-2*d^-1*cos(c+d*x)*sin(c+d*x)+-1//2*a^-2*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^8*csc(c+d*x)^2, x) == :(-9//8*x*a^-2+-1*a^-2*d^-1*cot(c+d*x)+-2*a^-2*d^-1*cos(c+d*x)+2*a^-2*d^-1*arctanh(cos(c+d*x))+-2//3*a^-2*d^-1*cos(c+d*x)^3+-1//4*a^-2*d^-1*sin(c+d*x)^3*cos(c+d*x)+1//8*a^-2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^8*csc(c+d*x)^3, x) == :(3*x*a^-2+(1/2)*a^-2*d^-1*arctanh(cos(c+d*x))+2*a^-2*d^-1*cot(c+d*x)+1//3*a^-2*d^-1*cos(c+d*x)^3+a^-2*d^-1*cos(c+d*x)*sin(c+d*x)+-1//2*a^-2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^8*csc(c+d*x)^4, x) == :(-1//2*x*a^-2+-3*a^-2*d^-1*arctanh(cos(c+d*x))+2*a^-2*d^-1*cos(c+d*x)+-1//3*a^-2*d^-1*cot(c+d*x)^3+a^-2*d^-1*cot(c+d*x)*csc(c+d*x)+-1//2*a^-2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^8*csc(c+d*x)^5, x) == :(-2*x*a^-2+-1*a^-2*d^-1*cos(c+d*x)+-2*a^-2*d^-1*cot(c+d*x)+2//3*a^-2*d^-1*cot(c+d*x)^3+9//8*a^-2*d^-1*arctanh(cos(c+d*x))+-1//4*a^-2*d^-1*csc(c+d*x)^3*cot(c+d*x)+1//8*a^-2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^8*csc(c+d*x)^6, x) == :(x*a^-2+a^-2*d^-1*cot(c+d*x)+-1//3*a^-2*d^-1*cot(c+d*x)^3+-1//5*a^-2*d^-1*cot(c+d*x)^5+3//4*a^-2*d^-1*arctanh(cos(c+d*x))+(1/2)*a^-2*d^-1*cot(c+d*x)^3*csc(c+d*x)+-3//4*a^-2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^8*csc(c+d*x)^7, x) == :(-7//16*a^-2*d^-1*arctanh(cos(c+d*x))+2//5*a^-2*d^-1*cot(c+d*x)^5+-1//4*a^-2*d^-1*cot(c+d*x)^3*csc(c+d*x)+-1//6*a^-2*d^-1*cot(c+d*x)^3*csc(c+d*x)^3+1//8*a^-2*d^-1*csc(c+d*x)^3*cot(c+d*x)+5//16*a^-2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^8*csc(c+d*x)^8, x) == :(-2//5*a^-2*d^-1*cot(c+d*x)^5+-1//7*a^-2*d^-1*cot(c+d*x)^7+1//8*a^-2*d^-1*arctanh(cos(c+d*x))+-7//12*a^-2*d^-1*csc(c+d*x)^3*cot(c+d*x)+1//3*a^-2*d^-1*csc(c+d*x)^5*cot(c+d*x)+1//8*a^-2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^8*csc(c+d*x)^9, x) == :(-11//128*a^-2*d^-1*arctanh(cos(c+d*x))+2//5*a^-2*d^-1*cot(c+d*x)^5+2//7*a^-2*d^-1*cot(c+d*x)^7+-11//128*a^-2*d^-1*cot(c+d*x)*csc(c+d*x)+-1//6*a^-2*d^-1*cot(c+d*x)^3*csc(c+d*x)^3+-1//8*a^-2*d^-1*cot(c+d*x)^3*csc(c+d*x)^5+1//16*a^-2*d^-1*csc(c+d*x)^5*cot(c+d*x)+7//64*a^-2*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^8*csc(c+d*x)^10, x) == :(-3//7*a^-2*d^-1*cot(c+d*x)^7+-2//5*a^-2*d^-1*cot(c+d*x)^5+-1//9*a^-2*d^-1*cot(c+d*x)^9+3//64*a^-2*d^-1*arctanh(cos(c+d*x))+-1//8*a^-2*d^-1*csc(c+d*x)^5*cot(c+d*x)+1//4*a^-2*d^-1*cot(c+d*x)^3*csc(c+d*x)^5+1//32*a^-2*d^-1*csc(c+d*x)^3*cot(c+d*x)+3//64*a^-2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^8*csc(c+d*x)^11, x) == :(-9//256*a^-2*d^-1*arctanh(cos(c+d*x))+2//5*a^-2*d^-1*cot(c+d*x)^5+2//9*a^-2*d^-1*cot(c+d*x)^9+4//7*a^-2*d^-1*cot(c+d*x)^7+-9//256*a^-2*d^-1*cot(c+d*x)*csc(c+d*x)+-3//128*a^-2*d^-1*csc(c+d*x)^3*cot(c+d*x)+-1//8*a^-2*d^-1*cot(c+d*x)^3*csc(c+d*x)^5+-1//10*a^-2*d^-1*cot(c+d*x)^3*csc(c+d*x)^7+3//80*a^-2*d^-1*csc(c+d*x)^7*cot(c+d*x)+9//160*a^-2*d^-1*csc(c+d*x)^5*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^8*csc(c+d*x)^12, x) == :(-5//7*a^-2*d^-1*cot(c+d*x)^7+-4//9*a^-2*d^-1*cot(c+d*x)^9+-2//5*a^-2*d^-1*cot(c+d*x)^5+-1//11*a^-2*d^-1*cot(c+d*x)^11+3//128*a^-2*d^-1*arctanh(cos(c+d*x))+-3//40*a^-2*d^-1*csc(c+d*x)^7*cot(c+d*x)+1//5*a^-2*d^-1*cot(c+d*x)^3*csc(c+d*x)^7+1//64*a^-2*d^-1*csc(c+d*x)^3*cot(c+d*x)+1//80*a^-2*d^-1*csc(c+d*x)^5*cot(c+d*x)+3//128*a^-2*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^8*sin(c+d*x)^3, x) == :(-29//128*x*a^-3+-4//3*a^-3*d^-1*cos(c+d*x)^3+-3//7*a^-3*d^-1*cos(c+d*x)^7+7//5*a^-3*d^-1*cos(c+d*x)^5+-29//128*a^-3*d^-1*cos(c+d*x)*sin(c+d*x)+1//8*a^-3*d^-1*cos(c+d*x)^3*sin(c+d*x)^5+29//48*a^-3*d^-1*cos(c+d*x)^3*sin(c+d*x)^3+29//64*a^-3*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^8*sin(c+d*x)^2, x) == :(5//16*x*a^-3+-1*a^-3*d^-1*cos(c+d*x)^5+1//7*a^-3*d^-1*cos(c+d*x)^7+4//3*a^-3*d^-1*cos(c+d*x)^3+-5//8*a^-3*d^-1*cos(c+d*x)^3*sin(c+d*x)+-1//2*a^-3*d^-1*cos(c+d*x)^3*sin(c+d*x)^3+5//16*a^-3*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^8*sin(c+d*x), x) == :(-7//16*x*a^-3+-7//30*a^-3*d^-1*cos(c+d*x)^5+-1//3*d^-1*(a+a*sin(c+d*x))^-3*cos(c+d*x)^9+-1//6*d^-1*(a^3+a^3*sin(c+d*x))^-1*cos(c+d*x)^7+-7//16*a^-3*d^-1*cos(c+d*x)*sin(c+d*x)+-7//24*a^-3*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^8*csc(c+d*x), x) == :(-13//8*x*a^-3+a^-3*d^-1*cos(c+d*x)+-1*a^-3*d^-1*cos(c+d*x)^3+-1*a^-3*d^-1*arctanh(cos(c+d*x))+-13//8*a^-3*d^-1*cos(c+d*x)*sin(c+d*x)+1//4*a^-3*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^8*csc(c+d*x)^2, x) == :((1/2)*x*a^-3+-1*a^-3*d^-1*cot(c+d*x)+-3*a^-3*d^-1*cos(c+d*x)+3*a^-3*d^-1*arctanh(cos(c+d*x))+1//3*a^-3*d^-1*cos(c+d*x)^3+3//2*a^-3*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^8*csc(c+d*x)^3, x) == :(5//2*x*a^-3+3*a^-3*d^-1*cos(c+d*x)+3*a^-3*d^-1*cot(c+d*x)+-5//2*a^-3*d^-1*arctanh(cos(c+d*x))+-1//2*a^-3*d^-1*cos(c+d*x)*sin(c+d*x)+-1//2*a^-3*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^8*csc(c+d*x)^4, x) == :(-3*x*a^-3+-1*a^-3*d^-1*cos(c+d*x)+-3*a^-3*d^-1*cot(c+d*x)+-1//2*a^-3*d^-1*arctanh(cos(c+d*x))+-1//3*a^-3*d^-1*cot(c+d*x)^3+3//2*a^-3*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^8*csc(c+d*x)^5, x) == :(x*a^-3+a^-3*d^-1*cot(c+d*x)^3+a^-3*d^-1*cot(c+d*x)+13//8*a^-3*d^-1*arctanh(cos(c+d*x))+-11//8*a^-3*d^-1*cot(c+d*x)*csc(c+d*x)+-1//4*a^-3*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^8*csc(c+d*x)^6, x) == :(-7//8*a^-3*d^-1*arctanh(cos(c+d*x))+-4//3*a^-3*d^-1*cot(c+d*x)^3+-1//5*a^-3*d^-1*cot(c+d*x)^5+1//8*a^-3*d^-1*cot(c+d*x)*csc(c+d*x)+3//4*a^-3*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^8*csc(c+d*x)^7, x) == :(3//5*a^-3*d^-1*cot(c+d*x)^5+4//3*a^-3*d^-1*cot(c+d*x)^3+7//16*a^-3*d^-1*arctanh(cos(c+d*x))+-17//24*a^-3*d^-1*csc(c+d*x)^3*cot(c+d*x)+-1//6*a^-3*d^-1*csc(c+d*x)^5*cot(c+d*x)+7//16*a^-3*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^8*csc(c+d*x)^8, x) == :(-1*a^-3*d^-1*cot(c+d*x)^5+-5//16*a^-3*d^-1*arctanh(cos(c+d*x))+-4//3*a^-3*d^-1*cot(c+d*x)^3+-1//7*a^-3*d^-1*cot(c+d*x)^7+(1/2)*a^-3*d^-1*csc(c+d*x)^5*cot(c+d*x)+-5//16*a^-3*d^-1*cot(c+d*x)*csc(c+d*x)+1//8*a^-3*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*cos(c+d*x)^8*csc(c+d*x)^9, x) == :(3//7*a^-3*d^-1*cot(c+d*x)^7+4//3*a^-3*d^-1*cot(c+d*x)^3+7//5*a^-3*d^-1*cot(c+d*x)^5+29//128*a^-3*d^-1*arctanh(cos(c+d*x))+-23//48*a^-3*d^-1*csc(c+d*x)^5*cot(c+d*x)+-1//8*a^-3*d^-1*csc(c+d*x)^7*cot(c+d*x)+29//128*a^-3*d^-1*cot(c+d*x)*csc(c+d*x)+29//192*a^-3*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate(sec(c+d*x)^2*sin(c+d*x)^4*(a+a*sin(c+d*x)), x) == :(-3//2*a*x+a*d^-1*sec(c+d*x)+2*a*d^-1*cos(c+d*x)+-1//3*a*d^-1*cos(c+d*x)^3+3//2*a*d^-1*tan(c+d*x)+-1//2*a*d^-1*sin(c+d*x)^2*tan(c+d*x))
@test integrate(sec(c+d*x)^2*sin(c+d*x)^3*(a+a*sin(c+d*x)), x) == :(-3//2*a*x+a*d^-1*cos(c+d*x)+a*d^-1*sec(c+d*x)+3//2*a*d^-1*tan(c+d*x)+-1//2*a*d^-1*sin(c+d*x)^2*tan(c+d*x))
@test integrate(sec(c+d*x)^2*sin(c+d*x)^2*(a+a*sin(c+d*x)), x) == :(-1*a*x+a*d^-1*cos(c+d*x)+a*d^-1*(1+-1*sin(c+d*x))^-1*cos(c+d*x))
@test integrate(sec(c+d*x)^2*(a+a*sin(c+d*x))*sin(c+d*x), x) == :(-1*a*x+a*d^-1*sec(c+d*x)+a*d^-1*tan(c+d*x))
@test integrate(sec(c+d*x)^2*(a+a*sin(c+d*x))*csc(c+d*x), x) == :(a*d^-1*sec(c+d*x)+a*d^-1*tan(c+d*x)+-1*a*d^-1*arctanh(cos(c+d*x)))
@test integrate(csc(c+d*x)^2*sec(c+d*x)^2*(a+a*sin(c+d*x)), x) == :(a*d^-1*sec(c+d*x)+a*d^-1*tan(c+d*x)+-1*a*d^-1*arctanh(cos(c+d*x))+-1*a*d^-1*cot(c+d*x))
@test integrate(csc(c+d*x)^3*sec(c+d*x)^2*(a+a*sin(c+d*x)), x) == :(a*d^-1*tan(c+d*x)+-1*a*d^-1*cot(c+d*x)+-3//2*a*d^-1*arctanh(cos(c+d*x))+3//2*a*d^-1*sec(c+d*x)+-1//2*a*d^-1*csc(c+d*x)^2*sec(c+d*x))
@test integrate(csc(c+d*x)^4*sec(c+d*x)^2*(a+a*sin(c+d*x)), x) == :(a*d^-1*tan(c+d*x)+-2*a*d^-1*cot(c+d*x)+-3//2*a*d^-1*arctanh(cos(c+d*x))+-1//3*a*d^-1*cot(c+d*x)^3+3//2*a*d^-1*sec(c+d*x)+-1//2*a*d^-1*csc(c+d*x)^2*sec(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*sec(c+d*x)^2*sin(c+d*x)^3, x) == :(-3*x*a^2+2*a^2*d^-1*sec(c+d*x)+3*a^2*d^-1*cos(c+d*x)+3*a^2*d^-1*tan(c+d*x)+-1//3*a^2*d^-1*cos(c+d*x)^3+-1*a^2*d^-1*sin(c+d*x)^2*tan(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*sec(c+d*x)^2*sin(c+d*x)^2, x) == :(-5//2*x*a^2+2*a^2*d^-1*cos(c+d*x)+(1/2)*a^2*d^-1*cos(c+d*x)*sin(c+d*x)+2*a^2*d^-1*(1+-1*sin(c+d*x))^-1*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*sec(c+d*x)^2*sin(c+d*x), x) == :(-2*x*a^2+d^-1*(a+a*sin(c+d*x))^2*sec(c+d*x)+2*a^2*d^-1*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*sec(c+d*x)^2*csc(c+d*x), x) == :(-1*a^2*d^-1*arctanh(cos(c+d*x))+2*a^2*d^-1*sec(c+d*x)+2*a^2*d^-1*tan(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*csc(c+d*x)^2*sec(c+d*x)^2, x) == :(-1*a^2*d^-1*cot(c+d*x)+-2*a^2*d^-1*arctanh(cos(c+d*x))+2*a^2*d^-1*sec(c+d*x)+2*a^2*d^-1*tan(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*csc(c+d*x)^3*sec(c+d*x)^2, x) == :(-2*a^2*d^-1*cot(c+d*x)+2*a^2*d^-1*tan(c+d*x)+-5//2*a^2*d^-1*arctanh(cos(c+d*x))+5//2*a^2*d^-1*sec(c+d*x)+-1//2*a^2*d^-1*csc(c+d*x)^2*sec(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*sec(c+d*x)^2*sin(c+d*x)^3, x) == :(-51//8*x*a^3+-1*a^3*d^-1*cos(c+d*x)^3+7*a^3*d^-1*cos(c+d*x)+4*a^3*d^-1*(1+-1*sin(c+d*x))^-1*cos(c+d*x)+1//4*a^3*d^-1*sin(c+d*x)^3*cos(c+d*x)+19//8*a^3*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*sec(c+d*x)^2*sin(c+d*x)^2, x) == :(-11//2*x*a^3+5*a^3*d^-1*cos(c+d*x)+-1//3*a^3*d^-1*cos(c+d*x)^3+4*a^3*d^-1*(1+-1*sin(c+d*x))^-1*cos(c+d*x)+3//2*a^3*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*sec(c+d*x)^2*sin(c+d*x), x) == :(-9//2*x*a^3+d^-1*(a+a*sin(c+d*x))^3*sec(c+d*x)+6*a^3*d^-1*cos(c+d*x)+3//2*a^3*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*sec(c+d*x)^2*csc(c+d*x), x) == :(-1*x*a^3+-1*a^3*d^-1*arctanh(cos(c+d*x))+4*a^3*d^-1*(1+-1*sin(c+d*x))^-1*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*csc(c+d*x)^2*sec(c+d*x)^2, x) == :(-1*a^3*d^-1*cot(c+d*x)+-3*a^3*d^-1*arctanh(cos(c+d*x))+4*a^3*d^-1*(1+-1*sin(c+d*x))^-1*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*csc(c+d*x)^3*sec(c+d*x)^2, x) == :(-3*a^3*d^-1*cot(c+d*x)+-9//2*a^3*d^-1*arctanh(cos(c+d*x))+4*a^3*d^-1*(1+-1*sin(c+d*x))^-1*cos(c+d*x)+-1//2*a^3*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*csc(c+d*x)^4*sec(c+d*x)^2, x) == :(-5*a^3*d^-1*cot(c+d*x)+-11//2*a^3*d^-1*arctanh(cos(c+d*x))+-1//3*a^3*d^-1*cot(c+d*x)^3+4*a^3*d^-1*(1+-1*sin(c+d*x))^-1*cos(c+d*x)+-3//2*a^3*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^2*sin(c+d*x)^4, x) == :(x*a^-1+a^-1*d^-1*cos(c+d*x)+-1*a^-1*d^-1*tan(c+d*x)+2*a^-1*d^-1*sec(c+d*x)+-1//3*a^-1*d^-1*sec(c+d*x)^3+1//3*a^-1*d^-1*tan(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^2*sin(c+d*x)^3, x) == :(-1*x*a^-1+a^-1*d^-1*tan(c+d*x)+-1*a^-1*d^-1*sec(c+d*x)+-1//3*a^-1*d^-1*tan(c+d*x)^3+1//3*a^-1*d^-1*sec(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^2*sin(c+d*x)^2, x) == :(a^-1*d^-1*sec(c+d*x)+-1//3*a^-1*d^-1*sec(c+d*x)^3+1//3*a^-1*d^-1*tan(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^2*sin(c+d*x), x) == :(-1//3*a^-1*d^-1*tan(c+d*x)^3+1//3*a^-1*d^-1*sec(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^2*csc(c+d*x), x) == :(a^-1*d^-1*sec(c+d*x)+-1*a^-1*d^-1*arctanh(cos(c+d*x))+-1*a^-1*d^-1*tan(c+d*x)+-1//3*a^-1*d^-1*tan(c+d*x)^3+1//3*a^-1*d^-1*sec(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-1*csc(c+d*x)^2*sec(c+d*x)^2, x) == :(a^-1*d^-1*arctanh(cos(c+d*x))+-1*a^-1*d^-1*cot(c+d*x)+-1*a^-1*d^-1*sec(c+d*x)+2*a^-1*d^-1*tan(c+d*x)+-1//3*a^-1*d^-1*sec(c+d*x)^3+1//3*a^-1*d^-1*tan(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-2*sec(c+d*x)^2*sin(c+d*x)^6, x) == :(-9//2*x*a^-2+-6*a^-2*d^-1*sec(c+d*x)+-2*a^-2*d^-1*cos(c+d*x)+2*a^-2*d^-1*sec(c+d*x)^3+-3//2*a^-2*d^-1*tan(c+d*x)^3+-2//5*a^-2*d^-1*sec(c+d*x)^5+9//2*a^-2*d^-1*tan(c+d*x)+9//10*a^-2*d^-1*tan(c+d*x)^5+-1//2*a^-2*d^-1*sin(c+d*x)^2*tan(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-2*sec(c+d*x)^2*sin(c+d*x)^5, x) == :(2*x*a^-2+a^-2*d^-1*cos(c+d*x)+-2*a^-2*d^-1*tan(c+d*x)+4*a^-2*d^-1*sec(c+d*x)+-5//3*a^-2*d^-1*sec(c+d*x)^3+-2//5*a^-2*d^-1*tan(c+d*x)^5+2//3*a^-2*d^-1*tan(c+d*x)^3+2//5*a^-2*d^-1*sec(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-2*sec(c+d*x)^2*sin(c+d*x)^4, x) == :(-1*x*a^-2+a^-2*d^-1*tan(c+d*x)+-2*a^-2*d^-1*sec(c+d*x)+-2//5*a^-2*d^-1*sec(c+d*x)^5+-1//3*a^-2*d^-1*tan(c+d*x)^3+2//5*a^-2*d^-1*tan(c+d*x)^5+4//3*a^-2*d^-1*sec(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-2*sec(c+d*x)^2*sin(c+d*x)^3, x) == :(a^-2*d^-1*sec(c+d*x)+-1*a^-2*d^-1*sec(c+d*x)^3+-2//5*a^-2*d^-1*tan(c+d*x)^5+2//5*a^-2*d^-1*sec(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-2*sec(c+d*x)^2*sin(c+d*x)^2, x) == :(-2//5*a^-2*d^-1*sec(c+d*x)^5+1//3*a^-2*d^-1*tan(c+d*x)^3+2//3*a^-2*d^-1*sec(c+d*x)^3+2//5*a^-2*d^-1*tan(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-2*sec(c+d*x)^2*sin(c+d*x), x) == :(-2//15*d^-1*(a^2+a^2*sin(c+d*x))^-1*sec(c+d*x)+1//5*d^-1*(a+a*sin(c+d*x))^-2*sec(c+d*x)+4//15*a^-2*d^-1*tan(c+d*x))
@test integrate((a+a*sin(c+d*x))^-2*sec(c+d*x)^2*csc(c+d*x), x) == :(a^-2*d^-1*sec(c+d*x)+-1*a^-2*d^-1*arctanh(cos(c+d*x))+-2*a^-2*d^-1*tan(c+d*x)+-4//3*a^-2*d^-1*tan(c+d*x)^3+-2//5*a^-2*d^-1*tan(c+d*x)^5+1//3*a^-2*d^-1*sec(c+d*x)^3+2//5*a^-2*d^-1*sec(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-2*csc(c+d*x)^2*sec(c+d*x)^2, x) == :(-1*a^-2*d^-1*cot(c+d*x)+-2*a^-2*d^-1*sec(c+d*x)+2*a^-2*d^-1*arctanh(cos(c+d*x))+4*a^-2*d^-1*tan(c+d*x)+-2//3*a^-2*d^-1*sec(c+d*x)^3+-2//5*a^-2*d^-1*sec(c+d*x)^5+2//5*a^-2*d^-1*tan(c+d*x)^5+5//3*a^-2*d^-1*tan(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-2*csc(c+d*x)^3*sec(c+d*x)^2, x) == :(-6*a^-2*d^-1*tan(c+d*x)+-2*a^-2*d^-1*tan(c+d*x)^3+2*a^-2*d^-1*cot(c+d*x)+-9//2*a^-2*d^-1*arctanh(cos(c+d*x))+-2//5*a^-2*d^-1*tan(c+d*x)^5+3//2*a^-2*d^-1*sec(c+d*x)^3+9//2*a^-2*d^-1*sec(c+d*x)+9//10*a^-2*d^-1*sec(c+d*x)^5+-1//2*a^-2*d^-1*csc(c+d*x)^2*sec(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-3*sec(c+d*x)^2*sin(c+d*x)^6, x) == :(3*x*a^-3+a^-3*d^-1*tan(c+d*x)^3+a^-3*d^-1*cos(c+d*x)+-5*a^-3*d^-1*sec(c+d*x)^3+-3*a^-3*d^-1*tan(c+d*x)+7*a^-3*d^-1*sec(c+d*x)+-4//7*a^-3*d^-1*sec(c+d*x)^7+-3//5*a^-3*d^-1*tan(c+d*x)^5+4//7*a^-3*d^-1*tan(c+d*x)^7+13//5*a^-3*d^-1*sec(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-3*sec(c+d*x)^2*sin(c+d*x)^5, x) == :(-1*x*a^-3+a^-3*d^-1*tan(c+d*x)+-3*a^-3*d^-1*sec(c+d*x)+-11//5*a^-3*d^-1*sec(c+d*x)^5+-4//7*a^-3*d^-1*tan(c+d*x)^7+-1//3*a^-3*d^-1*tan(c+d*x)^3+1//5*a^-3*d^-1*tan(c+d*x)^5+4//7*a^-3*d^-1*sec(c+d*x)^7+10//3*a^-3*d^-1*sec(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-3*sec(c+d*x)^2*sin(c+d*x)^4, x) == :(a^-3*d^-1*sec(c+d*x)+-2*a^-3*d^-1*sec(c+d*x)^3+-4//7*a^-3*d^-1*sec(c+d*x)^7+1//5*a^-3*d^-1*tan(c+d*x)^5+4//7*a^-3*d^-1*tan(c+d*x)^7+9//5*a^-3*d^-1*sec(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-3*sec(c+d*x)^2*sin(c+d*x)^3, x) == :(a^-3*d^-1*sec(c+d*x)^3+-7//5*a^-3*d^-1*sec(c+d*x)^5+-4//7*a^-3*d^-1*tan(c+d*x)^7+-3//5*a^-3*d^-1*tan(c+d*x)^5+4//7*a^-3*d^-1*sec(c+d*x)^7)
@test integrate((a+a*sin(c+d*x))^-3*sec(c+d*x)^2*sin(c+d*x)^2, x) == :(a^-3*d^-1*sec(c+d*x)^5+a^-3*d^-1*tan(c+d*x)^5+-4//7*a^-3*d^-1*sec(c+d*x)^7+-1//3*a^-3*d^-1*sec(c+d*x)^3+1//3*a^-3*d^-1*tan(c+d*x)^3+4//7*a^-3*d^-1*tan(c+d*x)^7)
@test integrate((a+a*sin(c+d*x))^-3*sec(c+d*x)^2*sin(c+d*x), x) == :(-3//35*d^-1*(a^3+a^3*sin(c+d*x))^-1*sec(c+d*x)+1//7*d^-1*(a+a*sin(c+d*x))^-3*sec(c+d*x)+6//35*a^-3*d^-1*tan(c+d*x)+-3//35*a^-1*d^-1*(a+a*sin(c+d*x))^-2*sec(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3*sec(c+d*x)^2*csc(c+d*x), x) == :(a^-3*d^-1*sec(c+d*x)+-1*a^-3*d^-1*arctanh(cos(c+d*x))+-3*a^-3*d^-1*tan(c+d*x)+-11//5*a^-3*d^-1*tan(c+d*x)^5+-10//3*a^-3*d^-1*tan(c+d*x)^3+-4//7*a^-3*d^-1*tan(c+d*x)^7+1//3*a^-3*d^-1*sec(c+d*x)^3+1//5*a^-3*d^-1*sec(c+d*x)^5+4//7*a^-3*d^-1*sec(c+d*x)^7)
@test integrate((a+a*sin(c+d*x))^-3*csc(c+d*x)^2*sec(c+d*x)^2, x) == :(-1*a^-3*d^-1*sec(c+d*x)^3+-1*a^-3*d^-1*cot(c+d*x)+-3*a^-3*d^-1*sec(c+d*x)+3*a^-3*d^-1*arctanh(cos(c+d*x))+5*a^-3*d^-1*tan(c+d*x)^3+7*a^-3*d^-1*tan(c+d*x)+-4//7*a^-3*d^-1*sec(c+d*x)^7+-3//5*a^-3*d^-1*sec(c+d*x)^5+4//7*a^-3*d^-1*tan(c+d*x)^7+13//5*a^-3*d^-1*tan(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^(1/2)*sec(c+d*x)^2*sin(c+d*x)^2, x) == :(4//63*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)+-2//9*a*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+-2//21*a^-1*d^-1*(a+a*sin(c+d*x))^3//2*cos(c+d*x)+2//9*d^-1*(a+a*sin(c+d*x))^(1/2)*sin(c+d*x)^3*cos(c+d*x)+2//63*a*d^-1*(a+a*sin(c+d*x))^-1//2*sin(c+d*x)^3*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^(1/2)*sec(c+d*x)^2*sin(c+d*x), x) == :(-4//105*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)+-18//35*a^-1*d^-1*(a+a*sin(c+d*x))^3//2*cos(c+d*x)+-16//105*a*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+2//7*a^-2*d^-1*(a+a*sin(c+d*x))^5//2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^(1/2)*sec(c+d*x)^2*csc(c+d*x), x) == :(-2*a^(1/2)*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+2//3*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)+2//3*a*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^(1/2)*csc(c+d*x)^2*sec(c+d*x)^2, x) == :(-1*a^(1/2)*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-1*d^-1*(a+a*sin(c+d*x))^(1/2)*cot(c+d*x)+3*a*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^(1/2)*csc(c+d*x)^3*sec(c+d*x)^2, x) == :(5//4*a^(1/2)*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-1//2*d^-1*(a+a*sin(c+d*x))^(1/2)*cot(c+d*x)*csc(c+d*x)+-1//4*a*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^(1/2)*csc(c+d*x)^4*sec(c+d*x)^2, x) == :(3//8*a^(1/2)*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-1//3*d^-1*(a+a*sin(c+d*x))^(1/2)*csc(c+d*x)^2*cot(c+d*x)+3//8*a*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//12*a*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^3//2*sec(c+d*x)^2*sin(c+d*x)^2, x) == :(-62//385*d^-1*(a+a*sin(c+d*x))^3//2*cos(c+d*x)+-62//165*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+2//11*d^-1*(a+a*sin(c+d*x))^3//2*sin(c+d*x)^3*cos(c+d*x)+124//1155*a*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)+-10//231*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*sin(c+d*x)^3*cos(c+d*x)+2//33*a*d^-1*(a+a*sin(c+d*x))^(1/2)*sin(c+d*x)^3*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^3//2*sec(c+d*x)^2*sin(c+d*x), x) == :(-4//105*d^-1*(a+a*sin(c+d*x))^3//2*cos(c+d*x)+-128//315*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+-32//315*a*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)+-22//63*a^-1*d^-1*(a+a*sin(c+d*x))^5//2*cos(c+d*x)+2//9*a^-2*d^-1*(a+a*sin(c+d*x))^7//2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^3//2*sec(c+d*x)^2*csc(c+d*x), x) == :(-2*a^3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+2//5*d^-1*(a+a*sin(c+d*x))^3//2*cos(c+d*x)+-2//5*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+2//5*a*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^3//2*csc(c+d*x)^2*sec(c+d*x)^2, x) == :(-1*d^-1*(a+a*sin(c+d*x))^3//2*cot(c+d*x)+-3*a^3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+5//3*a*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)+11//3*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^3//2*csc(c+d*x)^3*sec(c+d*x)^2, x) == :(1//4*a^3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-3//4*a*d^-1*(a+a*sin(c+d*x))^(1/2)*cot(c+d*x)+-1//2*d^-1*(a+a*sin(c+d*x))^3//2*cot(c+d*x)*csc(c+d*x)+13//4*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^3//2*csc(c+d*x)^4*sec(c+d*x)^2, x) == :(13//8*a^3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-1//3*d^-1*(a+a*sin(c+d*x))^3//2*csc(c+d*x)^2*cot(c+d*x)+5//24*a^2*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//4*a*d^-1*(a+a*sin(c+d*x))^(1/2)*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1//2*sec(c+d*x)^2*sin(c+d*x)^2, x) == :(-2//15*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+-2//35*a^-2*d^-1*(a+a*sin(c+d*x))^3//2*cos(c+d*x)+2//7*d^-1*(a+a*sin(c+d*x))^-1//2*sin(c+d*x)^3*cos(c+d*x)+4//105*a^-1*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1//2*sec(c+d*x)^2*sin(c+d*x), x) == :(4//15*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+-14//15*a^-1*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)+2//5*a^-2*d^-1*(a+a*sin(c+d*x))^3//2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1//2*sec(c+d*x)^2*csc(c+d*x), x) == :(-2*a^-1//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+2*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1//2*csc(c+d*x)^2*sec(c+d*x)^2, x) == :(a^-1//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-1*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1//2*csc(c+d*x)^3*sec(c+d*x)^2, x) == :(1//4*a^-1//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+1//4*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//2*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1//2*csc(c+d*x)^4*sec(c+d*x)^2, x) == :(1//8*a^-1//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+1//8*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//3*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^2*cot(c+d*x)+1//12*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3//2*sec(c+d*x)^2*sin(c+d*x)^2, x) == :(-2*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-4//5*a^-2*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x)+16//5*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+2//5*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*sin(c+d*x)^2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3//2*sec(c+d*x)^2*sin(c+d*x), x) == :(2*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-10//3*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)+2//3*a^-2*d^-1*(a+a*sin(c+d*x))^(1/2)*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3//2*sec(c+d*x)^2*csc(c+d*x), x) == :(-2*a^-3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+2*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-3//2*csc(c+d*x)^2*sec(c+d*x)^2, x) == :(3*a^-3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-1*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-2*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-3//2*csc(c+d*x)^3*sec(c+d*x)^2, x) == :(-11//4*a^-3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+2*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+5//4*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//2*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^-3//2*csc(c+d*x)^4*sec(c+d*x)^2, x) == :(23//8*a^-3//2*d^-1*arctanh(a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-2*2^(1/2)*a^-3//2*d^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sin(c+d*x))^-1//2*cos(c+d*x))+-9//8*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)+-1//3*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*csc(c+d*x)^2*cot(c+d*x)+7//12*a^-1*d^-1*(a+a*sin(c+d*x))^-1//2*cot(c+d*x)*csc(c+d*x))
@test integrate(sec(c+d*x)^4*sin(c+d*x)^6*(a+a*sin(c+d*x)), x) == :(5//2*a*x+-3*a*d^-1*cos(c+d*x)+-3*a*d^-1*sec(c+d*x)+-5//2*a*d^-1*tan(c+d*x)+1//3*a*d^-1*cos(c+d*x)^3+1//3*a*d^-1*sec(c+d*x)^3+5//6*a*d^-1*tan(c+d*x)^3+-1//2*a*d^-1*sin(c+d*x)^2*tan(c+d*x)^3)
@test integrate(sec(c+d*x)^4*sin(c+d*x)^5*(a+a*sin(c+d*x)), x) == :(5//2*a*x+-1*a*d^-1*cos(c+d*x)+-2*a*d^-1*sec(c+d*x)+-5//2*a*d^-1*tan(c+d*x)+1//3*a*d^-1*sec(c+d*x)^3+5//6*a*d^-1*tan(c+d*x)^3+-1//2*a*d^-1*sin(c+d*x)^2*tan(c+d*x)^3)
@test integrate(sec(c+d*x)^4*sin(c+d*x)^4*(a+a*sin(c+d*x)), x) == :(a*x+-1*a*d^-1*cos(c+d*x)+-1*a*d^-1*tan(c+d*x)+-2*a*d^-1*sec(c+d*x)+1//3*a*d^-1*sec(c+d*x)^3+1//3*a*d^-1*tan(c+d*x)^3)
@test integrate(sec(c+d*x)^4*sin(c+d*x)^3*(a+a*sin(c+d*x)), x) == :(a*x+-1*a*d^-1*sec(c+d*x)+-1*a*d^-1*tan(c+d*x)+1//3*a*d^-1*sec(c+d*x)^3+1//3*a*d^-1*tan(c+d*x)^3)
@test integrate(sec(c+d*x)^4*sin(c+d*x)^2*(a+a*sin(c+d*x)), x) == :(-1*a*d^-1*sec(c+d*x)+1//3*a*d^-1*sec(c+d*x)^3+1//3*a*d^-1*tan(c+d*x)^3)
@test integrate(sec(c+d*x)^4*(a+a*sin(c+d*x))*sin(c+d*x), x) == :(1//3*a*d^-1*sec(c+d*x)^3+1//3*a*d^-1*tan(c+d*x)^3)
@test integrate(sec(c+d*x)^4*(a+a*sin(c+d*x))*csc(c+d*x), x) == :(a*d^-1*sec(c+d*x)+a*d^-1*tan(c+d*x)+-1*a*d^-1*arctanh(cos(c+d*x))+1//3*a*d^-1*sec(c+d*x)^3+1//3*a*d^-1*tan(c+d*x)^3)
@test integrate(csc(c+d*x)^2*sec(c+d*x)^4*(a+a*sin(c+d*x)), x) == :(a*d^-1*sec(c+d*x)+-1*a*d^-1*arctanh(cos(c+d*x))+-1*a*d^-1*cot(c+d*x)+2*a*d^-1*tan(c+d*x)+1//3*a*d^-1*sec(c+d*x)^3+1//3*a*d^-1*tan(c+d*x)^3)
@test integrate(csc(c+d*x)^3*sec(c+d*x)^4*(a+a*sin(c+d*x)), x) == :(-1*a*d^-1*cot(c+d*x)+2*a*d^-1*tan(c+d*x)+-5//2*a*d^-1*arctanh(cos(c+d*x))+1//3*a*d^-1*tan(c+d*x)^3+5//2*a*d^-1*sec(c+d*x)+5//6*a*d^-1*sec(c+d*x)^3+-1//2*a*d^-1*csc(c+d*x)^2*sec(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^2*sec(c+d*x)^4*sin(c+d*x)^3, x) == :(2*x*a^2+-4//3*a^2*d^-1*cos(c+d*x)+-2*a^2*d^-1*(1+-1*sin(c+d*x))^-1*cos(c+d*x)+1//3*a^4*d^-1*(a+-1*a*sin(c+d*x))^-2*sin(c+d*x)^2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*sec(c+d*x)^4*sin(c+d*x)^2, x) == :(x*a^2+-5//3*a^2*d^-1*(1+-1*sin(c+d*x))^-1*cos(c+d*x)+1//3*a^4*d^-1*(a+-1*a*sin(c+d*x))^-2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*sec(c+d*x)^4*sin(c+d*x), x) == :(-2//3*a^2*d^-1*sec(c+d*x)+-2//3*a^2*d^-1*tan(c+d*x)+1//3*d^-1*(a+a*sin(c+d*x))^2*sec(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^2*sec(c+d*x)^4*csc(c+d*x), x) == :(-1*a^2*d^-1*arctanh(cos(c+d*x))+1//3*a^4*d^-1*(a+-1*a*sin(c+d*x))^-2*cos(c+d*x)+4//3*a^2*d^-1*(1+-1*sin(c+d*x))^-1*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*csc(c+d*x)^2*sec(c+d*x)^4, x) == :(-2*a^2*d^-1*arctanh(cos(c+d*x))+-10//3*a^2*d^-1*cot(c+d*x)+2*a^2*d^-1*(1+-1*sin(c+d*x))^-1*cot(c+d*x)+1//3*a^4*d^-1*(a+-1*a*sin(c+d*x))^-2*cot(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*csc(c+d*x)^3*sec(c+d*x)^4, x) == :(-16//3*a^2*d^-1*cot(c+d*x)+-7//2*a^2*d^-1*arctanh(cos(c+d*x))+-7//2*a^2*d^-1*cot(c+d*x)*csc(c+d*x)+1//3*a^4*d^-1*(a+-1*a*sin(c+d*x))^-2*cot(c+d*x)*csc(c+d*x)+8//3*a^2*d^-1*(1+-1*sin(c+d*x))^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*sec(c+d*x)^4*sin(c+d*x)^4, x) == :(17//2*x*a^3+-6*a^3*d^-1*cos(c+d*x)+1//3*a^3*d^-1*cos(c+d*x)^3+-25//3*a^3*d^-1*(1+-1*sin(c+d*x))^-1*cos(c+d*x)+-3//2*a^3*d^-1*cos(c+d*x)*sin(c+d*x)+2//3*a^3*d^-1*(1+-1*sin(c+d*x))^-2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*sec(c+d*x)^4*sin(c+d*x)^3, x) == :(11//2*x*a^3+-3*a^3*d^-1*cos(c+d*x)+-19//3*a^3*d^-1*(1+-1*sin(c+d*x))^-1*cos(c+d*x)+-1//2*a^3*d^-1*cos(c+d*x)*sin(c+d*x)+2//3*a^3*d^-1*(1+-1*sin(c+d*x))^-2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*sec(c+d*x)^4*sin(c+d*x)^2, x) == :(3*x*a^3+-3*a^3*d^-1*cos(c+d*x)+1//3*d^-1*(a+a*sin(c+d*x))^3*sec(c+d*x)^3+-2*a^5*d^-1*(a+-1*a*sin(c+d*x))^-2*cos(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^3*sec(c+d*x)^4*sin(c+d*x), x) == :(x*a^3+1//3*d^-1*(a+a*sin(c+d*x))^3*sec(c+d*x)^3+-2*a^5*d^-1*(a^2+-1*a^2*sin(c+d*x))^-1*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*sec(c+d*x)^4*csc(c+d*x), x) == :(-1*a^3*d^-1*arctanh(cos(c+d*x))+2//3*a^3*d^-1*(1+-1*sin(c+d*x))^-2*cos(c+d*x)+5//3*a^3*d^-1*(1+-1*sin(c+d*x))^-1*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*csc(c+d*x)^2*sec(c+d*x)^4, x) == :(-1*a^3*d^-1*cot(c+d*x)+-3*a^3*d^-1*arctanh(cos(c+d*x))+2//3*a^3*d^-1*(1+-1*sin(c+d*x))^-2*cos(c+d*x)+11//3*a^3*d^-1*(1+-1*sin(c+d*x))^-1*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*csc(c+d*x)^3*sec(c+d*x)^4, x) == :(-3*a^3*d^-1*cot(c+d*x)+-11//2*a^3*d^-1*arctanh(cos(c+d*x))+-1//2*a^3*d^-1*cot(c+d*x)*csc(c+d*x)+2//3*a^3*d^-1*(1+-1*sin(c+d*x))^-2*cos(c+d*x)+17//3*a^3*d^-1*(1+-1*sin(c+d*x))^-1*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*csc(c+d*x)^4*sec(c+d*x)^4, x) == :(-6*a^3*d^-1*cot(c+d*x)+-17//2*a^3*d^-1*arctanh(cos(c+d*x))+-1//3*a^3*d^-1*cot(c+d*x)^3+-3//2*a^3*d^-1*cot(c+d*x)*csc(c+d*x)+2//3*a^3*d^-1*(1+-1*sin(c+d*x))^-2*cos(c+d*x)+23//3*a^3*d^-1*(1+-1*sin(c+d*x))^-1*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^4*sec(c+d*x)^4*sin(c+d*x)^4, x) == :(163//8*x*a^4+-16*a^4*d^-1*cos(c+d*x)+4//3*a^4*d^-1*cos(c+d*x)^3+-56//3*a^4*d^-1*(1+-1*sin(c+d*x))^-1*cos(c+d*x)+-35//8*a^4*d^-1*cos(c+d*x)*sin(c+d*x)+-1//4*a^4*d^-1*sin(c+d*x)^3*cos(c+d*x)+4//3*a^4*d^-1*(1+-1*sin(c+d*x))^-2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^4*sec(c+d*x)^4*sin(c+d*x)^2, x) == :(17//2*x*a^4+-4*a^4*d^-1*cos(c+d*x)+-32//3*a^4*d^-1*(1+-1*sin(c+d*x))^-1*cos(c+d*x)+-1//2*a^4*d^-1*cos(c+d*x)*sin(c+d*x)+4//3*a^4*d^-1*(1+-1*sin(c+d*x))^-2*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^4*sin(c+d*x)^6, x) == :(-1*x*a^-1+a^-1*d^-1*sec(c+d*x)^3+a^-1*d^-1*tan(c+d*x)+-1*a^-1*d^-1*cos(c+d*x)+-3*a^-1*d^-1*sec(c+d*x)+-1//3*a^-1*d^-1*tan(c+d*x)^3+-1//5*a^-1*d^-1*sec(c+d*x)^5+1//5*a^-1*d^-1*tan(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^4*sin(c+d*x)^5, x) == :(x*a^-1+a^-1*d^-1*sec(c+d*x)+-1*a^-1*d^-1*tan(c+d*x)+-2//3*a^-1*d^-1*sec(c+d*x)^3+-1//5*a^-1*d^-1*tan(c+d*x)^5+1//3*a^-1*d^-1*tan(c+d*x)^3+1//5*a^-1*d^-1*sec(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^4*sin(c+d*x)^4, x) == :(-1*a^-1*d^-1*sec(c+d*x)+-1//5*a^-1*d^-1*sec(c+d*x)^5+1//5*a^-1*d^-1*tan(c+d*x)^5+2//3*a^-1*d^-1*sec(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^4*sin(c+d*x)^3, x) == :(-1//3*a^-1*d^-1*sec(c+d*x)^3+-1//5*a^-1*d^-1*tan(c+d*x)^5+1//5*a^-1*d^-1*sec(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^4*sin(c+d*x)^2, x) == :(-1//5*a^-1*d^-1*sec(c+d*x)^5+1//3*a^-1*d^-1*sec(c+d*x)^3+1//3*a^-1*d^-1*tan(c+d*x)^3+1//5*a^-1*d^-1*tan(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^4*sin(c+d*x), x) == :(-1//3*a^-1*d^-1*tan(c+d*x)^3+-1//5*a^-1*d^-1*tan(c+d*x)^5+1//5*a^-1*d^-1*sec(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^4*csc(c+d*x), x) == :(a^-1*d^-1*sec(c+d*x)+-1*a^-1*d^-1*arctanh(cos(c+d*x))+-1*a^-1*d^-1*tan(c+d*x)+-2//3*a^-1*d^-1*tan(c+d*x)^3+-1//5*a^-1*d^-1*tan(c+d*x)^5+1//3*a^-1*d^-1*sec(c+d*x)^3+1//5*a^-1*d^-1*sec(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-1*csc(c+d*x)^2*sec(c+d*x)^4, x) == :(a^-1*d^-1*tan(c+d*x)^3+a^-1*d^-1*arctanh(cos(c+d*x))+-1*a^-1*d^-1*cot(c+d*x)+-1*a^-1*d^-1*sec(c+d*x)+3*a^-1*d^-1*tan(c+d*x)+-1//3*a^-1*d^-1*sec(c+d*x)^3+-1//5*a^-1*d^-1*sec(c+d*x)^5+1//5*a^-1*d^-1*tan(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-2*sec(c+d*x)^4*sin(c+d*x)^7, x) == :(-2*x*a^-2+-1*a^-2*d^-1*cos(c+d*x)+-5*a^-2*d^-1*sec(c+d*x)+2*a^-2*d^-1*tan(c+d*x)+3*a^-2*d^-1*sec(c+d*x)^3+-7//5*a^-2*d^-1*sec(c+d*x)^5+-2//3*a^-2*d^-1*tan(c+d*x)^3+-2//7*a^-2*d^-1*tan(c+d*x)^7+2//5*a^-2*d^-1*tan(c+d*x)^5+2//7*a^-2*d^-1*sec(c+d*x)^7)
@test integrate((a+a*sin(c+d*x))^-2*sec(c+d*x)^4*sin(c+d*x)^6, x) == :(x*a^-2+-1*a^-2*d^-1*tan(c+d*x)+-2*a^-2*d^-1*sec(c+d*x)^3+2*a^-2*d^-1*sec(c+d*x)+-2//7*a^-2*d^-1*sec(c+d*x)^7+-1//5*a^-2*d^-1*tan(c+d*x)^5+1//3*a^-2*d^-1*tan(c+d*x)^3+2//7*a^-2*d^-1*tan(c+d*x)^7+6//5*a^-2*d^-1*sec(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-2*sec(c+d*x)^4*sin(c+d*x)^5, x) == :(-1*a^-2*d^-1*sec(c+d*x)^5+-1*a^-2*d^-1*sec(c+d*x)+-2//7*a^-2*d^-1*tan(c+d*x)^7+2//7*a^-2*d^-1*sec(c+d*x)^7+4//3*a^-2*d^-1*sec(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-2*sec(c+d*x)^4*sin(c+d*x)^4, x) == :(-2//3*a^-2*d^-1*sec(c+d*x)^3+-2//7*a^-2*d^-1*sec(c+d*x)^7+1//5*a^-2*d^-1*tan(c+d*x)^5+2//7*a^-2*d^-1*tan(c+d*x)^7+4//5*a^-2*d^-1*sec(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-2*sec(c+d*x)^4*sin(c+d*x)^3, x) == :(-3//5*a^-2*d^-1*sec(c+d*x)^5+-2//5*a^-2*d^-1*tan(c+d*x)^5+-2//7*a^-2*d^-1*tan(c+d*x)^7+1//3*a^-2*d^-1*sec(c+d*x)^3+2//7*a^-2*d^-1*sec(c+d*x)^7)
@test integrate((a+a*sin(c+d*x))^-2*sec(c+d*x)^4*sin(c+d*x)^2, x) == :(-2//7*a^-2*d^-1*sec(c+d*x)^7+1//3*a^-2*d^-1*tan(c+d*x)^3+2//5*a^-2*d^-1*sec(c+d*x)^5+2//7*a^-2*d^-1*tan(c+d*x)^7+3//5*a^-2*d^-1*tan(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-2*sec(c+d*x)^4*sin(c+d*x), x) == :(-2//35*d^-1*(a^2+a^2*sin(c+d*x))^-1*sec(c+d*x)^3+1//7*d^-1*(a+a*sin(c+d*x))^-2*sec(c+d*x)^3+8//35*a^-2*d^-1*tan(c+d*x)+8//105*a^-2*d^-1*tan(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-2*sec(c+d*x)^4*csc(c+d*x), x) == :(a^-2*d^-1*sec(c+d*x)+-1*a^-2*d^-1*arctanh(cos(c+d*x))+-2*a^-2*d^-1*tan(c+d*x)^3+-2*a^-2*d^-1*tan(c+d*x)+-6//5*a^-2*d^-1*tan(c+d*x)^5+-2//7*a^-2*d^-1*tan(c+d*x)^7+1//3*a^-2*d^-1*sec(c+d*x)^3+1//5*a^-2*d^-1*sec(c+d*x)^5+2//7*a^-2*d^-1*sec(c+d*x)^7)
@test integrate((a+a*sin(c+d*x))^-2*csc(c+d*x)^2*sec(c+d*x)^4, x) == :(-1*a^-2*d^-1*cot(c+d*x)+-2*a^-2*d^-1*sec(c+d*x)+2*a^-2*d^-1*arctanh(cos(c+d*x))+3*a^-2*d^-1*tan(c+d*x)^3+5*a^-2*d^-1*tan(c+d*x)+-2//3*a^-2*d^-1*sec(c+d*x)^3+-2//5*a^-2*d^-1*sec(c+d*x)^5+-2//7*a^-2*d^-1*sec(c+d*x)^7+2//7*a^-2*d^-1*tan(c+d*x)^7+7//5*a^-2*d^-1*tan(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-2*csc(c+d*x)^3*sec(c+d*x)^4, x) == :(-8*a^-2*d^-1*tan(c+d*x)+-4*a^-2*d^-1*tan(c+d*x)^3+2*a^-2*d^-1*cot(c+d*x)+-11//2*a^-2*d^-1*arctanh(cos(c+d*x))+-8//5*a^-2*d^-1*tan(c+d*x)^5+-2//7*a^-2*d^-1*tan(c+d*x)^7+11//2*a^-2*d^-1*sec(c+d*x)+11//6*a^-2*d^-1*sec(c+d*x)^3+11//10*a^-2*d^-1*sec(c+d*x)^5+11//14*a^-2*d^-1*sec(c+d*x)^7+-1//2*a^-2*d^-1*csc(c+d*x)^2*sec(c+d*x)^7)
@test integrate((a+a*sin(c+d*x))^-3*sec(c+d*x)^4*sin(c+d*x)^7, x) == :(x*a^-3+-1*a^-3*d^-1*tan(c+d*x)+3*a^-3*d^-1*sec(c+d*x)+-15//7*a^-3*d^-1*sec(c+d*x)^7+-13//3*a^-3*d^-1*sec(c+d*x)^3+-4//9*a^-3*d^-1*tan(c+d*x)^9+-1//5*a^-3*d^-1*tan(c+d*x)^5+1//3*a^-3*d^-1*tan(c+d*x)^3+1//7*a^-3*d^-1*tan(c+d*x)^7+4//9*a^-3*d^-1*sec(c+d*x)^9+21//5*a^-3*d^-1*sec(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-3*sec(c+d*x)^4*sin(c+d*x)^6, x) == :(-1*a^-3*d^-1*sec(c+d*x)+-3*a^-3*d^-1*sec(c+d*x)^5+-4//9*a^-3*d^-1*sec(c+d*x)^9+1//7*a^-3*d^-1*tan(c+d*x)^7+4//9*a^-3*d^-1*tan(c+d*x)^9+7//3*a^-3*d^-1*sec(c+d*x)^3+13//7*a^-3*d^-1*sec(c+d*x)^7)
@test integrate((a+a*sin(c+d*x))^-3*sec(c+d*x)^4*sin(c+d*x)^5, x) == :(-1*a^-3*d^-1*sec(c+d*x)^3+2*a^-3*d^-1*sec(c+d*x)^5+-11//7*a^-3*d^-1*sec(c+d*x)^7+-4//9*a^-3*d^-1*tan(c+d*x)^9+-3//7*a^-3*d^-1*tan(c+d*x)^7+4//9*a^-3*d^-1*sec(c+d*x)^9)
@test integrate((a+a*sin(c+d*x))^-3*sec(c+d*x)^4*sin(c+d*x)^4, x) == :(-6//5*a^-3*d^-1*sec(c+d*x)^5+-4//9*a^-3*d^-1*sec(c+d*x)^9+1//3*a^-3*d^-1*sec(c+d*x)^3+1//5*a^-3*d^-1*tan(c+d*x)^5+4//9*a^-3*d^-1*tan(c+d*x)^9+5//7*a^-3*d^-1*tan(c+d*x)^7+9//7*a^-3*d^-1*sec(c+d*x)^7)
@test integrate((a+a*sin(c+d*x))^-3*sec(c+d*x)^4*sin(c+d*x)^3, x) == :(-1*a^-3*d^-1*sec(c+d*x)^7+-1*a^-3*d^-1*tan(c+d*x)^7+-4//9*a^-3*d^-1*tan(c+d*x)^9+-3//5*a^-3*d^-1*tan(c+d*x)^5+3//5*a^-3*d^-1*sec(c+d*x)^5+4//9*a^-3*d^-1*sec(c+d*x)^9)
@test integrate((a+a*sin(c+d*x))^-3*sec(c+d*x)^4*sin(c+d*x)^2, x) == :(-4//9*a^-3*d^-1*sec(c+d*x)^9+-1//5*a^-3*d^-1*sec(c+d*x)^5+1//3*a^-3*d^-1*tan(c+d*x)^3+4//9*a^-3*d^-1*tan(c+d*x)^9+5//7*a^-3*d^-1*sec(c+d*x)^7+6//5*a^-3*d^-1*tan(c+d*x)^5+9//7*a^-3*d^-1*tan(c+d*x)^7)
@test integrate((a+a*sin(c+d*x))^-3*sec(c+d*x)^4*sin(c+d*x), x) == :(-1//21*d^-1*(a^3+a^3*sin(c+d*x))^-1*sec(c+d*x)^3+1//9*d^-1*(a+a*sin(c+d*x))^-3*sec(c+d*x)^3+4//21*a^-3*d^-1*tan(c+d*x)+4//63*a^-3*d^-1*tan(c+d*x)^3+-1//21*a^-1*d^-1*(a+a*sin(c+d*x))^-2*sec(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-3*sec(c+d*x)^4*csc(c+d*x), x) == :(a^-3*d^-1*sec(c+d*x)+-1*a^-3*d^-1*arctanh(cos(c+d*x))+-3*a^-3*d^-1*tan(c+d*x)+-21//5*a^-3*d^-1*tan(c+d*x)^5+-15//7*a^-3*d^-1*tan(c+d*x)^7+-13//3*a^-3*d^-1*tan(c+d*x)^3+-4//9*a^-3*d^-1*tan(c+d*x)^9+1//3*a^-3*d^-1*sec(c+d*x)^3+1//5*a^-3*d^-1*sec(c+d*x)^5+1//7*a^-3*d^-1*sec(c+d*x)^7+4//9*a^-3*d^-1*sec(c+d*x)^9)
@test integrate((a+a*sin(c+d*x))^-3*csc(c+d*x)^2*sec(c+d*x)^4, x) == :(-1*a^-3*d^-1*sec(c+d*x)^3+-1*a^-3*d^-1*cot(c+d*x)+-3*a^-3*d^-1*sec(c+d*x)+3*a^-3*d^-1*arctanh(cos(c+d*x))+8*a^-3*d^-1*tan(c+d*x)+-4//9*a^-3*d^-1*sec(c+d*x)^9+-3//5*a^-3*d^-1*sec(c+d*x)^5+-3//7*a^-3*d^-1*sec(c+d*x)^7+4//9*a^-3*d^-1*tan(c+d*x)^9+17//7*a^-3*d^-1*tan(c+d*x)^7+22//3*a^-3*d^-1*tan(c+d*x)^3+28//5*a^-3*d^-1*tan(c+d*x)^5)
@test integrate((a+a*sin(c+d*x))^-4*sec(c+d*x)^4*sin(c+d*x)^4, x) == :(-16//7*a^-4*d^-1*sec(c+d*x)^7+-8//11*a^-4*d^-1*sec(c+d*x)^11+1//5*a^-4*d^-1*tan(c+d*x)^5+4//5*a^-4*d^-1*sec(c+d*x)^5+8//11*a^-4*d^-1*tan(c+d*x)^11+9//7*a^-4*d^-1*tan(c+d*x)^7+16//9*a^-4*d^-1*tan(c+d*x)^9+20//9*a^-4*d^-1*sec(c+d*x)^9)
@test integrate((a+a*sin(c+d*x))^-4*sec(c+d*x)^4*sin(c+d*x)^3, x) == :(-20//9*a^-4*d^-1*tan(c+d*x)^9+-16//7*a^-4*d^-1*tan(c+d*x)^7+-16//9*a^-4*d^-1*sec(c+d*x)^9+-8//11*a^-4*d^-1*tan(c+d*x)^11+-4//5*a^-4*d^-1*tan(c+d*x)^5+-1//5*a^-4*d^-1*sec(c+d*x)^5+8//11*a^-4*d^-1*sec(c+d*x)^11+9//7*a^-4*d^-1*sec(c+d*x)^7)
@test integrate(sec(c+d*x)^5*sin(c+d*x)^6*(a+a*sin(c+d*x)), x) == :(-1*a*d^-1*sin(c+d*x)+-39//16*a*d^-1*log(1+-1*sin(c+d*x))+-9//16*a*d^-1*log(1+sin(c+d*x))+-5//4*a^2*d^-1*(a+-1*a*sin(c+d*x))^-1+-1//2*a*d^-1*sin(c+d*x)^2+-1//8*a^2*d^-1*(a+a*sin(c+d*x))^-1+1//8*a^3*d^-1*(a+-1*a*sin(c+d*x))^-2)
@test integrate(sec(c+d*x)^5*sin(c+d*x)^5*(a+a*sin(c+d*x)), x) == :(-1*a*d^-1*sin(c+d*x)+-1*a^2*d^-1*(a+-1*a*sin(c+d*x))^-1+-23//16*a*d^-1*log(1+-1*sin(c+d*x))+1//8*a^2*d^-1*(a+a*sin(c+d*x))^-1+1//8*a^3*d^-1*(a+-1*a*sin(c+d*x))^-2+7//16*a*d^-1*log(1+sin(c+d*x)))
@test integrate(sec(c+d*x)^5*sin(c+d*x)^4*(a+a*sin(c+d*x)), x) == :(-11//16*a*d^-1*log(1+-1*sin(c+d*x))+-5//16*a*d^-1*log(1+sin(c+d*x))+-3//4*a^2*d^-1*(a+-1*a*sin(c+d*x))^-1+-1//8*a^2*d^-1*(a+a*sin(c+d*x))^-1+1//8*a^3*d^-1*(a+-1*a*sin(c+d*x))^-2)
@test integrate(sec(c+d*x)^5*sin(c+d*x)^3*(a+a*sin(c+d*x)), x) == :(-1//2*a^2*d^-1*(a+-1*a*sin(c+d*x))^-1+1//8*a^2*d^-1*(a+a*sin(c+d*x))^-1+1//8*a^3*d^-1*(a+-1*a*sin(c+d*x))^-2+3//8*a*d^-1*arctanh(sin(c+d*x)))
@test integrate(sec(c+d*x)^5*sin(c+d*x)^2*(a+a*sin(c+d*x)), x) == :(-1//4*a^2*d^-1*(a+-1*a*sin(c+d*x))^-1+-1//8*a*d^-1*arctanh(sin(c+d*x))+-1//8*a^2*d^-1*(a+a*sin(c+d*x))^-1+1//8*a^3*d^-1*(a+-1*a*sin(c+d*x))^-2)
@test integrate(sec(c+d*x)^5*(a+a*sin(c+d*x))*sin(c+d*x), x) == :(-1//8*a*d^-1*arctanh(sin(c+d*x))+1//8*a^2*d^-1*(a+a*sin(c+d*x))^-1+1//8*a^3*d^-1*(a+-1*a*sin(c+d*x))^-2)
@test integrate(sec(c+d*x)^5*(a+a*sin(c+d*x))*csc(c+d*x), x) == :(a*d^-1*log(sin(c+d*x))+(1/2)*a^2*d^-1*(a+-1*a*sin(c+d*x))^-1+-11//16*a*d^-1*log(1+-1*sin(c+d*x))+-5//16*a*d^-1*log(1+sin(c+d*x))+1//8*a^2*d^-1*(a+a*sin(c+d*x))^-1+1//8*a^3*d^-1*(a+-1*a*sin(c+d*x))^-2)
@test integrate(csc(c+d*x)^2*sec(c+d*x)^5*(a+a*sin(c+d*x)), x) == :(a*d^-1*log(sin(c+d*x))+-1*a*d^-1*csc(c+d*x)+-23//16*a*d^-1*log(1+-1*sin(c+d*x))+-1//8*a^2*d^-1*(a+a*sin(c+d*x))^-1+1//8*a^3*d^-1*(a+-1*a*sin(c+d*x))^-2+3//4*a^2*d^-1*(a+-1*a*sin(c+d*x))^-1+7//16*a*d^-1*log(1+sin(c+d*x)))
@test integrate(csc(c+d*x)^3*sec(c+d*x)^5*(a+a*sin(c+d*x)), x) == :(a^2*d^-1*(a+-1*a*sin(c+d*x))^-1+-1*a*d^-1*csc(c+d*x)+3*a*d^-1*log(sin(c+d*x))+-39//16*a*d^-1*log(1+-1*sin(c+d*x))+-9//16*a*d^-1*log(1+sin(c+d*x))+-1//2*a*d^-1*csc(c+d*x)^2+1//8*a^2*d^-1*(a+a*sin(c+d*x))^-1+1//8*a^3*d^-1*(a+-1*a*sin(c+d*x))^-2)
@test integrate(csc(c+d*x)^4*sec(c+d*x)^5*(a+a*sin(c+d*x)), x) == :(-3*a*d^-1*csc(c+d*x)+3*a*d^-1*log(sin(c+d*x))+-59//16*a*d^-1*log(1+-1*sin(c+d*x))+-1//2*a*d^-1*csc(c+d*x)^2+-1//3*a*d^-1*csc(c+d*x)^3+-1//8*a^2*d^-1*(a+a*sin(c+d*x))^-1+1//8*a^3*d^-1*(a+-1*a*sin(c+d*x))^-2+5//4*a^2*d^-1*(a+-1*a*sin(c+d*x))^-1+11//16*a*d^-1*log(1+sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^2*sec(c+d*x)^5*sin(c+d*x)^5, x) == :(-2*a^2*d^-1*sin(c+d*x)+-31//8*a^2*d^-1*log(1+-1*sin(c+d*x))+-9//4*a^3*d^-1*(a+-1*a*sin(c+d*x))^-1+-1//2*a^2*d^-1*sin(c+d*x)^2+-1//8*a^2*d^-1*log(1+sin(c+d*x))+1//4*a^4*d^-1*(a+-1*a*sin(c+d*x))^-2)
@test integrate((a+a*sin(c+d*x))^2*sec(c+d*x)^5*sin(c+d*x)^4, x) == :(-1*a^2*d^-1*sin(c+d*x)+-17//8*a^2*d^-1*log(1+-1*sin(c+d*x))+-7//4*a^3*d^-1*(a+-1*a*sin(c+d*x))^-1+1//4*a^4*d^-1*(a+-1*a*sin(c+d*x))^-2+1//8*a^2*d^-1*log(1+sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^2*sec(c+d*x)^5*sin(c+d*x)^3, x) == :(-7//8*a^2*d^-1*log(1+-1*sin(c+d*x))+-5//4*a^3*d^-1*(a+-1*a*sin(c+d*x))^-1+-1//8*a^2*d^-1*log(1+sin(c+d*x))+1//4*a^4*d^-1*(a+-1*a*sin(c+d*x))^-2)
@test integrate((a+a*sin(c+d*x))^2*sec(c+d*x)^5*sin(c+d*x)^2, x) == :(-3//4*a^3*d^-1*(a+-1*a*sin(c+d*x))^-1+1//4*a^2*d^-1*arctanh(sin(c+d*x))+1//4*a^4*d^-1*(a+-1*a*sin(c+d*x))^-2)
@test integrate((a+a*sin(c+d*x))^2*sec(c+d*x)^5*sin(c+d*x), x) == :(-1//4*a^2*d^-1*arctanh(sin(c+d*x))+-1//4*a^3*d^-1*(a+-1*a*sin(c+d*x))^-1+1//4*a^4*d^-1*(a+-1*a*sin(c+d*x))^-2)
@test integrate((a+a*sin(c+d*x))^2*sec(c+d*x)^5*csc(c+d*x), x) == :(a^2*d^-1*log(sin(c+d*x))+-7//8*a^2*d^-1*log(1+-1*sin(c+d*x))+-1//8*a^2*d^-1*log(1+sin(c+d*x))+1//4*a^4*d^-1*(a+-1*a*sin(c+d*x))^-2+3//4*a^3*d^-1*(a+-1*a*sin(c+d*x))^-1)
@test integrate((a+a*sin(c+d*x))^2*csc(c+d*x)^2*sec(c+d*x)^5, x) == :(-1*a^2*d^-1*csc(c+d*x)+2*a^2*d^-1*log(sin(c+d*x))+-17//8*a^2*d^-1*log(1+-1*sin(c+d*x))+1//4*a^4*d^-1*(a+-1*a*sin(c+d*x))^-2+1//8*a^2*d^-1*log(1+sin(c+d*x))+5//4*a^3*d^-1*(a+-1*a*sin(c+d*x))^-1)
@test integrate((a+a*sin(c+d*x))^2*csc(c+d*x)^3*sec(c+d*x)^5, x) == :(-2*a^2*d^-1*csc(c+d*x)+4*a^2*d^-1*log(sin(c+d*x))+-31//8*a^2*d^-1*log(1+-1*sin(c+d*x))+-1//2*a^2*d^-1*csc(c+d*x)^2+-1//8*a^2*d^-1*log(1+sin(c+d*x))+1//4*a^4*d^-1*(a+-1*a*sin(c+d*x))^-2+7//4*a^3*d^-1*(a+-1*a*sin(c+d*x))^-1)
@test integrate((a+a*sin(c+d*x))^2*csc(c+d*x)^4*sec(c+d*x)^5, x) == :(-1*a^2*d^-1*csc(c+d*x)^2+-4*a^2*d^-1*csc(c+d*x)+6*a^2*d^-1*log(sin(c+d*x))+-49//8*a^2*d^-1*log(1+-1*sin(c+d*x))+-1//3*a^2*d^-1*csc(c+d*x)^3+1//4*a^4*d^-1*(a+-1*a*sin(c+d*x))^-2+1//8*a^2*d^-1*log(1+sin(c+d*x))+9//4*a^3*d^-1*(a+-1*a*sin(c+d*x))^-1)
@test integrate((a+a*sin(c+d*x))^3*sec(c+d*x)^5*sin(c+d*x)^5, x) == :((1/2)*a^5*d^-1*(a+-1*a*sin(c+d*x))^-2+-10*a^3*d^-1*log(1+-1*sin(c+d*x))+-6*a^3*d^-1*sin(c+d*x)+-5*a^4*d^-1*(a+-1*a*sin(c+d*x))^-1+-3//2*a^3*d^-1*sin(c+d*x)^2+-1//3*a^3*d^-1*sin(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^3*sec(c+d*x)^5*sin(c+d*x)^4, x) == :((1/2)*a^5*d^-1*(a+-1*a*sin(c+d*x))^-2+-6*a^3*d^-1*log(1+-1*sin(c+d*x))+-4*a^4*d^-1*(a+-1*a*sin(c+d*x))^-1+-3*a^3*d^-1*sin(c+d*x)+-1//2*a^3*d^-1*sin(c+d*x)^2)
@test integrate((a+a*sin(c+d*x))^3*sec(c+d*x)^5*sin(c+d*x)^3, x) == :((1/2)*a^5*d^-1*(a+-1*a*sin(c+d*x))^-2+-1*a^3*d^-1*sin(c+d*x)+-3*a^3*d^-1*log(1+-1*sin(c+d*x))+-3*a^4*d^-1*(a+-1*a*sin(c+d*x))^-1)
@test integrate((a+a*sin(c+d*x))^3*sec(c+d*x)^5*sin(c+d*x)^2, x) == :((1/2)*a^5*d^-1*(a+-1*a*sin(c+d*x))^-2+-1*a^3*d^-1*log(1+-1*sin(c+d*x))+-2*a^4*d^-1*(a+-1*a*sin(c+d*x))^-1)
@test integrate((a+a*sin(c+d*x))^3*sec(c+d*x)^5*sin(c+d*x), x) == :((1/2)*a^5*d^-1*(a+-1*a*sin(c+d*x))^-2*sin(c+d*x)^2)
@test integrate((a+a*sin(c+d*x))^3*sec(c+d*x)^5*csc(c+d*x), x) == :(a^3*d^-1*log(sin(c+d*x))+a^4*d^-1*(a+-1*a*sin(c+d*x))^-1+(1/2)*a^5*d^-1*(a+-1*a*sin(c+d*x))^-2+-1*a^3*d^-1*log(1+-1*sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^3*csc(c+d*x)^2*sec(c+d*x)^5, x) == :((1/2)*a^5*d^-1*(a+-1*a*sin(c+d*x))^-2+-1*a^3*d^-1*csc(c+d*x)+-3*a^3*d^-1*log(1+-1*sin(c+d*x))+2*a^4*d^-1*(a+-1*a*sin(c+d*x))^-1+3*a^3*d^-1*log(sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^3*csc(c+d*x)^3*sec(c+d*x)^5, x) == :((1/2)*a^5*d^-1*(a+-1*a*sin(c+d*x))^-2+-6*a^3*d^-1*log(1+-1*sin(c+d*x))+-3*a^3*d^-1*csc(c+d*x)+3*a^4*d^-1*(a+-1*a*sin(c+d*x))^-1+6*a^3*d^-1*log(sin(c+d*x))+-1//2*a^3*d^-1*csc(c+d*x)^2)
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^7*sin(c+d*x)^11, x) == :(-5*d^-1*(a+a*sin(c+d*x))^-1+125//128*d^-1*(a+-1*a*sin(c+d*x))^-1+5*a^-1*d^-1*sin(c+d*x)+-1795//256*a^-1*d^-1*log(1+sin(c+d*x))+-17//128*a*d^-1*(a+-1*a*sin(c+d*x))^-2+-3//16*a^2*d^-1*(a+a*sin(c+d*x))^-3+-1//2*a^-1*d^-1*sin(c+d*x)^2+1//3*a^-1*d^-1*sin(c+d*x)^3+1//64*a^3*d^-1*(a+a*sin(c+d*x))^-4+1//96*a^2*d^-1*(a+-1*a*sin(c+d*x))^-3+71//64*a*d^-1*(a+a*sin(c+d*x))^-2+515//256*a^-1*d^-1*log(1+-1*sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^7*sin(c+d*x)^10, x) == :(95//128*d^-1*(a+-1*a*sin(c+d*x))^-1+105//32*d^-1*(a+a*sin(c+d*x))^-1+(1/2)*a^-1*d^-1*sin(c+d*x)^2+-1*a^-1*d^-1*sin(c+d*x)+-55//64*a*d^-1*(a+a*sin(c+d*x))^-2+-15//128*a*d^-1*(a+-1*a*sin(c+d*x))^-2+-1//64*a^3*d^-1*(a+a*sin(c+d*x))^-4+1//6*a^2*d^-1*(a+a*sin(c+d*x))^-3+1//96*a^2*d^-1*(a+-1*a*sin(c+d*x))^-3+325//256*a^-1*d^-1*log(1+-1*sin(c+d*x))+955//256*a^-1*d^-1*log(1+sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^7*sin(c+d*x)^9, x) == :(-2*d^-1*(a+a*sin(c+d*x))^-1+69//128*d^-1*(a+-1*a*sin(c+d*x))^-1+a^-1*d^-1*sin(c+d*x)+-443//256*a^-1*d^-1*log(1+sin(c+d*x))+-13//128*a*d^-1*(a+-1*a*sin(c+d*x))^-2+-7//48*a^2*d^-1*(a+a*sin(c+d*x))^-3+1//64*a^3*d^-1*(a+a*sin(c+d*x))^-4+1//96*a^2*d^-1*(a+-1*a*sin(c+d*x))^-3+41//64*a*d^-1*(a+a*sin(c+d*x))^-2+187//256*a^-1*d^-1*log(1+-1*sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^7*sin(c+d*x)^8, x) == :(35//32*d^-1*(a+a*sin(c+d*x))^-1+47//128*d^-1*(a+-1*a*sin(c+d*x))^-1+-29//64*a*d^-1*(a+a*sin(c+d*x))^-2+-11//128*a*d^-1*(a+-1*a*sin(c+d*x))^-2+-1//64*a^3*d^-1*(a+a*sin(c+d*x))^-4+1//8*a^2*d^-1*(a+a*sin(c+d*x))^-3+1//96*a^2*d^-1*(a+-1*a*sin(c+d*x))^-3+93//256*a^-1*d^-1*log(1+-1*sin(c+d*x))+163//256*a^-1*d^-1*log(1+sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^7*sin(c+d*x)^7, x) == :(-35//128*a^-1*d^-1*arctanh(sin(c+d*x))+1//8*a^-1*d^-1*tan(c+d*x)^8+-35//192*a^-1*d^-1*tan(c+d*x)^3*sec(c+d*x)+-1//8*a^-1*d^-1*tan(c+d*x)^7*sec(c+d*x)+7//48*a^-1*d^-1*tan(c+d*x)^5*sec(c+d*x)+35//128*a^-1*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^7*sin(c+d*x)^6, x) == :(-5//128*a^-1*d^-1*arctanh(sin(c+d*x))+-1//8*a^-1*d^-1*tan(c+d*x)^8+-5//48*a^-1*d^-1*sec(c+d*x)^3*tan(c+d*x)^3+-5//128*a^-1*d^-1*sec(c+d*x)*tan(c+d*x)+1//8*a^-1*d^-1*sec(c+d*x)^3*tan(c+d*x)^5+5//64*a^-1*d^-1*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^7*sin(c+d*x)^5, x) == :(1//6*a^-1*d^-1*tan(c+d*x)^6+1//8*a^-1*d^-1*tan(c+d*x)^8+5//128*a^-1*d^-1*arctanh(sin(c+d*x))+-5//64*a^-1*d^-1*sec(c+d*x)^3*tan(c+d*x)+-1//8*a^-1*d^-1*sec(c+d*x)^3*tan(c+d*x)^5+5//48*a^-1*d^-1*sec(c+d*x)^3*tan(c+d*x)^3+5//128*a^-1*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^7*sin(c+d*x)^4, x) == :(-1//6*a^-1*d^-1*tan(c+d*x)^6+-1//8*a^-1*d^-1*tan(c+d*x)^8+3//128*a^-1*d^-1*arctanh(sin(c+d*x))+-1//16*a^-1*d^-1*sec(c+d*x)^5*tan(c+d*x)+1//8*a^-1*d^-1*sec(c+d*x)^5*tan(c+d*x)^3+1//64*a^-1*d^-1*sec(c+d*x)^3*tan(c+d*x)+3//128*a^-1*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^7*sin(c+d*x)^3, x) == :(-3//128*a^-1*d^-1*arctanh(sin(c+d*x))+-1//6*a^-1*d^-1*sec(c+d*x)^6+1//8*a^-1*d^-1*sec(c+d*x)^8+-3//128*a^-1*d^-1*sec(c+d*x)*tan(c+d*x)+-1//8*a^-1*d^-1*sec(c+d*x)^5*tan(c+d*x)^3+-1//64*a^-1*d^-1*sec(c+d*x)^3*tan(c+d*x)+1//16*a^-1*d^-1*sec(c+d*x)^5*tan(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^7*sin(c+d*x)^2, x) == :(-5//128*a^-1*d^-1*arctanh(sin(c+d*x))+-1//8*a^-1*d^-1*sec(c+d*x)^8+1//6*a^-1*d^-1*sec(c+d*x)^6+-5//128*a^-1*d^-1*sec(c+d*x)*tan(c+d*x)+-5//192*a^-1*d^-1*sec(c+d*x)^3*tan(c+d*x)+-1//48*a^-1*d^-1*sec(c+d*x)^5*tan(c+d*x)+1//8*a^-1*d^-1*sec(c+d*x)^7*tan(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^7*sin(c+d*x), x) == :(1//8*a^-1*d^-1*sec(c+d*x)^8+5//128*a^-1*d^-1*arctanh(sin(c+d*x))+-1//8*a^-1*d^-1*sec(c+d*x)^7*tan(c+d*x)+1//48*a^-1*d^-1*sec(c+d*x)^5*tan(c+d*x)+5//128*a^-1*d^-1*sec(c+d*x)*tan(c+d*x)+5//192*a^-1*d^-1*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^7, x) == :(-5//32*d^-1*(a+a*sin(c+d*x))^-1+15//128*d^-1*(a+-1*a*sin(c+d*x))^-1+-5//64*a*d^-1*(a+a*sin(c+d*x))^-2+-1//24*a^2*d^-1*(a+a*sin(c+d*x))^-3+-1//64*a^3*d^-1*(a+a*sin(c+d*x))^-4+1//96*a^2*d^-1*(a+-1*a*sin(c+d*x))^-3+5//128*a*d^-1*(a+-1*a*sin(c+d*x))^-2+35//128*a^-1*d^-1*arctanh(sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^7*csc(c+d*x), x) == :((1/2)*d^-1*(a+a*sin(c+d*x))^-1+29//128*d^-1*(a+-1*a*sin(c+d*x))^-1+a^-1*d^-1*log(sin(c+d*x))+-163//256*a^-1*d^-1*log(1+sin(c+d*x))+-93//256*a^-1*d^-1*log(1+-1*sin(c+d*x))+1//16*a^2*d^-1*(a+a*sin(c+d*x))^-3+1//64*a^3*d^-1*(a+a*sin(c+d*x))^-4+1//96*a^2*d^-1*(a+-1*a*sin(c+d*x))^-3+7//128*a*d^-1*(a+-1*a*sin(c+d*x))^-2+11//64*a*d^-1*(a+a*sin(c+d*x))^-2)
@test integrate((a+a*sin(c+d*x))^-1*csc(c+d*x)^2*sec(c+d*x)^7, x) == :(-35//32*d^-1*(a+a*sin(c+d*x))^-1+47//128*d^-1*(a+-1*a*sin(c+d*x))^-1+-1*a^-1*d^-1*csc(c+d*x)+-1*a^-1*d^-1*log(sin(c+d*x))+-187//256*a^-1*d^-1*log(1+-1*sin(c+d*x))+-19//64*a*d^-1*(a+a*sin(c+d*x))^-2+-1//12*a^2*d^-1*(a+a*sin(c+d*x))^-3+-1//64*a^3*d^-1*(a+a*sin(c+d*x))^-4+1//96*a^2*d^-1*(a+-1*a*sin(c+d*x))^-3+9//128*a*d^-1*(a+-1*a*sin(c+d*x))^-2+443//256*a^-1*d^-1*log(1+sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-1*csc(c+d*x)^3*sec(c+d*x)^7, x) == :(2*d^-1*(a+a*sin(c+d*x))^-1+69//128*d^-1*(a+-1*a*sin(c+d*x))^-1+a^-1*d^-1*csc(c+d*x)+5*a^-1*d^-1*log(sin(c+d*x))+-955//256*a^-1*d^-1*log(1+sin(c+d*x))+-325//256*a^-1*d^-1*log(1+-1*sin(c+d*x))+-1//2*a^-1*d^-1*csc(c+d*x)^2+1//64*a^3*d^-1*(a+a*sin(c+d*x))^-4+1//96*a^2*d^-1*(a+-1*a*sin(c+d*x))^-3+5//48*a^2*d^-1*(a+a*sin(c+d*x))^-3+11//128*a*d^-1*(a+-1*a*sin(c+d*x))^-2+29//64*a*d^-1*(a+a*sin(c+d*x))^-2)
@test integrate((a+a*sin(c+d*x))^-1*csc(c+d*x)^4*sec(c+d*x)^7, x) == :(-105//32*d^-1*(a+a*sin(c+d*x))^-1+95//128*d^-1*(a+-1*a*sin(c+d*x))^-1+(1/2)*a^-1*d^-1*csc(c+d*x)^2+-5*a^-1*d^-1*csc(c+d*x)+-5*a^-1*d^-1*log(sin(c+d*x))+-515//256*a^-1*d^-1*log(1+-1*sin(c+d*x))+-41//64*a*d^-1*(a+a*sin(c+d*x))^-2+-1//3*a^-1*d^-1*csc(c+d*x)^3+-1//8*a^2*d^-1*(a+a*sin(c+d*x))^-3+-1//64*a^3*d^-1*(a+a*sin(c+d*x))^-4+1//96*a^2*d^-1*(a+-1*a*sin(c+d*x))^-3+13//128*a*d^-1*(a+-1*a*sin(c+d*x))^-2+1795//256*a^-1*d^-1*log(1+sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^2*sec(c+d*x)^8*sin(c+d*x)^3, x) == :(-3//5*a^2*d^-1*sec(c+d*x)^5+1//3*a^2*d^-1*sec(c+d*x)^3+2//5*a^2*d^-1*tan(c+d*x)^5+2//7*a^2*d^-1*sec(c+d*x)^7+2//7*a^2*d^-1*tan(c+d*x)^7)
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^9*sin(c+d*x)^12, x) == :(-1155//256*d^-1*(a+a*sin(c+d*x))^-1+-39//32*d^-1*(a+-1*a*sin(c+d*x))^-1+a^-1*d^-1*sin(c+d*x)+-2229//512*a^-1*d^-1*log(1+sin(c+d*x))+-843//512*a^-1*d^-1*log(1+-1*sin(c+d*x))+-53//128*a^2*d^-1*(a+a*sin(c+d*x))^-3+-3//64*a^2*d^-1*(a+-1*a*sin(c+d*x))^-3+-1//2*a^-1*d^-1*sin(c+d*x)^2+-1//160*a^4*d^-1*(a+a*sin(c+d*x))^-5+1//256*a^3*d^-1*(a+-1*a*sin(c+d*x))^-4+19//256*a^3*d^-1*(a+a*sin(c+d*x))^-4+141//512*a*d^-1*(a+-1*a*sin(c+d*x))^-2+765//512*a*d^-1*(a+a*sin(c+d*x))^-2)
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^9*sin(c+d*x)^11, x) == :(-203//256*d^-1*(a+-1*a*sin(c+d*x))^-1+5//2*d^-1*(a+a*sin(c+d*x))^-1+-1*a^-1*d^-1*sin(c+d*x)+-515//512*a*d^-1*(a+a*sin(c+d*x))^-2+-437//512*a^-1*d^-1*log(1+-1*sin(c+d*x))+-17//256*a^3*d^-1*(a+a*sin(c+d*x))^-4+-1//24*a^2*d^-1*(a+-1*a*sin(c+d*x))^-3+1//160*a^4*d^-1*(a+a*sin(c+d*x))^-5+1//256*a^3*d^-1*(a+-1*a*sin(c+d*x))^-4+109//512*a*d^-1*(a+-1*a*sin(c+d*x))^-2+125//384*a^2*d^-1*(a+a*sin(c+d*x))^-3+949//512*a^-1*d^-1*log(1+sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^9*sin(c+d*x)^10, x) == :(-315//256*d^-1*(a+a*sin(c+d*x))^-1+-61//128*d^-1*(a+-1*a*sin(c+d*x))^-1+-319//512*a^-1*d^-1*log(1+sin(c+d*x))+-193//512*a^-1*d^-1*log(1+-1*sin(c+d*x))+-95//384*a^2*d^-1*(a+a*sin(c+d*x))^-3+-7//192*a^2*d^-1*(a+-1*a*sin(c+d*x))^-3+-1//160*a^4*d^-1*(a+a*sin(c+d*x))^-5+1//256*a^3*d^-1*(a+-1*a*sin(c+d*x))^-4+15//256*a^3*d^-1*(a+a*sin(c+d*x))^-4+81//512*a*d^-1*(a+-1*a*sin(c+d*x))^-2+325//512*a*d^-1*(a+a*sin(c+d*x))^-2)
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^9*sin(c+d*x)^9, x) == :(1//10*a^-1*d^-1*tan(c+d*x)^10+63//256*a^-1*d^-1*arctanh(sin(c+d*x))+-63//256*a^-1*d^-1*sec(c+d*x)*tan(c+d*x)+-21//160*a^-1*d^-1*tan(c+d*x)^5*sec(c+d*x)+-1//10*a^-1*d^-1*tan(c+d*x)^9*sec(c+d*x)+9//80*a^-1*d^-1*tan(c+d*x)^7*sec(c+d*x)+21//128*a^-1*d^-1*tan(c+d*x)^3*sec(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^9*sin(c+d*x)^8, x) == :(-1//10*a^-1*d^-1*tan(c+d*x)^10+7//256*a^-1*d^-1*arctanh(sin(c+d*x))+-7//80*a^-1*d^-1*sec(c+d*x)^3*tan(c+d*x)^5+-7//128*a^-1*d^-1*sec(c+d*x)^3*tan(c+d*x)+1//10*a^-1*d^-1*sec(c+d*x)^3*tan(c+d*x)^7+7//96*a^-1*d^-1*sec(c+d*x)^3*tan(c+d*x)^3+7//256*a^-1*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^9*sin(c+d*x)^7, x) == :(-7//256*a^-1*d^-1*arctanh(sin(c+d*x))+1//8*a^-1*d^-1*tan(c+d*x)^8+1//10*a^-1*d^-1*tan(c+d*x)^10+-7//96*a^-1*d^-1*sec(c+d*x)^3*tan(c+d*x)^3+-7//256*a^-1*d^-1*sec(c+d*x)*tan(c+d*x)+-1//10*a^-1*d^-1*sec(c+d*x)^3*tan(c+d*x)^7+7//80*a^-1*d^-1*sec(c+d*x)^3*tan(c+d*x)^5+7//128*a^-1*d^-1*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^9*sin(c+d*x)^6, x) == :(-3//256*a^-1*d^-1*arctanh(sin(c+d*x))+-1//8*a^-1*d^-1*tan(c+d*x)^8+-1//10*a^-1*d^-1*tan(c+d*x)^10+-3//256*a^-1*d^-1*sec(c+d*x)*tan(c+d*x)+-1//16*a^-1*d^-1*sec(c+d*x)^5*tan(c+d*x)^3+-1//128*a^-1*d^-1*sec(c+d*x)^3*tan(c+d*x)+1//10*a^-1*d^-1*sec(c+d*x)^5*tan(c+d*x)^5+1//32*a^-1*d^-1*sec(c+d*x)^5*tan(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^9*sin(c+d*x)^5, x) == :(-1//4*a^-1*d^-1*sec(c+d*x)^8+1//6*a^-1*d^-1*sec(c+d*x)^6+1//10*a^-1*d^-1*sec(c+d*x)^10+3//256*a^-1*d^-1*arctanh(sin(c+d*x))+-1//10*a^-1*d^-1*sec(c+d*x)^5*tan(c+d*x)^5+-1//32*a^-1*d^-1*sec(c+d*x)^5*tan(c+d*x)+1//16*a^-1*d^-1*sec(c+d*x)^5*tan(c+d*x)^3+1//128*a^-1*d^-1*sec(c+d*x)^3*tan(c+d*x)+3//256*a^-1*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^9*sin(c+d*x)^4, x) == :(-1//6*a^-1*d^-1*sec(c+d*x)^6+-1//10*a^-1*d^-1*sec(c+d*x)^10+1//4*a^-1*d^-1*sec(c+d*x)^8+3//256*a^-1*d^-1*arctanh(sin(c+d*x))+-3//80*a^-1*d^-1*sec(c+d*x)^7*tan(c+d*x)+1//10*a^-1*d^-1*sec(c+d*x)^7*tan(c+d*x)^3+1//128*a^-1*d^-1*sec(c+d*x)^3*tan(c+d*x)+1//160*a^-1*d^-1*sec(c+d*x)^5*tan(c+d*x)+3//256*a^-1*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^9*sin(c+d*x)^3, x) == :(-3//256*a^-1*d^-1*arctanh(sin(c+d*x))+-1//8*a^-1*d^-1*sec(c+d*x)^8+1//10*a^-1*d^-1*sec(c+d*x)^10+-3//256*a^-1*d^-1*sec(c+d*x)*tan(c+d*x)+-1//10*a^-1*d^-1*sec(c+d*x)^7*tan(c+d*x)^3+-1//128*a^-1*d^-1*sec(c+d*x)^3*tan(c+d*x)+-1//160*a^-1*d^-1*sec(c+d*x)^5*tan(c+d*x)+3//80*a^-1*d^-1*sec(c+d*x)^7*tan(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^9*sin(c+d*x)^2, x) == :(-7//256*a^-1*d^-1*arctanh(sin(c+d*x))+-1//10*a^-1*d^-1*sec(c+d*x)^10+1//8*a^-1*d^-1*sec(c+d*x)^8+-7//256*a^-1*d^-1*sec(c+d*x)*tan(c+d*x)+-7//384*a^-1*d^-1*sec(c+d*x)^3*tan(c+d*x)+-7//480*a^-1*d^-1*sec(c+d*x)^5*tan(c+d*x)+-1//80*a^-1*d^-1*sec(c+d*x)^7*tan(c+d*x)+1//10*a^-1*d^-1*sec(c+d*x)^9*tan(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^9*sin(c+d*x), x) == :(1//10*a^-1*d^-1*sec(c+d*x)^10+7//256*a^-1*d^-1*arctanh(sin(c+d*x))+-1//10*a^-1*d^-1*sec(c+d*x)^9*tan(c+d*x)+1//80*a^-1*d^-1*sec(c+d*x)^7*tan(c+d*x)+7//256*a^-1*d^-1*sec(c+d*x)*tan(c+d*x)+7//384*a^-1*d^-1*sec(c+d*x)^3*tan(c+d*x)+7//480*a^-1*d^-1*sec(c+d*x)^5*tan(c+d*x))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^9, x) == :(-35//256*d^-1*(a+a*sin(c+d*x))^-1+7//64*d^-1*(a+-1*a*sin(c+d*x))^-1+-35//512*a*d^-1*(a+a*sin(c+d*x))^-2+-5//128*a^2*d^-1*(a+a*sin(c+d*x))^-3+-5//256*a^3*d^-1*(a+a*sin(c+d*x))^-4+-1//160*a^4*d^-1*(a+a*sin(c+d*x))^-5+1//64*a^2*d^-1*(a+-1*a*sin(c+d*x))^-3+1//256*a^3*d^-1*(a+-1*a*sin(c+d*x))^-4+21//512*a*d^-1*(a+-1*a*sin(c+d*x))^-2+63//256*a^-1*d^-1*arctanh(sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^9*csc(c+d*x), x) == :((1/2)*d^-1*(a+a*sin(c+d*x))^-1+65//256*d^-1*(a+-1*a*sin(c+d*x))^-1+a^-1*d^-1*log(sin(c+d*x))+-319//512*a^-1*d^-1*log(1+sin(c+d*x))+-193//512*a^-1*d^-1*log(1+-1*sin(c+d*x))+1//48*a^2*d^-1*(a+-1*a*sin(c+d*x))^-3+1//160*a^4*d^-1*(a+a*sin(c+d*x))^-5+1//256*a^3*d^-1*(a+-1*a*sin(c+d*x))^-4+7//256*a^3*d^-1*(a+a*sin(c+d*x))^-4+29//384*a^2*d^-1*(a+a*sin(c+d*x))^-3+37//512*a*d^-1*(a+-1*a*sin(c+d*x))^-2+93//512*a*d^-1*(a+a*sin(c+d*x))^-2)
@test integrate((a+a*sin(c+d*x))^-1*csc(c+d*x)^2*sec(c+d*x)^9, x) == :(-315//256*d^-1*(a+a*sin(c+d*x))^-1+61//128*d^-1*(a+-1*a*sin(c+d*x))^-1+-1*a^-1*d^-1*csc(c+d*x)+-1*a^-1*d^-1*log(sin(c+d*x))+-437//512*a^-1*d^-1*log(1+-1*sin(c+d*x))+-187//512*a*d^-1*(a+a*sin(c+d*x))^-2+-47//384*a^2*d^-1*(a+a*sin(c+d*x))^-3+-9//256*a^3*d^-1*(a+a*sin(c+d*x))^-4+-1//160*a^4*d^-1*(a+a*sin(c+d*x))^-5+1//256*a^3*d^-1*(a+-1*a*sin(c+d*x))^-4+5//192*a^2*d^-1*(a+-1*a*sin(c+d*x))^-3+57//512*a*d^-1*(a+-1*a*sin(c+d*x))^-2+949//512*a^-1*d^-1*log(1+sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-1*csc(c+d*x)^3*sec(c+d*x)^9, x) == :(5//2*d^-1*(a+a*sin(c+d*x))^-1+203//256*d^-1*(a+-1*a*sin(c+d*x))^-1+a^-1*d^-1*csc(c+d*x)+6*a^-1*d^-1*log(sin(c+d*x))+-2229//512*a^-1*d^-1*log(1+sin(c+d*x))+-843//512*a^-1*d^-1*log(1+-1*sin(c+d*x))+-1//2*a^-1*d^-1*csc(c+d*x)^2+1//32*a^2*d^-1*(a+-1*a*sin(c+d*x))^-3+1//160*a^4*d^-1*(a+a*sin(c+d*x))^-5+1//256*a^3*d^-1*(a+-1*a*sin(c+d*x))^-4+11//256*a^3*d^-1*(a+a*sin(c+d*x))^-4+23//128*a^2*d^-1*(a+a*sin(c+d*x))^-3+81//512*a*d^-1*(a+-1*a*sin(c+d*x))^-2+325//512*a*d^-1*(a+a*sin(c+d*x))^-2)
@test integrate((a+a*sin(e+f*x))^4*(c+d*sin(e+f*x))^n*cos(e+f*x), x) == :(a^4*d^-5*f^-1*(5+n)^-1*(c+d*sin(e+f*x))^(5+n)+a^4*d^-5*f^-1*(1+n)^-1*(c+-1d)^4*(c+d*sin(e+f*x))^(1+n)+-4*a^4*d^-5*f^-1*(2+n)^-1*(c+-1d)^3*(c+d*sin(e+f*x))^(2+n)+-4*a^4*d^-5*f^-1*(4+n)^-1*(c+d*sin(e+f*x))^(4+n)*(c+-1d)+6*a^4*d^-5*f^-1*(3+n)^-1*(c+-1d)^2*(c+d*sin(e+f*x))^(3+n))
@test integrate((a+a*sin(e+f*x))^3*(c+d*sin(e+f*x))^n*cos(e+f*x), x) == :(a^3*d^-4*f^-1*(4+n)^-1*(c+d*sin(e+f*x))^(4+n)+-1*a^3*d^-4*f^-1*(1+n)^-1*(c+-1d)^3*(c+d*sin(e+f*x))^(1+n)+-3*a^3*d^-4*f^-1*(3+n)^-1*(c+d*sin(e+f*x))^(3+n)*(c+-1d)+3*a^3*d^-4*f^-1*(2+n)^-1*(c+-1d)^2*(c+d*sin(e+f*x))^(2+n))
@test integrate((a+a*sin(e+f*x))^2*(c+d*sin(e+f*x))^n*cos(e+f*x), x) == :(a^2*d^-3*f^-1*(3+n)^-1*(c+d*sin(e+f*x))^(3+n)+a^2*d^-3*f^-1*(1+n)^-1*(c+-1d)^2*(c+d*sin(e+f*x))^(1+n)+-2*a^2*d^-3*f^-1*(2+n)^-1*(c+d*sin(e+f*x))^(2+n)*(c+-1d))
@test integrate((c+d*sin(e+f*x))^n*(a+a*sin(e+f*x))*cos(e+f*x), x) == :(a*d^-2*f^-1*(2+n)^-1*(c+d*sin(e+f*x))^(2+n)+-1*a*d^-2*f^-1*(1+n)^-1*(c+d*sin(e+f*x))^(1+n)*(c+-1d))
@test integrate((a+a*sin(e+f*x))^m*(c+d*sin(e+f*x))^4*cos(e+f*x), x) == :(a^-1*f^-1*(1+m)^-1*(a+a*sin(e+f*x))^(1+m)*(c+-1d)^4+a^-5*d^4*f^-1*(5+m)^-1*(a+a*sin(e+f*x))^(5+m)+a^-4*d^3*f^-1*(4+m)^-1*(a+a*sin(e+f*x))^(4+m)*(-4d+4c)+4*d*a^-2*f^-1*(2+m)^-1*(a+a*sin(e+f*x))^(2+m)*(c+-1d)^3+6*a^-3*d^2*f^-1*(3+m)^-1*(a+a*sin(e+f*x))^(3+m)*(c+-1d)^2)
@test integrate((a+a*sin(e+f*x))^m*(c+d*sin(e+f*x))^3*cos(e+f*x), x) == :(a^-1*f^-1*(1+m)^-1*(a+a*sin(e+f*x))^(1+m)*(c+-1d)^3+a^-4*d^3*f^-1*(4+m)^-1*(a+a*sin(e+f*x))^(4+m)+a^-3*d^2*f^-1*(3+m)^-1*(a+a*sin(e+f*x))^(3+m)*(-3d+3c)+3*d*a^-2*f^-1*(2+m)^-1*(a+a*sin(e+f*x))^(2+m)*(c+-1d)^2)
@test integrate((a+a*sin(e+f*x))^m*(c+d*sin(e+f*x))^2*cos(e+f*x), x) == :(a^-1*f^-1*(1+m)^-1*(a+a*sin(e+f*x))^(1+m)*(c+-1d)^2+a^-3*d^2*f^-1*(3+m)^-1*(a+a*sin(e+f*x))^(3+m)+d*a^-2*f^-1*(2+m)^-1*(a+a*sin(e+f*x))^(2+m)*(-2d+2c))
@test integrate((a+a*sin(e+f*x))^m*(c+d*sin(e+f*x))*cos(e+f*x), x) == :(d*a^-2*f^-1*(2+m)^-1*(a+a*sin(e+f*x))^(2+m)+a^-1*f^-1*(1+m)^-1*(a+a*sin(e+f*x))^(1+m)*(c+-1d))
@test integrate((a+a*sin(c+d*x))^m*sin(c+d*x)^4*cos(c+d*x), x) == :(a^-1*d^-1*(1+m)^-1*(a+a*sin(c+d*x))^(1+m)+a^-5*d^-1*(5+m)^-1*(a+a*sin(c+d*x))^(5+m)+-4*a^-4*d^-1*(4+m)^-1*(a+a*sin(c+d*x))^(4+m)+-4*a^-2*d^-1*(2+m)^-1*(a+a*sin(c+d*x))^(2+m)+6*a^-3*d^-1*(3+m)^-1*(a+a*sin(c+d*x))^(3+m))
@test integrate((a+a*sin(c+d*x))^m*sin(c+d*x)^3*cos(c+d*x), x) == :(a^-4*d^-1*(4+m)^-1*(a+a*sin(c+d*x))^(4+m)+-1*a^-1*d^-1*(1+m)^-1*(a+a*sin(c+d*x))^(1+m)+-3*a^-3*d^-1*(3+m)^-1*(a+a*sin(c+d*x))^(3+m)+3*a^-2*d^-1*(2+m)^-1*(a+a*sin(c+d*x))^(2+m))
@test integrate((a+a*sin(c+d*x))^m*sin(c+d*x)^2*cos(c+d*x), x) == :(a^-1*d^-1*(1+m)^-1*(a+a*sin(c+d*x))^(1+m)+a^-3*d^-1*(3+m)^-1*(a+a*sin(c+d*x))^(3+m)+-2*a^-2*d^-1*(2+m)^-1*(a+a*sin(c+d*x))^(2+m))
@test integrate((a+a*sin(c+d*x))^m*cos(c+d*x)*sin(c+d*x), x) == :(a^-2*d^-1*(2+m)^-1*(a+a*sin(c+d*x))^(2+m)+-1*a^-1*d^-1*(1+m)^-1*(a+a*sin(c+d*x))^(1+m))
@test integrate((a+a*sin(e+f*x))^-3//2*(c+d*sin(e+f*x))^-1*cos(e+f*x)^2, x) == :(-2*2^(1/2)*a^-3//2*f^-1*(c+-1d)^-1*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sin(e+f*x))^-1//2*cos(e+f*x))+2*a^-3//2*d^-1//2*f^-1*(c+d)^(1/2)*(c+-1d)^-1*arctanh(a^(1/2)*d^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+d)^-1//2*cos(e+f*x)))
@test integrate((a+a*sin(e+f*x))^-3//2*(c+d*sin(e+f*x))^-1//2*cos(e+f*x)^2, x) == :(2*a^-3//2*d^-1//2*f^-1*arctan(a^(1/2)*d^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+d*sin(e+f*x))^-1//2*cos(e+f*x))+-2*2^(1/2)*a^-3//2*f^-1*(c+-1d)^-1//2*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sin(e+f*x))^-1//2*(c+-1d)^(1/2)*(c+d*sin(e+f*x))^-1//2*cos(e+f*x)))
@test integrate(cos(c+d*x)^7*(A+B*sin(c+d*x))*(a+a*sin(c+d*x)), x) == :(-1//3*a^-5*d^-1*(a+a*sin(c+d*x))^6*(-10B+6A)+-1//8*a^-7*d^-1*(a+a*sin(c+d*x))^8*(A+-7B)+-1//9*B*a^-8*d^-1*(a+a*sin(c+d*x))^9+1//5*a^-4*d^-1*(a+a*sin(c+d*x))^5*(-8B+8A)+1//7*a^-6*d^-1*(a+a*sin(c+d*x))^7*(-18B+6A))
@test integrate(cos(c+d*x)^5*(A+B*sin(c+d*x))*(a+a*sin(c+d*x)), x) == :(a^-3*d^-1*(a+a*sin(c+d*x))^4*(A+-1B)+-1//5*a^-4*d^-1*(a+a*sin(c+d*x))^5*(-8B+4A)+1//6*a^-5*d^-1*(a+a*sin(c+d*x))^6*(A+-5B)+1//7*B*a^-6*d^-1*(a+a*sin(c+d*x))^7)
@test integrate(cos(c+d*x)^3*(A+B*sin(c+d*x))*(a+a*sin(c+d*x)), x) == :(-1//4*a^-3*d^-1*(a+a*sin(c+d*x))^4*(A+-3B)+-1//5*B*a^-4*d^-1*(a+a*sin(c+d*x))^5+1//3*a^-2*d^-1*(a+a*sin(c+d*x))^3*(-2B+2A))
@test integrate((A+B*sin(c+d*x))*(a+a*sin(c+d*x))*cos(c+d*x), x) == :(A*a*d^-1*sin(c+d*x)+(1/2)*a*d^-1*sin(c+d*x)^2*(A+B)+1//3*B*a*d^-1*sin(c+d*x)^3)
@test integrate((A+B*sin(c+d*x))*(a+a*sin(c+d*x))*sec(c+d*x), x) == :(-1*B*a*d^-1*sin(c+d*x)+-1*a*d^-1*(A+B)*log(1+-1*sin(c+d*x)))
@test integrate(sec(c+d*x)^3*(A+B*sin(c+d*x))*(a+a*sin(c+d*x)), x) == :((1/2)*a*d^-1*(A+-1B)*arctanh(sin(c+d*x))+(1/2)*a^2*d^-1*(a+-1*a*sin(c+d*x))^-1*(A+B))
@test integrate(sec(c+d*x)^5*(A+B*sin(c+d*x))*(a+a*sin(c+d*x)), x) == :(-1//8*a^2*d^-1*(a+a*sin(c+d*x))^-1*(A+-1B)+1//4*A*a^2*d^-1*(a+-1*a*sin(c+d*x))^-1+1//8*a*d^-1*(-1B+3A)*arctanh(sin(c+d*x))+1//8*a^3*d^-1*(a+-1*a*sin(c+d*x))^-2*(A+B))
@test integrate(sec(c+d*x)^7*(A+B*sin(c+d*x))*(a+a*sin(c+d*x)), x) == :(-1//16*a^2*d^-1*(a+a*sin(c+d*x))^-1*(-1B+2A)+-1//32*a^3*d^-1*(a+a*sin(c+d*x))^-2*(A+-1B)+1//16*a*d^-1*(-1B+5A)*arctanh(sin(c+d*x))+1//24*a^4*d^-1*(a+-1*a*sin(c+d*x))^-3*(A+B)+1//32*a^3*d^-1*(a+-1*a*sin(c+d*x))^-2*(B+3A)+3//16*A*a^2*d^-1*(a+-1*a*sin(c+d*x))^-1)
@test integrate(cos(c+d*x)^6*(A+B*sin(c+d*x))*(a+a*sin(c+d*x)), x) == :(5//128*a*x*(B+8A)+-1//8*B*d^-1*cos(c+d*x)^7*(a+a*sin(c+d*x))+-1//56*a*d^-1*cos(c+d*x)^7*(B+8A)+1//48*a*d^-1*cos(c+d*x)^5*(B+8A)*sin(c+d*x)+5//128*a*d^-1*(B+8A)*cos(c+d*x)*sin(c+d*x)+5//192*a*d^-1*cos(c+d*x)^3*(B+8A)*sin(c+d*x))
@test integrate(cos(c+d*x)^4*(A+B*sin(c+d*x))*(a+a*sin(c+d*x)), x) == :(1//16*a*x*(B+6A)+-1//6*B*d^-1*cos(c+d*x)^5*(a+a*sin(c+d*x))+-1//30*a*d^-1*cos(c+d*x)^5*(B+6A)+1//16*a*d^-1*(B+6A)*cos(c+d*x)*sin(c+d*x)+1//24*a*d^-1*cos(c+d*x)^3*(B+6A)*sin(c+d*x))
@test integrate(cos(c+d*x)^2*(A+B*sin(c+d*x))*(a+a*sin(c+d*x)), x) == :(1//8*a*x*(B+4A)+-1//4*B*d^-1*cos(c+d*x)^3*(a+a*sin(c+d*x))+-1//12*a*d^-1*cos(c+d*x)^3*(B+4A)+1//8*a*d^-1*(B+4A)*cos(c+d*x)*sin(c+d*x))
@test integrate(sec(c+d*x)^2*(A+B*sin(c+d*x))*(a+a*sin(c+d*x)), x) == :(-1*B*a*x+d^-1*(A+B)*(a+a*sin(c+d*x))*sec(c+d*x))
@test integrate(sec(c+d*x)^4*(A+B*sin(c+d*x))*(a+a*sin(c+d*x)), x) == :(1//3*a*d^-1*(-1B+2A)*tan(c+d*x)+1//3*d^-1*sec(c+d*x)^3*(A+B)*(a+a*sin(c+d*x)))
@test integrate(sec(c+d*x)^6*(A+B*sin(c+d*x))*(a+a*sin(c+d*x)), x) == :(1//5*a*d^-1*(-1B+4A)*tan(c+d*x)+1//5*d^-1*sec(c+d*x)^5*(A+B)*(a+a*sin(c+d*x))+1//15*a*d^-1*tan(c+d*x)^3*(-1B+4A))
@test integrate(sec(c+d*x)^8*(A+B*sin(c+d*x))*(a+a*sin(c+d*x)), x) == :(1//7*a*d^-1*(-1B+6A)*tan(c+d*x)+1//7*d^-1*sec(c+d*x)^7*(A+B)*(a+a*sin(c+d*x))+1//35*a*d^-1*tan(c+d*x)^5*(-1B+6A)+2//21*a*d^-1*tan(c+d*x)^3*(-1B+6A))
@test integrate(sec(c+d*x)^10*(A+B*sin(c+d*x))*(a+a*sin(c+d*x)), x) == :(1//9*a*d^-1*tan(c+d*x)^3*(-1B+8A)+1//9*a*d^-1*(-1B+8A)*tan(c+d*x)+1//9*d^-1*sec(c+d*x)^9*(A+B)*(a+a*sin(c+d*x))+1//15*a*d^-1*tan(c+d*x)^5*(-1B+8A)+1//63*a*d^-1*tan(c+d*x)^7*(-1B+8A))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^7*(A+B*sin(c+d*x)), x) == :(-1//7*a^-5*d^-1*(a+a*sin(c+d*x))^7*(-20B+12A)+-1//9*a^-7*d^-1*(a+a*sin(c+d*x))^9*(A+-7B)+-1//10*B*a^-8*d^-1*(a+a*sin(c+d*x))^10+1//3*a^-4*d^-1*(a+a*sin(c+d*x))^6*(-4B+4A)+1//4*a^-6*d^-1*(a+a*sin(c+d*x))^8*(-9B+3A))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^5*(A+B*sin(c+d*x)), x) == :(-1//3*a^-4*d^-1*(a+a*sin(c+d*x))^6*(-4B+2A)+1//5*a^-3*d^-1*(a+a*sin(c+d*x))^5*(-4B+4A)+1//7*a^-5*d^-1*(a+a*sin(c+d*x))^7*(A+-5B)+1//8*B*a^-6*d^-1*(a+a*sin(c+d*x))^8)
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^3*(A+B*sin(c+d*x)), x) == :((1/2)*a^-2*d^-1*(a+a*sin(c+d*x))^4*(A+-1B)+-1//5*a^-3*d^-1*(a+a*sin(c+d*x))^5*(A+-3B)+-1//6*B*a^-4*d^-1*(a+a*sin(c+d*x))^6)
@test integrate((a+a*sin(c+d*x))^2*(A+B*sin(c+d*x))*cos(c+d*x), x) == :(1//3*a^-1*d^-1*(a+a*sin(c+d*x))^3*(A+-1B)+1//4*B*a^-2*d^-1*(a+a*sin(c+d*x))^4)
@test integrate((a+a*sin(c+d*x))^2*(A+B*sin(c+d*x))*sec(c+d*x), x) == :(-1//2*B*d^-1*(a+a*sin(c+d*x))^2+-1*a^2*d^-1*(A+B)*sin(c+d*x)+-2*a^2*d^-1*(A+B)*log(1+-1*sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^2*sec(c+d*x)^3*(A+B*sin(c+d*x)), x) == :(B*a^2*d^-1*log(1+-1*sin(c+d*x))+a^3*d^-1*(a+-1*a*sin(c+d*x))^-1*(A+B))
@test integrate((a+a*sin(c+d*x))^2*sec(c+d*x)^5*(A+B*sin(c+d*x)), x) == :(1//4*a^2*d^-1*(A+-1B)*arctanh(sin(c+d*x))+1//4*a^3*d^-1*(a+-1*a*sin(c+d*x))^-1*(A+-1B)+1//4*a^4*d^-1*(a+-1*a*sin(c+d*x))^-2*(A+B))
@test integrate((a+a*sin(c+d*x))^2*sec(c+d*x)^7*(A+B*sin(c+d*x)), x) == :(-1//16*a^3*d^-1*(a+a*sin(c+d*x))^-1*(A+-1B)+1//8*A*a^4*d^-1*(a+-1*a*sin(c+d*x))^-2+1//8*a^2*d^-1*(-1B+2A)*arctanh(sin(c+d*x))+1//12*a^5*d^-1*(a+-1*a*sin(c+d*x))^-3*(A+B)+1//16*a^3*d^-1*(a+-1*a*sin(c+d*x))^-1*(-1B+3A))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^6*(A+B*sin(c+d*x)), x) == :(5//128*x*a^2*(2B+9A)+-1//9*B*d^-1*(a+a*sin(c+d*x))^2*cos(c+d*x)^7+-1//56*a^2*d^-1*cos(c+d*x)^7*(2B+9A)+-1//72*d^-1*cos(c+d*x)^7*(a^2+a^2*sin(c+d*x))*(2B+9A)+1//48*a^2*d^-1*cos(c+d*x)^5*(2B+9A)*sin(c+d*x)+5//128*a^2*d^-1*(2B+9A)*cos(c+d*x)*sin(c+d*x)+5//192*a^2*d^-1*cos(c+d*x)^3*(2B+9A)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^4*(A+B*sin(c+d*x)), x) == :(1//16*x*a^2*(2B+7A)+-1//7*B*d^-1*(a+a*sin(c+d*x))^2*cos(c+d*x)^5+-1//30*a^2*d^-1*cos(c+d*x)^5*(2B+7A)+-1//42*d^-1*cos(c+d*x)^5*(a^2+a^2*sin(c+d*x))*(2B+7A)+1//16*a^2*d^-1*(2B+7A)*cos(c+d*x)*sin(c+d*x)+1//24*a^2*d^-1*cos(c+d*x)^3*(2B+7A)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*cos(c+d*x)^2*(A+B*sin(c+d*x)), x) == :(1//8*x*a^2*(2B+5A)+-1//5*B*d^-1*(a+a*sin(c+d*x))^2*cos(c+d*x)^3+-1//12*a^2*d^-1*cos(c+d*x)^3*(2B+5A)+-1//20*d^-1*cos(c+d*x)^3*(a^2+a^2*sin(c+d*x))*(2B+5A)+1//8*a^2*d^-1*(2B+5A)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*sec(c+d*x)^2*(A+B*sin(c+d*x)), x) == :(-1*x*a^2*(A+2B)+a^2*d^-1*(A+2B)*cos(c+d*x)+d^-1*(a+a*sin(c+d*x))^2*(A+B)*sec(c+d*x))
@test integrate((a+a*sin(c+d*x))^2*sec(c+d*x)^4*(A+B*sin(c+d*x)), x) == :(1//3*a^2*d^-1*(A+-2B)*sec(c+d*x)+1//3*a^2*d^-1*(A+-2B)*tan(c+d*x)+1//3*d^-1*(a+a*sin(c+d*x))^2*sec(c+d*x)^3*(A+B))
@test integrate((a+a*sin(c+d*x))^2*sec(c+d*x)^6*(A+B*sin(c+d*x)), x) == :(1//5*a^2*d^-1*(-2B+3A)*tan(c+d*x)+1//5*d^-1*(a+a*sin(c+d*x))^2*sec(c+d*x)^5*(A+B)+1//15*a^2*d^-1*sec(c+d*x)^3*(-2B+3A)+1//15*a^2*d^-1*tan(c+d*x)^3*(-2B+3A))
@test integrate((a+a*sin(c+d*x))^2*sec(c+d*x)^8*(A+B*sin(c+d*x)), x) == :(1//7*a^2*d^-1*(-2B+5A)*tan(c+d*x)+1//7*d^-1*(a+a*sin(c+d*x))^2*sec(c+d*x)^7*(A+B)+1//35*a^2*d^-1*sec(c+d*x)^5*(-2B+5A)+1//35*a^2*d^-1*tan(c+d*x)^5*(-2B+5A)+2//21*a^2*d^-1*tan(c+d*x)^3*(-2B+5A))
@test integrate((a+a*sin(c+d*x))^2*sec(c+d*x)^10*(A+B*sin(c+d*x)), x) == :(1//9*a^2*d^-1*tan(c+d*x)^3*(-2B+7A)+1//9*a^2*d^-1*(-2B+7A)*tan(c+d*x)+1//9*d^-1*(a+a*sin(c+d*x))^2*sec(c+d*x)^9*(A+B)+1//15*a^2*d^-1*tan(c+d*x)^5*(-2B+7A)+1//63*a^2*d^-1*sec(c+d*x)^7*(-2B+7A)+1//63*a^2*d^-1*tan(c+d*x)^7*(-2B+7A))
@test integrate((a+a*sin(c+d*x))^2*sec(c+d*x)^12*(A+B*sin(c+d*x)), x) == :(1//11*a^2*d^-1*(-2B+9A)*tan(c+d*x)+1//11*d^-1*(a+a*sin(c+d*x))^2*sec(c+d*x)^11*(A+B)+1//99*a^2*d^-1*sec(c+d*x)^9*(-2B+9A)+1//99*a^2*d^-1*tan(c+d*x)^9*(-2B+9A)+4//33*a^2*d^-1*tan(c+d*x)^3*(-2B+9A)+4//77*a^2*d^-1*tan(c+d*x)^7*(-2B+9A)+6//55*a^2*d^-1*tan(c+d*x)^5*(-2B+9A))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^7*(A+B*sin(c+d*x)), x) == :(-1//2*a^-5*d^-1*(a+a*sin(c+d*x))^8*(-5B+3A)+-1//10*a^-7*d^-1*(a+a*sin(c+d*x))^10*(A+-7B)+-1//11*B*a^-8*d^-1*(a+a*sin(c+d*x))^11+1//3*a^-6*d^-1*(a+a*sin(c+d*x))^9*(-6B+2A)+1//7*a^-4*d^-1*(a+a*sin(c+d*x))^7*(-8B+8A))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^5*(A+B*sin(c+d*x)), x) == :(-1//7*a^-4*d^-1*(a+a*sin(c+d*x))^7*(-8B+4A)+1//3*a^-3*d^-1*(a+a*sin(c+d*x))^6*(-2B+2A)+1//8*a^-5*d^-1*(a+a*sin(c+d*x))^8*(A+-5B)+1//9*B*a^-6*d^-1*(a+a*sin(c+d*x))^9)
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^3*(A+B*sin(c+d*x)), x) == :(-1//6*a^-3*d^-1*(a+a*sin(c+d*x))^6*(A+-3B)+-1//7*B*a^-4*d^-1*(a+a*sin(c+d*x))^7+1//5*a^-2*d^-1*(a+a*sin(c+d*x))^5*(-2B+2A))
@test integrate((a+a*sin(c+d*x))^3*(A+B*sin(c+d*x))*cos(c+d*x), x) == :(1//4*a^-1*d^-1*(a+a*sin(c+d*x))^4*(A+-1B)+1//5*B*a^-2*d^-1*(a+a*sin(c+d*x))^5)
@test integrate((a+a*sin(c+d*x))^3*(A+B*sin(c+d*x))*sec(c+d*x), x) == :(-1//3*B*d^-1*(a+a*sin(c+d*x))^3+-4*a^3*d^-1*(A+B)*log(1+-1*sin(c+d*x))+-3*a^3*d^-1*(A+B)*sin(c+d*x)+-1//2*a^3*d^-1*sin(c+d*x)^2*(A+B))
@test integrate((a+a*sin(c+d*x))^3*sec(c+d*x)^3*(A+B*sin(c+d*x)), x) == :(B*a^3*d^-1*sin(c+d*x)+a^3*d^-1*(A+3B)*log(1+-1*sin(c+d*x))+2*a^4*d^-1*(a+-1*a*sin(c+d*x))^-1*(A+B))
@test integrate((a+a*sin(c+d*x))^3*sec(c+d*x)^5*(A+B*sin(c+d*x)), x) == :(a^3*d^-1*(a+-1*a*sin(c+d*x))^-2*(2A+2B)^-1*(A*a+B*a*sin(c+d*x))^2)
@test integrate((a+a*sin(c+d*x))^3*sec(c+d*x)^7*(A+B*sin(c+d*x)), x) == :(1//6*a^6*d^-1*(a+-1*a*sin(c+d*x))^-3*(A+B)+1//8*a^3*d^-1*(A+-1B)*arctanh(sin(c+d*x))+1//8*a^4*d^-1*(a+-1*a*sin(c+d*x))^-1*(A+-1B)+1//8*a^5*d^-1*(a+-1*a*sin(c+d*x))^-2*(A+-1B))
@test integrate((a+a*sin(c+d*x))^3*sec(c+d*x)^9*(A+B*sin(c+d*x)), x) == :(-1//32*a^4*d^-1*(a+a*sin(c+d*x))^-1*(A+-1B)+1//12*A*a^6*d^-1*(a+-1*a*sin(c+d*x))^-3+1//16*a^4*d^-1*(a+-1*a*sin(c+d*x))^-1*(-1B+2A)+1//16*a^7*d^-1*(a+-1*a*sin(c+d*x))^-4*(A+B)+1//32*a^3*d^-1*(-3B+5A)*arctanh(sin(c+d*x))+1//32*a^5*d^-1*(a+-1*a*sin(c+d*x))^-2*(-1B+3A))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^6*(A+B*sin(c+d*x)), x) == :(11//256*x*a^3*(3B+10A)+-11//560*a^3*d^-1*cos(c+d*x)^7*(3B+10A)+-1//10*B*d^-1*(a+a*sin(c+d*x))^3*cos(c+d*x)^7+-1//720*d^-1*cos(c+d*x)^7*(a^3+a^3*sin(c+d*x))*(33B+110A)+-1//90*a*d^-1*(a+a*sin(c+d*x))^2*cos(c+d*x)^7*(3B+10A)+11//256*a^3*d^-1*(3B+10A)*cos(c+d*x)*sin(c+d*x)+11//384*a^3*d^-1*cos(c+d*x)^3*(3B+10A)*sin(c+d*x)+11//480*a^3*d^-1*cos(c+d*x)^5*(3B+10A)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^4*(A+B*sin(c+d*x)), x) == :(9//128*x*a^3*(3B+8A)+-3//80*a^3*d^-1*cos(c+d*x)^5*(3B+8A)+-1//8*B*d^-1*(a+a*sin(c+d*x))^3*cos(c+d*x)^5+-1//112*d^-1*cos(c+d*x)^5*(a^3+a^3*sin(c+d*x))*(9B+24A)+-1//56*a*d^-1*(a+a*sin(c+d*x))^2*cos(c+d*x)^5*(3B+8A)+3//64*a^3*d^-1*cos(c+d*x)^3*(3B+8A)*sin(c+d*x)+9//128*a^3*d^-1*(3B+8A)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*cos(c+d*x)^2*(A+B*sin(c+d*x)), x) == :(7//16*x*a^3*(B+2A)+-7//24*a^3*d^-1*cos(c+d*x)^3*(B+2A)+-1//6*B*d^-1*(a+a*sin(c+d*x))^3*cos(c+d*x)^3+-1//40*d^-1*cos(c+d*x)^3*(a^3+a^3*sin(c+d*x))*(7B+14A)+-1//10*a*d^-1*(a+a*sin(c+d*x))^2*cos(c+d*x)^3*(B+2A)+7//16*a^3*d^-1*(B+2A)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*sec(c+d*x)^2*(A+B*sin(c+d*x)), x) == :(-3//2*x*a^3*(2A+3B)+d^-1*(a+a*sin(c+d*x))^3*(A+B)*sec(c+d*x)+2*a^3*d^-1*(2A+3B)*cos(c+d*x)+(1/2)*a^3*d^-1*(2A+3B)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*sec(c+d*x)^4*(A+B*sin(c+d*x)), x) == :(B*x*a^3+1//3*d^-1*(a+a*sin(c+d*x))^3*sec(c+d*x)^3*(A+B)+-2*B*a^5*d^-1*(a^2+-1*a^2*sin(c+d*x))^-1*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*sec(c+d*x)^6*(A+B*sin(c+d*x)), x) == :(1//5*d^-1*(a+a*sin(c+d*x))^3*sec(c+d*x)^5*(A+B)+1//15*a^5*d^-1*(a+-1*a*sin(c+d*x))^-2*(-3B+2A)*cos(c+d*x)+1//15*a^5*d^-1*(a^2+-1*a^2*sin(c+d*x))^-1*(-3B+2A)*cos(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*sec(c+d*x)^8*(A+B*sin(c+d*x)), x) == :(1//7*d^-1*(a+a*sin(c+d*x))^3*sec(c+d*x)^7*(A+B)+1//35*a^3*d^-1*tan(c+d*x)^3*(-3B+4A)+1//35*d^-1*sec(c+d*x)^5*(a^3+a^3*sin(c+d*x))*(-6B+8A)+3//35*a^3*d^-1*(-3B+4A)*tan(c+d*x))
@test integrate((a+a*sin(c+d*x))^3*sec(c+d*x)^10*(A+B*sin(c+d*x)), x) == :(1//9*d^-1*(a+a*sin(c+d*x))^3*sec(c+d*x)^9*(A+B)+1//21*a^3*d^-1*tan(c+d*x)^5*(-1B+2A)+1//21*d^-1*sec(c+d*x)^7*(a^3+a^3*sin(c+d*x))*(-2B+4A)+5//21*a^3*d^-1*(-1B+2A)*tan(c+d*x)+10//63*a^3*d^-1*tan(c+d*x)^3*(-1B+2A))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^7*(A+B*sin(c+d*x)), x) == :(-1*a^-5*d^-1*(a+-1*a*sin(c+d*x))^4*(A+B)+-1//6*a^-7*d^-1*(a+-1*a*sin(c+d*x))^6*(A+5B)+1//5*a^-6*d^-1*(a+-1*a*sin(c+d*x))^5*(4A+8B)+1//7*B*a^-8*d^-1*(a+-1*a*sin(c+d*x))^7)
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^5*(A+B*sin(c+d*x)), x) == :(-1//5*B*a^-6*d^-1*(a+-1*a*sin(c+d*x))^5+1//3*a^-4*d^-1*(a+-1*a*sin(c+d*x))^3*(-2A+-2B)+1//4*a^-5*d^-1*(a+-1*a*sin(c+d*x))^4*(A+3B))
@test integrate((a+a*sin(c+d*x))^-1*cos(c+d*x)^3*(A+B*sin(c+d*x)), x) == :(A*a^-1*d^-1*sin(c+d*x)+-1//2*a^-1*d^-1*sin(c+d*x)^2*(A+-1B)+-1//3*B*a^-1*d^-1*sin(c+d*x)^3)
@test integrate((a+a*sin(c+d*x))^-1*(A+B*sin(c+d*x))*cos(c+d*x), x) == :(B*a^-1*d^-1*sin(c+d*x)+a^-1*d^-1*(A+-1B)*log(1+sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-1*(A+B*sin(c+d*x))*sec(c+d*x), x) == :(-1//2*d^-1*(a+a*sin(c+d*x))^-1*(A+-1B)+(1/2)*a^-1*d^-1*(A+B)*arctanh(sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^3*(A+B*sin(c+d*x)), x) == :(-1//4*A*d^-1*(a+a*sin(c+d*x))^-1+1//8*d^-1*(a+-1*a*sin(c+d*x))^-1*(A+B)+-1//8*a*d^-1*(a+a*sin(c+d*x))^-2*(A+-1B)+1//8*a^-1*d^-1*(B+3A)*arctanh(sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^5*(A+B*sin(c+d*x)), x) == :(-3//16*A*d^-1*(a+a*sin(c+d*x))^-1+1//16*d^-1*(a+-1*a*sin(c+d*x))^-1*(B+2A)+-1//24*a^2*d^-1*(a+a*sin(c+d*x))^-3*(A+-1B)+-1//32*a*d^-1*(a+a*sin(c+d*x))^-2*(-1B+3A)+1//16*a^-1*d^-1*(B+5A)*arctanh(sin(c+d*x))+1//32*a*d^-1*(a+-1*a*sin(c+d*x))^-2*(A+B))
@test integrate((a+a*sin(c+d*x))^-1*sec(c+d*x)^7*(A+B*sin(c+d*x)), x) == :(-5//32*A*d^-1*(a+a*sin(c+d*x))^-1+1//128*d^-1*(a+-1*a*sin(c+d*x))^-1*(5B+15A)+-1//48*a^2*d^-1*(a+a*sin(c+d*x))^-3*(-1B+2A)+-1//64*a*d^-1*(a+a*sin(c+d*x))^-2*(-1B+5A)+-1//64*a^3*d^-1*(a+a*sin(c+d*x))^-4*(A+-1B)+1//96*a^2*d^-1*(a+-1*a*sin(c+d*x))^-3*(A+B)+1//128*a*d^-1*(a+-1*a*sin(c+d*x))^-2*(3B+5A)+1//128*a^-1*d^-1*(5B+35A)*arctanh(sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^7*(A+B*sin(c+d*x)), x) == :(-1//2*a^-6*d^-1*(a+-1*a*sin(c+d*x))^4*(A+B)+-1//6*B*a^-8*d^-1*(a+-1*a*sin(c+d*x))^6+1//5*a^-7*d^-1*(a+-1*a*sin(c+d*x))^5*(A+3B))
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^5*(A+B*sin(c+d*x)), x) == :(-1//3*a^-5*d^-1*(a+-1*a*sin(c+d*x))^3*(A+B)+1//4*B*a^-6*d^-1*(a+-1*a*sin(c+d*x))^4)
@test integrate((a+a*sin(c+d*x))^-2*cos(c+d*x)^3*(A+B*sin(c+d*x)), x) == :(a^-2*d^-1*(-2B+2A)*log(1+sin(c+d*x))+-1*a^-2*d^-1*(A+-1B)*sin(c+d*x)+-1//2*B*a^-4*d^-1*(a+-1*a*sin(c+d*x))^2)
@test integrate((a+a*sin(c+d*x))^-2*(A+B*sin(c+d*x))*cos(c+d*x), x) == :(-1*d^-1*(a^2+a^2*sin(c+d*x))^-1*(A+-1B)+B*a^-2*d^-1*log(1+sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-2*(A+B*sin(c+d*x))*sec(c+d*x), x) == :(-1//4*d^-1*(a+a*sin(c+d*x))^-2*(A+-1B)+-1//4*d^-1*(a^2+a^2*sin(c+d*x))^-1*(A+B)+1//4*a^-2*d^-1*(A+B)*arctanh(sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-2*sec(c+d*x)^3*(A+B*sin(c+d*x)), x) == :(-1//8*A*d^-1*(a+a*sin(c+d*x))^-2+-1//16*d^-1*(a^2+a^2*sin(c+d*x))^-1*(B+3A)+1//16*d^-1*(a^2+-1*a^2*sin(c+d*x))^-1*(A+B)+-1//12*a*d^-1*(a+a*sin(c+d*x))^-3*(A+-1B)+1//8*a^-2*d^-1*(B+2A)*arctanh(sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-2*sec(c+d*x)^5*(A+B*sin(c+d*x)), x) == :(-3//32*A*d^-1*(a+a*sin(c+d*x))^-2+-1//32*d^-1*(a^2+a^2*sin(c+d*x))^-1*(B+5A)+1//64*d^-1*(a+-1*a*sin(c+d*x))^-2*(A+B)+1//64*d^-1*(a^2+-1*a^2*sin(c+d*x))^-1*(3B+5A)+-1//32*a^2*d^-1*(a+a*sin(c+d*x))^-4*(A+-1B)+-1//48*a*d^-1*(a+a*sin(c+d*x))^-3*(-1B+3A)+1//64*a^-2*d^-1*(5B+15A)*arctanh(sin(c+d*x)))
@test integrate((a+a*sin(c+d*x))^-2*sec(c+d*x)^7*(A+B*sin(c+d*x)), x) == :(-5//64*A*d^-1*(a+a*sin(c+d*x))^-2+-1//256*d^-1*(a^2+a^2*sin(c+d*x))^-1*(5B+35A)+1//128*d^-1*(a+-1*a*sin(c+d*x))^-2*(2B+3A)+1//256*d^-1*(a^2+-1*a^2*sin(c+d*x))^-1*(9B+21A)+-1//64*a^2*d^-1*(a+a*sin(c+d*x))^-4*(-1B+2A)+-1//80*a^3*d^-1*(a+a*sin(c+d*x))^-5*(A+-1B)+-1//96*a*d^-1*(a+a*sin(c+d*x))^-3*(-1B+5A)+1//128*a^-2*d^-1*(7B+28A)*arctanh(sin(c+d*x))+1//192*a*d^-1*(a+-1*a*sin(c+d*x))^-3*(A+B))
@test integrate((a+a*sin(e+f*x))^m*cos(e+f*x)^7*(A+B*sin(e+f*x)), x) == :(a^-6*f^-1*(6+m)^-1*(a+a*sin(e+f*x))^(6+m)*(-18B+6A)+a^-4*f^-1*(4+m)^-1*(a+a*sin(e+f*x))^(4+m)*(-8B+8A)+-1*B*a^-8*f^-1*(8+m)^-1*(a+a*sin(e+f*x))^(8+m)+-1*a^-7*f^-1*(7+m)^-1*(a+a*sin(e+f*x))^(7+m)*(A+-7B)+-1*a^-5*f^-1*(5+m)^-1*(a+a*sin(e+f*x))^(5+m)*(-20B+12A))
@test integrate((a+a*sin(e+f*x))^m*cos(e+f*x)^5*(A+B*sin(e+f*x)), x) == :(B*a^-6*f^-1*(6+m)^-1*(a+a*sin(e+f*x))^(6+m)+a^-5*f^-1*(5+m)^-1*(a+a*sin(e+f*x))^(5+m)*(A+-5B)+a^-3*f^-1*(3+m)^-1*(a+a*sin(e+f*x))^(3+m)*(-4B+4A)+-1*a^-4*f^-1*(4+m)^-1*(a+a*sin(e+f*x))^(4+m)*(-8B+4A))
@test integrate((a+a*sin(e+f*x))^m*cos(e+f*x)^3*(A+B*sin(e+f*x)), x) == :(a^-2*f^-1*(2+m)^-1*(a+a*sin(e+f*x))^(2+m)*(-2B+2A)+-1*B*a^-4*f^-1*(4+m)^-1*(a+a*sin(e+f*x))^(4+m)+-1*a^-3*f^-1*(3+m)^-1*(a+a*sin(e+f*x))^(3+m)*(A+-3B))
@test integrate((a+a*sin(e+f*x))^m*(A+B*sin(e+f*x))*cos(e+f*x), x) == :(B*a^-2*f^-1*(2+m)^-1*(a+a*sin(e+f*x))^(2+m)+a^-1*f^-1*(1+m)^-1*(a+a*sin(e+f*x))^(1+m)*(A+-1B))
@test integrate((g*cos(e+f*x))^p*(a+a*sin(e+f*x))^m*(A*m+-1*A*(1+m+p)*sin(e+f*x)), x) == :(A*f^-1*g^-1*(g*cos(e+f*x))^(1+p)*(a+a*sin(e+f*x))^m)
@test integrate((g*cos(e+f*x))^p*(a+-1*a*sin(e+f*x))^m*(A*m+A*(1+m+p)*sin(e+f*x)), x) == :(-1*A*f^-1*g^-1*(g*cos(e+f*x))^(1+p)*(a+-1*a*sin(e+f*x))^m)
@test integrate(cos(c+d*x)^2*sin(c+d*x)^3*(a+b*sin(c+d*x)), x) == :(1//16*b*x+-1//3*a*d^-1*cos(c+d*x)^3+1//5*a*d^-1*cos(c+d*x)^5+-1//6*b*d^-1*cos(c+d*x)^3*sin(c+d*x)^3+-1//8*b*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//16*b*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^2*sin(c+d*x)^2*(a+b*sin(c+d*x)), x) == :(1//8*a*x+-1//3*b*d^-1*cos(c+d*x)^3+1//5*b*d^-1*cos(c+d*x)^5+-1//4*a*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//8*a*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^2*(a+b*sin(c+d*x))*sin(c+d*x), x) == :(1//8*b*x+-1//3*a*d^-1*cos(c+d*x)^3+-1//4*b*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//8*b*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^2*(a+b*sin(c+d*x))*csc(c+d*x), x) == :((1/2)*b*x+a*d^-1*cos(c+d*x)+-1*a*d^-1*arctanh(cos(c+d*x))+(1/2)*b*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^2*csc(c+d*x)^2*(a+b*sin(c+d*x)), x) == :(-1*a*x+b*d^-1*cos(c+d*x)+-1*a*d^-1*cot(c+d*x)+-1*b*d^-1*arctanh(cos(c+d*x)))
@test integrate(cos(c+d*x)^2*csc(c+d*x)^3*(a+b*sin(c+d*x)), x) == :(-1*b*x+(1/2)*a*d^-1*arctanh(cos(c+d*x))+-1*b*d^-1*cot(c+d*x)+-1//2*a*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate(cos(c+d*x)^2*csc(c+d*x)^4*(a+b*sin(c+d*x)), x) == :((1/2)*b*d^-1*arctanh(cos(c+d*x))+-1//3*a*d^-1*cot(c+d*x)^3+-1//2*b*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate(cos(c+d*x)^2*csc(c+d*x)^5*(a+b*sin(c+d*x)), x) == :(-1//3*b*d^-1*cot(c+d*x)^3+1//8*a*d^-1*arctanh(cos(c+d*x))+-1//4*a*d^-1*csc(c+d*x)^3*cot(c+d*x)+1//8*a*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate(cos(c+d*x)^2*csc(c+d*x)^6*(a+b*sin(c+d*x)), x) == :(-1//3*a*d^-1*cot(c+d*x)^3+-1//5*a*d^-1*cot(c+d*x)^5+1//8*b*d^-1*arctanh(cos(c+d*x))+-1//4*b*d^-1*csc(c+d*x)^3*cot(c+d*x)+1//8*b*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^2*sin(c+d*x)^3, x) == :(-1//35*d^-1*(4*b^2+7*a^2)*cos(c+d*x)+1//8*a*b*x+1//105*d^-1*cos(c+d*x)^3*(4*b^2+7*a^2)+1//7*d^-1*(a+b*sin(c+d*x))^2*sin(c+d*x)^4*cos(c+d*x)+1//35*d^-1*sin(c+d*x)^4*(-1*b^2+2*a^2)*cos(c+d*x)+-1//8*a*b*d^-1*cos(c+d*x)*sin(c+d*x)+-1//12*a*b*d^-1*sin(c+d*x)^3*cos(c+d*x)+1//21*a*b*d^-1*sin(c+d*x)^5*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^2*sin(c+d*x)^2, x) == :(x*(1//8*a^2+1//16*b^2)+-2//5*a*b*d^-1*cos(c+d*x)+-1//16*d^-1*(b^2+2*a^2)*cos(c+d*x)*sin(c+d*x)+1//6*d^-1*(a+b*sin(c+d*x))^2*sin(c+d*x)^3*cos(c+d*x)+1//24*d^-1*sin(c+d*x)^3*(-1*b^2+2*a^2)*cos(c+d*x)+2//15*a*b*d^-1*cos(c+d*x)^3+1//15*a*b*d^-1*sin(c+d*x)^4*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^2*sin(c+d*x), x) == :(-1//5*d^-1*(a+b*sin(c+d*x))^2*cos(c+d*x)^3+-1//30*d^-1*cos(c+d*x)^3*(a^2+4*b^2)+1//4*a*b*x+-1//10*a*d^-1*cos(c+d*x)^3*(a+b*sin(c+d*x))+1//4*a*b*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^2*csc(c+d*x), x) == :(a*b*x+-1*a^2*d^-1*arctanh(cos(c+d*x))+1//3*d^-1*(a+b*sin(c+d*x))^2*cos(c+d*x)+1//3*d^-1*(-1*b^2+2*a^2)*cos(c+d*x)+1//3*a*b*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^2*csc(c+d*x)^2, x) == :((1/2)*x*b^2+-1*x*a^2+-1*a^2*d^-1*cot(c+d*x)+(1/2)*b^2*d^-1*cos(c+d*x)*sin(c+d*x)+-2*a*b*d^-1*arctanh(cos(c+d*x))+2*a*b*d^-1*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^2*csc(c+d*x)^3, x) == :((1/2)*d^-1*(a^2+-2*b^2)*arctanh(cos(c+d*x))+-2*a*b*x+3//2*b^2*d^-1*cos(c+d*x)+-1*a*b*d^-1*cot(c+d*x)+-1//2*d^-1*(a+b*sin(c+d*x))^2*cot(c+d*x)*csc(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^2*csc(c+d*x)^4, x) == :(-1*x*b^2+1//3*d^-1*(a^2+-2*b^2)*cot(c+d*x)+a*b*d^-1*arctanh(cos(c+d*x))+-1//3*d^-1*(a+b*sin(c+d*x))^2*csc(c+d*x)^2*cot(c+d*x)+-1//3*a*b*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^2*csc(c+d*x)^5, x) == :(1//8*d^-1*(a^2+4*b^2)*arctanh(cos(c+d*x))+-1//4*d^-1*(a+b*sin(c+d*x))^2*csc(c+d*x)^3*cot(c+d*x)+1//8*d^-1*(a^2+-2*b^2)*cot(c+d*x)*csc(c+d*x)+2//3*a*b*d^-1*cot(c+d*x)+-1//6*a*b*d^-1*csc(c+d*x)^2*cot(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^2*csc(c+d*x)^6, x) == :(1//15*d^-1*(2*a^2+5*b^2)*cot(c+d*x)+-1//5*d^-1*(a+b*sin(c+d*x))^2*csc(c+d*x)^4*cot(c+d*x)+1//4*a*b*d^-1*arctanh(cos(c+d*x))+1//15*d^-1*csc(c+d*x)^2*(a^2+-2*b^2)*cot(c+d*x)+-1//10*a*b*d^-1*csc(c+d*x)^3*cot(c+d*x)+1//4*a*b*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^2*csc(c+d*x)^7, x) == :(1//16*d^-1*(a^2+2*b^2)*arctanh(cos(c+d*x))+-1//6*d^-1*(a+b*sin(c+d*x))^2*csc(c+d*x)^5*cot(c+d*x)+1//16*d^-1*(a^2+2*b^2)*cot(c+d*x)*csc(c+d*x)+1//24*d^-1*csc(c+d*x)^3*(a^2+-2*b^2)*cot(c+d*x)+2//5*a*b*d^-1*cot(c+d*x)+2//15*a*b*d^-1*cot(c+d*x)^3+-1//15*a*b*d^-1*csc(c+d*x)^4*cot(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*cos(c+d*x)^2*sin(c+d*x)^2, x) == :(1//16*a*x*(2*a^2+3*b^2)+-1//35*b*d^-1*(4*b^2+21*a^2)*cos(c+d*x)+1//7*d^-1*(a+b*sin(c+d*x))^3*sin(c+d*x)^3*cos(c+d*x)+1//105*b*d^-1*cos(c+d*x)^3*(4*b^2+21*a^2)+-1//16*a*d^-1*(2*a^2+3*b^2)*cos(c+d*x)*sin(c+d*x)+1//14*a*d^-1*(a+b*sin(c+d*x))^2*sin(c+d*x)^3*cos(c+d*x)+1//35*b*d^-1*sin(c+d*x)^4*(a^2+-1*b^2)*cos(c+d*x)+1//56*a*d^-1*sin(c+d*x)^3*(-7*b^2+2*a^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*cos(c+d*x)^2*sin(c+d*x), x) == :(-1//6*d^-1*(a+b*sin(c+d*x))^3*cos(c+d*x)^3+1//16*b*x*(b^2+6*a^2)+-1//10*a*d^-1*(a+b*sin(c+d*x))^2*cos(c+d*x)^3+-1//40*d^-1*cos(c+d*x)^3*(a+b*sin(c+d*x))*(2*a^2+5*b^2)+-1//120*a*d^-1*cos(c+d*x)^3*(2*a^2+33*b^2)+1//16*b*d^-1*(b^2+6*a^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*cos(c+d*x)^2*csc(c+d*x), x) == :(-1*a^3*d^-1*arctanh(cos(c+d*x))+1//4*d^-1*(a+b*sin(c+d*x))^3*cos(c+d*x)+1//8*b*x*(b^2+12*a^2)+(1/2)*a*d^-1*(a^2+-2*b^2)*cos(c+d*x)+1//4*a*d^-1*(a+b*sin(c+d*x))^2*cos(c+d*x)+1//8*b*d^-1*(-1*b^2+2*a^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*cos(c+d*x)^2*csc(c+d*x)^2, x) == :(-1*x*a^3+-1*a^3*d^-1*cot(c+d*x)+-1//3*b^3*d^-1*cos(c+d*x)^3+3//2*a*x*b^2+-3*b*a^2*d^-1*arctanh(cos(c+d*x))+3*b*a^2*d^-1*cos(c+d*x)+3//2*a*b^2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*cos(c+d*x)^2*csc(c+d*x)^3, x) == :(-1//2*b*x*(-1*b^2+6*a^2)+(1/2)*a*d^-1*(a^2+-6*b^2)*arctanh(cos(c+d*x))+-3//2*b*d^-1*(a+b*sin(c+d*x))^2*cot(c+d*x)+-1//2*d^-1*(a+b*sin(c+d*x))^3*cot(c+d*x)*csc(c+d*x)+5//2*b^3*d^-1*cos(c+d*x)*sin(c+d*x)+15//2*a*b^2*d^-1*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*cos(c+d*x)^2*csc(c+d*x)^4, x) == :(-3*a*x*b^2+11//6*b^3*d^-1*cos(c+d*x)+(1/2)*b*d^-1*(-2*b^2+3*a^2)*arctanh(cos(c+d*x))+-1//3*d^-1*(a+b*sin(c+d*x))^3*csc(c+d*x)^2*cot(c+d*x)+1//3*a*d^-1*(a^2+-3*b^2)*cot(c+d*x)+-1//2*b*d^-1*(a+b*sin(c+d*x))^2*cot(c+d*x)*csc(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*cos(c+d*x)^2*csc(c+d*x)^5, x) == :(-1*x*b^3+(1/2)*b*d^-1*(-1*b^2+2*a^2)*cot(c+d*x)+-1//4*d^-1*(a+b*sin(c+d*x))^3*csc(c+d*x)^3*cot(c+d*x)+1//8*a*d^-1*(a^2+12*b^2)*arctanh(cos(c+d*x))+-1//4*b*d^-1*(a+b*sin(c+d*x))^2*csc(c+d*x)^2*cot(c+d*x)+1//8*a*d^-1*(a^2+-2*b^2)*cot(c+d*x)*csc(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*cos(c+d*x)^2*csc(c+d*x)^6, x) == :(-1//5*d^-1*(a+b*sin(c+d*x))^3*csc(c+d*x)^4*cot(c+d*x)+1//8*b*d^-1*(3*a^2+4*b^2)*arctanh(cos(c+d*x))+1//15*a*d^-1*(2*a^2+15*b^2)*cot(c+d*x)+-3//20*b*d^-1*(a+b*sin(c+d*x))^2*csc(c+d*x)^3*cot(c+d*x)+1//30*a*d^-1*csc(c+d*x)^2*(-3*b^2+2*a^2)*cot(c+d*x)+3//40*b*d^-1*(-2*b^2+5*a^2)*cot(c+d*x)*csc(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*cos(c+d*x)^2*csc(c+d*x)^7, x) == :(-1//6*d^-1*(a+b*sin(c+d*x))^3*csc(c+d*x)^5*cot(c+d*x)+1//15*b*d^-1*(5*b^2+6*a^2)*cot(c+d*x)+1//16*a*d^-1*(a^2+6*b^2)*arctanh(cos(c+d*x))+-1//10*b*d^-1*(a+b*sin(c+d*x))^2*csc(c+d*x)^4*cot(c+d*x)+1//15*b*d^-1*csc(c+d*x)^2*(-1*b^2+3*a^2)*cot(c+d*x)+1//16*a*d^-1*(a^2+6*b^2)*cot(c+d*x)*csc(c+d*x)+1//120*a*d^-1*csc(c+d*x)^3*(-6*b^2+5*a^2)*cot(c+d*x))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^2*sin(c+d*x)^3, x) == :(a*x*b^-5*(-1*b^2+4*a^2)+1//3*b^-4*d^-1*(-1*b^2+12*a^2)*cos(c+d*x)+4//3*b^-2*d^-1*sin(c+d*x)^2*cos(c+d*x)+-1*b^-1*d^-1*(a+b*sin(c+d*x))^-1*sin(c+d*x)^3*cos(c+d*x)+-2*a*b^-3*d^-1*cos(c+d*x)*sin(c+d*x)+-2*a^2*b^-5*d^-1*(a^2+-1*b^2)^-1//2*(-3*b^2+4*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^2*sin(c+d*x)^2, x) == :(-1//2*x*b^-4*(-1*b^2+6*a^2)+-3*a*b^-3*d^-1*cos(c+d*x)+3//2*b^-2*d^-1*cos(c+d*x)*sin(c+d*x)+-1*b^-1*d^-1*(a+b*sin(c+d*x))^-1*sin(c+d*x)^2*cos(c+d*x)+2*a*b^-4*d^-1*(a^2+-1*b^2)^-1//2*(-2*b^2+3*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^2*sin(c+d*x), x) == :(2*a*x*b^-3+b^-2*d^-1*(a+b*sin(c+d*x))^-1*(2a+b*sin(c+d*x))*cos(c+d*x)+-1*b^-3*d^-1*(a^2+-1*b^2)^-1//2*(-2*b^2+4*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^2*csc(c+d*x), x) == :(-1*a^-2*d^-1*arctanh(cos(c+d*x))+a^-1*d^-1*(a+b*sin(c+d*x))^-1*cos(c+d*x)+-2*b*a^-2*d^-1*(a^2+-1*b^2)^-1//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^2*csc(c+d*x)^2, x) == :(-2*a^-2*d^-1*cot(c+d*x)+a^-1*d^-1*(a+b*sin(c+d*x))^-1*cot(c+d*x)+2*b*a^-3*d^-1*arctanh(cos(c+d*x))+-1*a^-3*d^-1*(a^2+-1*b^2)^-1//2*(-4*b^2+2*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^2*csc(c+d*x)^3, x) == :((1/2)*a^-4*d^-1*(a^2+-6*b^2)*arctanh(cos(c+d*x))+3*b*a^-3*d^-1*cot(c+d*x)+-3//2*a^-2*d^-1*cot(c+d*x)*csc(c+d*x)+a^-1*d^-1*(a+b*sin(c+d*x))^-1*cot(c+d*x)*csc(c+d*x)+2*b*a^-4*d^-1*(a^2+-1*b^2)^-1//2*(-3*b^2+2*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^2*csc(c+d*x)^4, x) == :(-4//3*a^-2*d^-1*csc(c+d*x)^2*cot(c+d*x)+1//3*a^-4*d^-1*(a^2+-12*b^2)*cot(c+d*x)+a^-1*d^-1*(a+b*sin(c+d*x))^-1*csc(c+d*x)^2*cot(c+d*x)+-1*b*a^-5*d^-1*(a^2+-4*b^2)*arctanh(cos(c+d*x))+2*b*a^-3*d^-1*cot(c+d*x)*csc(c+d*x)+-2*a^-5*b^2*d^-1*(a^2+-1*b^2)^-1//2*(-4*b^2+3*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-3*cos(c+d*x)^2*sin(c+d*x)^3, x) == :(-1//2*x*b^-5*(-1*b^2+12*a^2)+-1//2*b^-1*d^-1*(a+b*sin(c+d*x))^-2*sin(c+d*x)^3*cos(c+d*x)+a*b^-5*d^-1*(a^2+-1*b^2)^-3//2*(6*b^4+12*a^4+-19*a^2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+(1/2)*b^-3*d^-1*(a^2+-1*b^2)^-1*(-5*b^2+6*a^2)*cos(c+d*x)*sin(c+d*x)+-1//2*a*b^-4*d^-1*(a^2+-1*b^2)^-1*(-11*b^2+12*a^2)*cos(c+d*x)+-1//2*b^-2*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-1*sin(c+d*x)^2*(-3*b^2+4*a^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-3*cos(c+d*x)^2*sin(c+d*x)^2, x) == :(3*a*x*b^-4+3//2*b^-3*d^-1*cos(c+d*x)+-1*b^-4*d^-1*(a^2+-1*b^2)^-3//2*(2*b^4+6*a^4+-9*a^2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//2*b^-1*d^-1*(a+b*sin(c+d*x))^-2*sin(c+d*x)^2*cos(c+d*x)+(1/2)*a*b^-3*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-1*(-2*b^2+3*a^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-3*cos(c+d*x)^2*sin(c+d*x), x) == :(-1*x*b^-3+-1*a*d^-1*(a+b*sin(c+d*x))^-2*(-2*b^2+2*a^2)^-1*cos(c+d*x)^3+a*b^-3*d^-1*(a^2+-1*b^2)^-3//2*(-3*b^2+2*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//2*b^-2*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-1*(-2*b^2+2*a^2+a*b*sin(c+d*x))*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-3*cos(c+d*x)^2*csc(c+d*x), x) == :(-1*a^-3*d^-1*arctanh(cos(c+d*x))+(1/2)*a^-1*d^-1*(a+b*sin(c+d*x))^-2*cos(c+d*x)+(1/2)*a^-2*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-1*(a^2+-2*b^2)*cos(c+d*x)+-1*b*a^-3*d^-1*(a^2+-1*b^2)^-3//2*(-2*b^2+3*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-3*cos(c+d*x)^2*csc(c+d*x)^2, x) == :((1/2)*a^-1*d^-1*(a+b*sin(c+d*x))^-2*cot(c+d*x)+3*b*a^-4*d^-1*arctanh(cos(c+d*x))+-1*a^-4*d^-1*(a^2+-1*b^2)^-3//2*(2*a^4+6*b^4+-9*a^2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//2*a^-3*d^-1*(a^2+-1*b^2)^-1*(-6*b^2+5*a^2)*cot(c+d*x)+(1/2)*a^-2*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-1*(-3*b^2+2*a^2)*cot(c+d*x))
@test integrate((a+b*sin(c+d*x))^-3*cos(c+d*x)^2*csc(c+d*x)^3, x) == :((1/2)*a^-5*d^-1*(a^2+-12*b^2)*arctanh(cos(c+d*x))+(1/2)*a^-1*d^-1*(a+b*sin(c+d*x))^-2*cot(c+d*x)*csc(c+d*x)+b*a^-5*d^-1*(a^2+-1*b^2)^-3//2*(6*a^4+12*b^4+-19*a^2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+(1/2)*b*a^-4*d^-1*(a^2+-1*b^2)^-1*(-12*b^2+11*a^2)*cot(c+d*x)+-1//2*a^-3*d^-1*(a^2+-1*b^2)^-1*(-6*b^2+5*a^2)*cot(c+d*x)*csc(c+d*x)+(1/2)*a^-2*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-1*(-4*b^2+3*a^2)*cot(c+d*x)*csc(c+d*x))
@test integrate((d*sin(e+f*x))^-1//2*(a+b*sin(e+f*x))^-5//2*cos(e+f*x)^2, x) == :(2//3*a^-1*d^-1*f^-1*(d*sin(e+f*x))^(1/2)*(a+b*sin(e+f*x))^-3//2*cos(e+f*x)+4//3*b*a^-1*f^-1*(d*sin(e+f*x))^-1//2*(a+b*sin(e+f*x))^-1//2*(a^2+-1*b^2)^-1*cos(e+f*x)+-4//3*a^-2*d^-1//2*f^-1*(a*(a+b)^-1*(1+-1*csc(e+f*x)))^(1/2)*(a*(a+-1b)^-1*(1+csc(e+f*x)))^(1/2)*(a+b)^-1//2*Elliptic.F(arcsin(d^(1/2)*(d*sin(e+f*x))^-1//2*(a+b)^-1//2*(a+b*sin(e+f*x))^(1/2)),-1*(a+-1b)^-1*(a+b))*tan(e+f*x)+-4//3*b*a^-3*d^-1//2*f^-1*(a*(a+b)^-1*(1+-1*csc(e+f*x)))^(1/2)*(a*(a+-1b)^-1*(1+csc(e+f*x)))^(1/2)*(a+b)^-1//2*Elliptic.E(arcsin(d^(1/2)*(d*sin(e+f*x))^-1//2*(a+b)^-1//2*(a+b*sin(e+f*x))^(1/2)),-1*(a+-1b)^-1*(a+b))*tan(e+f*x))
@test integrate(cos(c+d*x)^4*sin(c+d*x)^4*(a+b*sin(c+d*x)), x) == :(3//128*a*x+-1//5*b*d^-1*cos(c+d*x)^5+-1//9*b*d^-1*cos(c+d*x)^9+2//7*b*d^-1*cos(c+d*x)^7+-1//8*a*d^-1*cos(c+d*x)^5*sin(c+d*x)^3+-1//16*a*d^-1*cos(c+d*x)^5*sin(c+d*x)+1//64*a*d^-1*cos(c+d*x)^3*sin(c+d*x)+3//128*a*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^4*sin(c+d*x)^3*(a+b*sin(c+d*x)), x) == :(3//128*b*x+-1//5*a*d^-1*cos(c+d*x)^5+1//7*a*d^-1*cos(c+d*x)^7+-1//8*b*d^-1*cos(c+d*x)^5*sin(c+d*x)^3+-1//16*b*d^-1*cos(c+d*x)^5*sin(c+d*x)+1//64*b*d^-1*cos(c+d*x)^3*sin(c+d*x)+3//128*b*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^4*sin(c+d*x)^2*(a+b*sin(c+d*x)), x) == :(1//16*a*x+-1//5*b*d^-1*cos(c+d*x)^5+1//7*b*d^-1*cos(c+d*x)^7+-1//6*a*d^-1*cos(c+d*x)^5*sin(c+d*x)+1//16*a*d^-1*cos(c+d*x)*sin(c+d*x)+1//24*a*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate(cos(c+d*x)^4*(a+b*sin(c+d*x))*sin(c+d*x), x) == :(1//16*b*x+-1//5*a*d^-1*cos(c+d*x)^5+-1//6*b*d^-1*cos(c+d*x)^5*sin(c+d*x)+1//16*b*d^-1*cos(c+d*x)*sin(c+d*x)+1//24*b*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate(cos(c+d*x)^4*(a+b*sin(c+d*x))*csc(c+d*x), x) == :(3//8*b*x+a*d^-1*cos(c+d*x)+-1*a*d^-1*arctanh(cos(c+d*x))+1//3*a*d^-1*cos(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)^4*csc(c+d*x)^2*(a+b*sin(c+d*x)), x) == :(-3//2*a*x+b*d^-1*cos(c+d*x)+-1*b*d^-1*arctanh(cos(c+d*x))+-3//2*a*d^-1*cot(c+d*x)+1//3*b*d^-1*cos(c+d*x)^3+(1/2)*a*d^-1*cos(c+d*x)^2*cot(c+d*x))
@test integrate(cos(c+d*x)^4*csc(c+d*x)^3*(a+b*sin(c+d*x)), x) == :(-3//2*b*x+-3//2*a*d^-1*cos(c+d*x)+-3//2*b*d^-1*cot(c+d*x)+3//2*a*d^-1*arctanh(cos(c+d*x))+(1/2)*b*d^-1*cos(c+d*x)^2*cot(c+d*x)+-1//2*a*d^-1*cot(c+d*x)^2*cos(c+d*x))
@test integrate(cos(c+d*x)^4*csc(c+d*x)^4*(a+b*sin(c+d*x)), x) == :(a*x+a*d^-1*cot(c+d*x)+-3//2*b*d^-1*cos(c+d*x)+-1//3*a*d^-1*cot(c+d*x)^3+3//2*b*d^-1*arctanh(cos(c+d*x))+-1//2*b*d^-1*cot(c+d*x)^2*cos(c+d*x))
@test integrate(cos(c+d*x)^4*csc(c+d*x)^5*(a+b*sin(c+d*x)), x) == :(b*x+b*d^-1*cot(c+d*x)+-3//8*a*d^-1*arctanh(cos(c+d*x))+-1//3*b*d^-1*cot(c+d*x)^3+-1//4*a*d^-1*cot(c+d*x)^3*csc(c+d*x)+3//8*a*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate(cos(c+d*x)^4*csc(c+d*x)^6*(a+b*sin(c+d*x)), x) == :(-3//8*b*d^-1*arctanh(cos(c+d*x))+-1//5*a*d^-1*cot(c+d*x)^5+-1//4*b*d^-1*cot(c+d*x)^3*csc(c+d*x)+3//8*b*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate(cos(c+d*x)^4*csc(c+d*x)^7*(a+b*sin(c+d*x)), x) == :(-1//5*b*d^-1*cot(c+d*x)^5+-1//16*a*d^-1*arctanh(cos(c+d*x))+-1//6*a*d^-1*cot(c+d*x)^3*csc(c+d*x)^3+-1//16*a*d^-1*cot(c+d*x)*csc(c+d*x)+1//8*a*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate(cos(c+d*x)^4*csc(c+d*x)^8*(a+b*sin(c+d*x)), x) == :(-1//5*a*d^-1*cot(c+d*x)^5+-1//7*a*d^-1*cot(c+d*x)^7+-1//16*b*d^-1*arctanh(cos(c+d*x))+-1//6*b*d^-1*cot(c+d*x)^3*csc(c+d*x)^3+-1//16*b*d^-1*cot(c+d*x)*csc(c+d*x)+1//8*b*d^-1*csc(c+d*x)^3*cot(c+d*x))
@test integrate(cos(c+d*x)^4*csc(c+d*x)^9*(a+b*sin(c+d*x)), x) == :(-3//128*a*d^-1*arctanh(cos(c+d*x))+-1//5*b*d^-1*cot(c+d*x)^5+-1//7*b*d^-1*cot(c+d*x)^7+-3//128*a*d^-1*cot(c+d*x)*csc(c+d*x)+-1//8*a*d^-1*cot(c+d*x)^3*csc(c+d*x)^5+-1//64*a*d^-1*csc(c+d*x)^3*cot(c+d*x)+1//16*a*d^-1*csc(c+d*x)^5*cot(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^4*sin(c+d*x)^3, x) == :(-1//105*d^-1*(4*b^2+9*a^2)*cos(c+d*x)+1//315*d^-1*cos(c+d*x)^3*(4*b^2+9*a^2)+3//64*a*b*x+-3//64*a*b*d^-1*cos(c+d*x)*sin(c+d*x)+-1//9*b^-1*d^-1*(a+b*sin(c+d*x))^3*sin(c+d*x)^5*cos(c+d*x)+-1//32*a*b*d^-1*sin(c+d*x)^3*cos(c+d*x)+-1//630*b^-2*d^-1*sin(c+d*x)^4*(6*b^4+15*a^4+-44*a^2*b^2)*cos(c+d*x)+-1//252*b^-2*d^-1*(a+b*sin(c+d*x))^2*sin(c+d*x)^4*(-40*b^2+15*a^2)*cos(c+d*x)+-1//504*a*b^-1*d^-1*sin(c+d*x)^5*(-29*b^2+10*a^2)*cos(c+d*x)+1//12*a*b^-2*d^-1*(a+b*sin(c+d*x))^3*sin(c+d*x)^4*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^4*sin(c+d*x)^2, x) == :(x*(1//16*a^2+3//128*b^2)+-6//35*a*b*d^-1*cos(c+d*x)+-1//128*d^-1*(3*b^2+8*a^2)*cos(c+d*x)*sin(c+d*x)+2//35*a*b*d^-1*cos(c+d*x)^3+-1//8*b^-1*d^-1*(a+b*sin(c+d*x))^3*sin(c+d*x)^4*cos(c+d*x)+-1//1344*b^-2*d^-1*sin(c+d*x)^3*(21*b^4+40*a^4+-140*a^2*b^2)*cos(c+d*x)+-1//336*b^-2*d^-1*(a+b*sin(c+d*x))^2*sin(c+d*x)^3*(-63*b^2+20*a^2)*cos(c+d*x)+-1//840*a*b^-1*d^-1*sin(c+d*x)^4*(-69*b^2+20*a^2)*cos(c+d*x)+5//56*a*b^-2*d^-1*(a+b*sin(c+d*x))^3*sin(c+d*x)^3*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^4*sin(c+d*x), x) == :(-1//7*d^-1*(a+b*sin(c+d*x))^2*cos(c+d*x)^5+-1//105*d^-1*cos(c+d*x)^5*(a^2+6*b^2)+1//8*a*b*x+-1//21*a*d^-1*cos(c+d*x)^5*(a+b*sin(c+d*x))+1//8*a*b*d^-1*cos(c+d*x)*sin(c+d*x)+1//12*a*b*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^4*csc(c+d*x)^2, x) == :(x*(-3//2*a^2+3//8*b^2)+-1*a^-1*d^-1*(a+b*sin(c+d*x))^3*cot(c+d*x)+-2*a*b*d^-1*arctanh(cos(c+d*x))+-1//4*b^-1*d^-1*(a+b*sin(c+d*x))^3*cos(c+d*x)+1//24*d^-1*(2*a^2+39*b^2)*cos(c+d*x)*sin(c+d*x)+1//6*a*b^-1*d^-1*(a^2+28*b^2)*cos(c+d*x)+1//12*a^-1*b^-1*d^-1*(a+b*sin(c+d*x))^2*(a^2+12*b^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^4*csc(c+d*x)^3, x) == :((1/2)*d^-1*(-2*b^2+3*a^2)*arctanh(cos(c+d*x))+-3*a*b*x+-1//6*d^-1*(-23*b^2+4*a^2)*cos(c+d*x)+-1//2*b*a^-2*d^-1*(a+b*sin(c+d*x))^3*cot(c+d*x)+-1//2*a^-1*d^-1*(a+b*sin(c+d*x))^3*cot(c+d*x)*csc(c+d*x)+-1//6*a^-2*d^-1*(a+b*sin(c+d*x))^2*(-3*b^2+2*a^2)*cos(c+d*x)+-1//3*b*a^-1*d^-1*(a^2+-3*b^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^4*csc(c+d*x)^4, x) == :(x*a^2+-3//2*x*b^2+a^2*d^-1*cot(c+d*x)+-3//2*b^2*d^-1*cot(c+d*x)+-1//3*a^2*d^-1*cot(c+d*x)^3+(1/2)*b^2*d^-1*cos(c+d*x)^2*cot(c+d*x)+-3*a*b*d^-1*cos(c+d*x)+3*a*b*d^-1*arctanh(cos(c+d*x))+-1*a*b*d^-1*cot(c+d*x)^2*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^4*csc(c+d*x)^5, x) == :(2*a*b*x+-1//8*d^-1*(-12*b^2+3*a^2)*arctanh(cos(c+d*x))+5//8*d^-1*(a+b*sin(c+d*x))^2*cot(c+d*x)*csc(c+d*x)+17//12*a*b*d^-1*cot(c+d*x)+-1//4*a^-1*d^-1*(a+b*sin(c+d*x))^3*csc(c+d*x)^3*cot(c+d*x)+-1//24*a^-2*b^2*d^-1*(2*b^2+39*a^2)*cos(c+d*x)+1//12*b*a^-2*d^-1*(a+b*sin(c+d*x))^3*csc(c+d*x)^2*cot(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^4*csc(c+d*x)^6, x) == :(x*b^2+-3//4*a*b*d^-1*arctanh(cos(c+d*x))+-1//15*a^-2*d^-1*(b^4+3*a^4+-14*a^2*b^2)*cot(c+d*x)+-1//5*a^-1*d^-1*(a+b*sin(c+d*x))^3*csc(c+d*x)^4*cot(c+d*x)+1//10*b*a^-2*d^-1*(a+b*sin(c+d*x))^3*csc(c+d*x)^3*cot(c+d*x)+1//30*a^-2*d^-1*(a+b*sin(c+d*x))^2*csc(c+d*x)^2*(-1*b^2+12*a^2)*cot(c+d*x)+1//60*b*a^-1*d^-1*(-2*b^2+27*a^2)*cot(c+d*x)*csc(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^4*csc(c+d*x)^7, x) == :(-1//16*d^-1*(a^2+6*b^2)*arctanh(cos(c+d*x))+-2//5*a*b*d^-1*cot(c+d*x)+-1//6*a^-1*d^-1*(a+b*sin(c+d*x))^3*csc(c+d*x)^5*cot(c+d*x)+-1//240*a^-2*d^-1*(12*b^4+15*a^4+-80*a^2*b^2)*cot(c+d*x)*csc(c+d*x)+1//10*b*a^-2*d^-1*(a+b*sin(c+d*x))^3*csc(c+d*x)^4*cot(c+d*x)+1//60*b*a^-1*d^-1*csc(c+d*x)^2*(-2*b^2+13*a^2)*cot(c+d*x)+1//120*a^-2*d^-1*(a+b*sin(c+d*x))^2*csc(c+d*x)^3*(-6*b^2+35*a^2)*cot(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^4*csc(c+d*x)^8, x) == :(-1//35*d^-1*(2*a^2+7*b^2)*cot(c+d*x)+-1//8*a*b*d^-1*arctanh(cos(c+d*x))+-1//7*a^-1*d^-1*(a+b*sin(c+d*x))^3*csc(c+d*x)^6*cot(c+d*x)+-1//8*a*b*d^-1*cot(c+d*x)*csc(c+d*x)+-1//105*a^-2*d^-1*csc(c+d*x)^2*(3*a^4+4*b^4+-18*a^2*b^2)*cot(c+d*x)+1//35*a^-2*d^-1*(a+b*sin(c+d*x))^2*csc(c+d*x)^4*(-2*b^2+8*a^2)*cot(c+d*x)+1//420*b*a^-1*d^-1*csc(c+d*x)^3*(-12*b^2+53*a^2)*cot(c+d*x)+2//21*b*a^-2*d^-1*(a+b*sin(c+d*x))^3*csc(c+d*x)^5*cot(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*cos(c+d*x)^4*sin(c+d*x)^2, x) == :(1//128*a*x*(8*a^2+9*b^2)+-1//105*b*d^-1*(4*b^2+27*a^2)*cos(c+d*x)+1//315*b*d^-1*cos(c+d*x)^3*(4*b^2+27*a^2)+-1//9*b^-1*d^-1*(a+b*sin(c+d*x))^4*sin(c+d*x)^4*cos(c+d*x)+-1//128*a*d^-1*(8*a^2+9*b^2)*cos(c+d*x)*sin(c+d*x)+-1//2520*b^-1*d^-1*sin(c+d*x)^4*(20*a^4+24*b^4+-93*a^2*b^2)*cos(c+d*x)+-1//126*b^-2*d^-1*(a+b*sin(c+d*x))^3*sin(c+d*x)^3*(-20*b^2+5*a^2)*cos(c+d*x)+-1//4032*a*b^-2*d^-1*sin(c+d*x)^3*(40*a^4+189*b^4+-188*a^2*b^2)*cos(c+d*x)+5//72*a*b^-2*d^-1*(a+b*sin(c+d*x))^4*sin(c+d*x)^3*cos(c+d*x)+-1//1008*a*b^-2*d^-1*(a+b*sin(c+d*x))^2*sin(c+d*x)^3*(-87*b^2+20*a^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*cos(c+d*x)^4*sin(c+d*x), x) == :(-1//8*d^-1*(a+b*sin(c+d*x))^3*cos(c+d*x)^5+3//128*b*x*(b^2+8*a^2)+-3//56*a*d^-1*(a+b*sin(c+d*x))^2*cos(c+d*x)^5+-1//112*d^-1*cos(c+d*x)^5*(a+b*sin(c+d*x))*(2*a^2+7*b^2)+-1//560*a*d^-1*cos(c+d*x)^5*(2*a^2+61*b^2)+1//64*b*d^-1*cos(c+d*x)^3*(b^2+8*a^2)*sin(c+d*x)+3//128*b*d^-1*(b^2+8*a^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*cos(c+d*x)^4*csc(c+d*x), x) == :(-1*a^3*d^-1*arctanh(cos(c+d*x))+1//16*b*x*(b^2+18*a^2)+-1//6*b^-1*d^-1*(a+b*sin(c+d*x))^4*cos(c+d*x)*sin(c+d*x)+-1//60*a*b^-2*d^-1*(2*a^4+36*b^4+-43*a^2*b^2)*cos(c+d*x)+-1//120*b^-2*d^-1*(a+b*sin(c+d*x))^3*(-35*b^2+2*a^2)*cos(c+d*x)+-1//240*b^-1*d^-1*(4*a^4+15*b^4+-84*a^2*b^2)*cos(c+d*x)*sin(c+d*x)+1//15*a*b^-2*d^-1*(a+b*sin(c+d*x))^4*cos(c+d*x)+-1//120*a*b^-2*d^-1*(a+b*sin(c+d*x))^2*(-39*b^2+2*a^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*cos(c+d*x)^4*csc(c+d*x)^2, x) == :(-3//8*a*x*(-3*b^2+4*a^2)+-1*a^-1*d^-1*(a+b*sin(c+d*x))^4*cot(c+d*x)+-3*b*a^2*d^-1*arctanh(cos(c+d*x))+-1//5*b^-1*d^-1*(a+b*sin(c+d*x))^4*cos(c+d*x)+1//10*b^-1*d^-1*(a^4+-2*b^4+56*a^2*b^2)*cos(c+d*x)+1//20*b^-1*d^-1*(a+b*sin(c+d*x))^2*(a^2+28*b^2)*cos(c+d*x)+1//40*a*d^-1*(2*a^2+83*b^2)*cos(c+d*x)*sin(c+d*x)+1//20*a^-1*b^-1*d^-1*(a+b*sin(c+d*x))^3*(a^2+20*b^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*cos(c+d*x)^4*csc(c+d*x)^3, x) == :(-3//8*b*x*(-1*b^2+12*a^2)+-1//2*a*d^-1*(a^2+-17*b^2)*cos(c+d*x)+3//2*a*d^-1*(a^2+-2*b^2)*arctanh(cos(c+d*x))+-1*b*a^-2*d^-1*(a+b*sin(c+d*x))^4*cot(c+d*x)+-1//2*a^-1*d^-1*(a+b*sin(c+d*x))^4*cot(c+d*x)*csc(c+d*x)+-1//4*a^-1*d^-1*(a+b*sin(c+d*x))^2*(a^2+-6*b^2)*cos(c+d*x)+-1//4*a^-2*d^-1*(a+b*sin(c+d*x))^3*(a^2+-4*b^2)*cos(c+d*x)+-1//8*b*d^-1*(-21*b^2+2*a^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*cos(c+d*x)^4*csc(c+d*x)^4, x) == :(x*a^3+a^3*d^-1*cot(c+d*x)+b^3*d^-1*cos(c+d*x)+-1*b^3*d^-1*arctanh(cos(c+d*x))+-9//2*a*x*b^2+-1//3*a^3*d^-1*cot(c+d*x)^3+1//3*b^3*d^-1*cos(c+d*x)^3+-9//2*a*b^2*d^-1*cot(c+d*x)+-9//2*b*a^2*d^-1*cos(c+d*x)+9//2*b*a^2*d^-1*arctanh(cos(c+d*x))+-3//2*b*a^2*d^-1*cot(c+d*x)^2*cos(c+d*x)+3//2*a*b^2*d^-1*cos(c+d*x)^2*cot(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*cos(c+d*x)^4*csc(c+d*x)^5, x) == :(3//2*b*x*(-1*b^2+2*a^2)+-13//4*b^3*d^-1*cos(c+d*x)*sin(c+d*x)+-3//8*a*d^-1*(a^2+-12*b^2)*arctanh(cos(c+d*x))+5//8*d^-1*(a+b*sin(c+d*x))^3*cot(c+d*x)*csc(c+d*x)+17//8*b*d^-1*(a+b*sin(c+d*x))^2*cot(c+d*x)+-1//4*a^-1*d^-1*(a+b*sin(c+d*x))^4*csc(c+d*x)^3*cot(c+d*x)+-1//8*a^-1*b^2*d^-1*(-2*b^2+73*a^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*cos(c+d*x)^4*csc(c+d*x)^6, x) == :(3*a*x*b^2+-3//8*b*d^-1*(-4*b^2+3*a^2)*arctanh(cos(c+d*x))+-1//20*a*d^-1*(-29*b^2+4*a^2)*cot(c+d*x)+2//5*d^-1*(a+b*sin(c+d*x))^3*csc(c+d*x)^2*cot(c+d*x)+-1//5*a^-1*d^-1*(a+b*sin(c+d*x))^4*csc(c+d*x)^4*cot(c+d*x)+-1//40*a^-2*b^3*d^-1*(2*b^2+83*a^2)*cos(c+d*x)+27//40*b*d^-1*(a+b*sin(c+d*x))^2*cot(c+d*x)*csc(c+d*x)+1//20*b*a^-2*d^-1*(a+b*sin(c+d*x))^4*csc(c+d*x)^3*cot(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*cos(c+d*x)^4*csc(c+d*x)^7, x) == :(x*b^3+-1//16*a*d^-1*(a^2+18*b^2)*arctanh(cos(c+d*x))+-1//6*a^-1*d^-1*(a+b*sin(c+d*x))^4*csc(c+d*x)^5*cot(c+d*x)+-1//60*b*a^-2*d^-1*(2*b^4+36*a^4+-43*a^2*b^2)*cot(c+d*x)+-1//240*a^-1*d^-1*(4*b^4+15*a^4+-84*a^2*b^2)*cot(c+d*x)*csc(c+d*x)+1//15*b*a^-2*d^-1*(a+b*sin(c+d*x))^4*csc(c+d*x)^4*cot(c+d*x)+1//120*a^-2*d^-1*(a+b*sin(c+d*x))^3*csc(c+d*x)^3*(-2*b^2+35*a^2)*cot(c+d*x)+1//120*b*a^-2*d^-1*(a+b*sin(c+d*x))^2*csc(c+d*x)^2*(-2*b^2+39*a^2)*cot(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*cos(c+d*x)^4*csc(c+d*x)^8, x) == :(-3//16*b*d^-1*(a^2+2*b^2)*arctanh(cos(c+d*x))+-1//35*a*d^-1*(2*a^2+21*b^2)*cot(c+d*x)+-1//7*a^-1*d^-1*(a+b*sin(c+d*x))^4*csc(c+d*x)^6*cot(c+d*x)+-1//140*a^-1*d^-1*csc(c+d*x)^2*(2*b^4+4*a^4+-19*a^2*b^2)*cot(c+d*x)+-1//560*b*a^-2*d^-1*(12*b^4+105*a^4+-116*a^2*b^2)*cot(c+d*x)*csc(c+d*x)+1//14*b*a^-2*d^-1*(a+b*sin(c+d*x))^4*csc(c+d*x)^5*cot(c+d*x)+1//35*a^-2*d^-1*(a+b*sin(c+d*x))^3*csc(c+d*x)^4*(-1*b^2+8*a^2)*cot(c+d*x)+1//280*b*a^-2*d^-1*(a+b*sin(c+d*x))^2*csc(c+d*x)^3*(-6*b^2+53*a^2)*cot(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*cos(c+d*x)^4*csc(c+d*x)^9, x) == :(-3//128*a*d^-1*(a^2+8*b^2)*arctanh(cos(c+d*x))+-1//35*b*d^-1*(6*a^2+7*b^2)*cot(c+d*x)+-3//128*a*d^-1*(a^2+8*b^2)*cot(c+d*x)*csc(c+d*x)+-1//8*a^-1*d^-1*(a+b*sin(c+d*x))^4*csc(c+d*x)^7*cot(c+d*x)+-1//2240*a^-1*d^-1*csc(c+d*x)^3*(24*b^4+35*a^4+-148*a^2*b^2)*cot(c+d*x)+-1//280*b*a^-2*d^-1*csc(c+d*x)^2*(4*b^4+24*a^4+-25*a^2*b^2)*cot(c+d*x)+1//14*b*a^-2*d^-1*(a+b*sin(c+d*x))^4*csc(c+d*x)^6*cot(c+d*x)+1//112*a^-2*d^-1*(a+b*sin(c+d*x))^3*csc(c+d*x)^5*(-4*b^2+21*a^2)*cot(c+d*x)+3//560*b*a^-2*d^-1*(a+b*sin(c+d*x))^2*csc(c+d*x)^4*(-4*b^2+23*a^2)*cot(c+d*x))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^4*sin(c+d*x)^3, x) == :(-3//4*a*x*b^-7*(b^4+8*a^4+-8*a^2*b^2)+-1//5*b^-6*d^-1*(b^4+30*a^4+-25*a^2*b^2)*cos(c+d*x)+-1//5*b^-2*d^-1*sin(c+d*x)^4*cos(c+d*x)+-1//5*b^-4*d^-1*sin(c+d*x)^2*(-7*b^2+10*a^2)*cos(c+d*x)+(1/2)*a^-1*b^-3*d^-1*sin(c+d*x)^3*(-2*b^2+3*a^2)*cos(c+d*x)+6*a^2*b^-7*d^-1*(a^2+-1*b^2)^-1//2*(b^4+2*a^4+-3*a^2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+3//4*a*b^-5*d^-1*(-3*b^2+4*a^2)*cos(c+d*x)*sin(c+d*x)+-1*a^-1*b^-2*d^-1*(a+b*sin(c+d*x))^-1*sin(c+d*x)^4*(a^2+-1*b^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^4*sin(c+d*x)^2, x) == :(1//8*x*b^-6*(3*b^4+40*a^4+-36*a^2*b^2)+-1//4*b^-2*d^-1*sin(c+d*x)^3*cos(c+d*x)+-1//8*b^-4*d^-1*(-13*b^2+20*a^2)*cos(c+d*x)*sin(c+d*x)+1//3*a*b^-5*d^-1*(-11*b^2+15*a^2)*cos(c+d*x)+-2*a*b^-6*d^-1*(a^2+-1*b^2)^-1//2*(2*b^4+5*a^4+-7*a^2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+1//3*a^-1*b^-3*d^-1*sin(c+d*x)^2*(-3*b^2+5*a^2)*cos(c+d*x)+-1*a^-1*b^-2*d^-1*(a+b*sin(c+d*x))^-1*sin(c+d*x)^3*(a^2+-1*b^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^4*sin(c+d*x), x) == :(-1*a*x*b^-5*(-3*b^2+4*a^2)+-1*b^-4*d^-1*(-1*b^2+4*a^2+-2*a*b*sin(c+d*x))*cos(c+d*x)+b^-5*d^-1*(a^2+-1*b^2)^-1//2*(2*b^4+8*a^4+-10*a^2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+1//3*b^-2*d^-1*(a+b*sin(c+d*x))^-1*cos(c+d*x)^3*(4a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^4*csc(c+d*x), x) == :(-1*a^-2*d^-1*arctanh(cos(c+d*x))+-1*b^-2*d^-1*cos(c+d*x)+-2*a*x*b^-3+-1*a^-1*b^-2*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)*cos(c+d*x)+2*a^-2*b^-3*d^-1*(a^2+-1*b^2)^(1/2)*(b^2+2*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^4*csc(c+d*x)^2, x) == :(x*b^-2+-1*a^-1*d^-1*(a+b*sin(c+d*x))^-1*cot(c+d*x)+2*b*a^-3*d^-1*arctanh(cos(c+d*x))+a^-2*b^-1*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-2*b^2)*cos(c+d*x)+-1*a^-3*b^-2*d^-1*(a^2+-1*b^2)^-1//2*(-4*b^4+2*a^4+2*a^2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^4*csc(c+d*x)^4, x) == :(1//3*a^-4*d^-1*(-12*b^2+7*a^2)*cot(c+d*x)+a^-5*d^-1*(a^2+-1*b^2)^-1//2*(2*a^4+8*b^4+-10*a^2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1*b*a^-5*d^-1*(-4*b^2+3*a^2)*arctanh(cos(c+d*x))+-1//3*a^-1*d^-1*(a+b*sin(c+d*x))^-1*csc(c+d*x)^2*cot(c+d*x)+-1*a^-3*b^-1*d^-1*(a^2+-2*b^2)*cot(c+d*x)*csc(c+d*x)+1//3*a^-2*b^-1*d^-1*(a+b*sin(c+d*x))^-1*(-4*b^2+3*a^2)*cot(c+d*x)*csc(c+d*x))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^4*csc(c+d*x)^5, x) == :(-1//8*a^-6*d^-1*(3*a^4+40*b^4+-36*a^2*b^2)*arctanh(cos(c+d*x))+-1//3*b*a^-5*d^-1*(-15*b^2+11*a^2)*cot(c+d*x)+-1//4*a^-1*d^-1*(a+b*sin(c+d*x))^-1*csc(c+d*x)^3*cot(c+d*x)+1//8*a^-4*d^-1*(-20*b^2+13*a^2)*cot(c+d*x)*csc(c+d*x)+-2*b*a^-6*d^-1*(a^2+-1*b^2)^-1//2*(2*a^4+5*b^4+-7*a^2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//3*a^-3*b^-1*d^-1*csc(c+d*x)^2*(-5*b^2+3*a^2)*cot(c+d*x)+1//4*a^-2*b^-1*d^-1*(a+b*sin(c+d*x))^-1*csc(c+d*x)^2*(-5*b^2+4*a^2)*cot(c+d*x))
@test integrate((a+b*sin(c+d*x))^-3*cos(c+d*x)^4*sin(c+d*x)^3, x) == :(1//8*x*b^-7*(3*b^4+120*a^4+-72*a^2*b^2)+(1/2)*a*b^-6*d^-1*(-13*b^2+30*a^2)*cos(c+d*x)+-1//8*b^-5*d^-1*(-21*b^2+60*a^2)*cos(c+d*x)*sin(c+d*x)+(1/2)*a^-1*b^-4*d^-1*sin(c+d*x)^2*(-3*b^2+10*a^2)*cos(c+d*x)+-3*a*b^-7*d^-1*(a^2+-1*b^2)^-1//2*(2*b^4+10*a^4+-11*a^2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//4*a^-2*b^-3*d^-1*sin(c+d*x)^3*(-4*b^2+15*a^2)*cos(c+d*x)+(1/2)*a^-2*b^-2*d^-1*(a+b*sin(c+d*x))^-1*sin(c+d*x)^4*(-2*b^2+7*a^2)*cos(c+d*x)+-1//2*a^-1*b^-2*d^-1*(a+b*sin(c+d*x))^-2*sin(c+d*x)^4*(a^2+-1*b^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-3*cos(c+d*x)^4*sin(c+d*x)^2, x) == :((1/2)*a*x*b^-4*(9+-20*a^2*b^-2)+-1//6*b^-5*d^-1*(-17*b^2+60*a^2)*cos(c+d*x)+b^-6*d^-1*(a^2+-1*b^2)^-1//2*(2*b^4+20*a^4+-19*a^2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+a^-1*b^-4*d^-1*(-1*b^2+5*a^2)*cos(c+d*x)*sin(c+d*x)+-1//6*a^-2*b^-3*d^-1*sin(c+d*x)^2*(-3*b^2+20*a^2)*cos(c+d*x)+(1/2)*a^-2*b^-2*d^-1*(a+b*sin(c+d*x))^-1*sin(c+d*x)^3*(-1*b^2+6*a^2)*cos(c+d*x)+-1//2*a^-1*b^-2*d^-1*(a+b*sin(c+d*x))^-2*sin(c+d*x)^3*(a^2+-1*b^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-3*cos(c+d*x)^4*sin(c+d*x), x) == :((1/2)*x*b^-5*(-3*b^2+12*a^2)+(1/2)*b^-2*d^-1*(a+b*sin(c+d*x))^-2*cos(c+d*x)^3*(2a+b*sin(c+d*x))+3//2*b^-4*d^-1*(a+b*sin(c+d*x))^-1*(-1*b^2+4*a^2+2*a*b*sin(c+d*x))*cos(c+d*x)+-3*a*b^-5*d^-1*(a^2+-1*b^2)^-1//2*(-3*b^2+4*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-3*cos(c+d*x)^4*csc(c+d*x), x) == :(x*b^-3+-1*a^-3*d^-1*arctanh(cos(c+d*x))+(1/2)*a^-2*b^-2*d^-1*(a+b*sin(c+d*x))^-1*(2*b^2+3*a^2)*cos(c+d*x)+-1*a^-3*b^-3*d^-1*(a^2+-1*b^2)^-1//2*(2*a^4+2*b^4+-1*a^2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//2*a^-1*b^-2*d^-1*(a+b*sin(c+d*x))^-2*(a^2+-1*b^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-3*cos(c+d*x)^4*csc(c+d*x)^2, x) == :(-1*a^-1*d^-1*(a+b*sin(c+d*x))^-2*cot(c+d*x)+3*b*a^-4*d^-1*arctanh(cos(c+d*x))+-1*a^-4*d^-1*(a^2+-1*b^2)^-1//2*(-6*b^2+3*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+(1/2)*a^-2*b^-1*d^-1*(a+b*sin(c+d*x))^-2*(a^2+-3*b^2)*cos(c+d*x)+-1//2*a^-3*b^-1*d^-1*(a+b*sin(c+d*x))^-1*(a^2+6*b^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-3*cos(c+d*x)^4*csc(c+d*x)^3, x) == :((1/2)*a^-5*d^-1*(-12*b^2+3*a^2)*arctanh(cos(c+d*x))+-3*b*a^-3*d^-1*(a+b*sin(c+d*x))^-1*cot(c+d*x)+-1//2*a^-1*d^-1*(a+b*sin(c+d*x))^-2*cot(c+d*x)*csc(c+d*x)+-1//2*a^-4*b^-1*d^-1*(a^2+-12*b^2)*cot(c+d*x)+(1/2)*a^-2*b^-1*d^-1*(a+b*sin(c+d*x))^-2*(a^2+-2*b^2)*cot(c+d*x)+3*b*a^-5*d^-1*(a^2+-1*b^2)^-1//2*(-4*b^2+3*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-3*cos(c+d*x)^4*csc(c+d*x)^4, x) == :(1//6*a^-5*d^-1*(-60*b^2+17*a^2)*cot(c+d*x)+a^-6*d^-1*(a^2+-1*b^2)^-1//2*(2*a^4+20*b^4+-19*a^2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//2*b*a^-6*d^-1*(-20*b^2+9*a^2)*arctanh(cos(c+d*x))+-1//3*a^-1*d^-1*(a+b*sin(c+d*x))^-2*csc(c+d*x)^2*cot(c+d*x)+-1*a^-4*b^-1*d^-1*(a^2+-5*b^2)*cot(c+d*x)*csc(c+d*x)+1//6*a^-3*b^-1*d^-1*(a+b*sin(c+d*x))^-1*(-20*b^2+3*a^2)*cot(c+d*x)*csc(c+d*x)+1//6*a^-2*b^-1*d^-1*(a+b*sin(c+d*x))^-2*(-5*b^2+3*a^2)*cot(c+d*x)*csc(c+d*x))
@test integrate((a+b*sin(c+d*x))^-3*cos(c+d*x)^4*csc(c+d*x)^5, x) == :(-1//8*a^-7*d^-1*(3*a^4+120*b^4+-72*a^2*b^2)*arctanh(cos(c+d*x))+-1//2*b*a^-6*d^-1*(-30*b^2+13*a^2)*cot(c+d*x)+-1//4*a^-1*d^-1*(a+b*sin(c+d*x))^-2*csc(c+d*x)^3*cot(c+d*x)+1//8*a^-5*d^-1*(-60*b^2+21*a^2)*cot(c+d*x)*csc(c+d*x)+-3*b*a^-7*d^-1*(a^2+-1*b^2)^-1//2*(2*a^4+10*b^4+-11*a^2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//2*a^-4*b^-1*d^-1*csc(c+d*x)^2*(-10*b^2+3*a^2)*cot(c+d*x)+1//4*a^-3*b^-1*d^-1*(a+b*sin(c+d*x))^-1*csc(c+d*x)^2*(-15*b^2+4*a^2)*cot(c+d*x)+1//4*a^-2*b^-1*d^-1*(a+b*sin(c+d*x))^-2*csc(c+d*x)^2*(-3*b^2+2*a^2)*cot(c+d*x))
@test integrate((a+b*sin(c+d*x))^(1/2)*cos(c+d*x)^4*sin(c+d*x)^2, x) == :(-2//13*b^-1*d^-1*(a+b*sin(c+d*x))^3//2*sin(c+d*x)^4*cos(c+d*x)+-1//45045*b^-5*d^-1*(a+b*sin(c+d*x))^3//2*(1848*b^4+3840*a^4+-7496*a^2*b^2)*cos(c+d*x)+-1//1287*b^-3*d^-1*(a+b*sin(c+d*x))^3//2*sin(c+d*x)^2*(-330*b^2+160*a^2)*cos(c+d*x)+-1//45045*b^-6*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^-1//2*(a+b*sin(c+d*x))^(1/2)*(-5544*b^6+2560*a^6+-6384*a^4*b^2+3480*a^2*b^4)*Elliptic.E((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1)+16//45045*a*b^-5*d^-1*(a+b*sin(c+d*x))^(1/2)*(27*b^4+160*a^4+-279*a^2*b^2)*cos(c+d*x)+20//143*a*b^-2*d^-1*(a+b*sin(c+d*x))^3//2*sin(c+d*x)^3*cos(c+d*x)+8//3003*a*b^-4*d^-1*(a+b*sin(c+d*x))^3//2*(-81*b^2+40*a^2)*cos(c+d*x)*sin(c+d*x)+16//45045*a*b^-6*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^(1/2)*(a+b*sin(c+d*x))^-1//2*(-27*b^6+160*a^6+-439*a^4*b^2+306*a^2*b^4)*Elliptic.F((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*sin(c+d*x))^(1/2)*cos(c+d*x)^4*sin(c+d*x), x) == :(-2//11*d^-1*(a+b*sin(c+d*x))^(1/2)*cos(c+d*x)^5+-2//693*b^-2*d^-1*(a+b*sin(c+d*x))^(1/2)*cos(c+d*x)^3*(-9*b^2+8*a^2+-7*a*b*sin(c+d*x))+4//3465*b^-4*d^-1*(a+b*sin(c+d*x))^(1/2)*(32*a^4+45*b^4+-69*a^2*b^2+-24*a*b*(a^2+-2*b^2)*sin(c+d*x))*cos(c+d*x)+-1//3465*b^-5*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^(1/2)*(a+b*sin(c+d*x))^-1//2*(-360*b^6+256*a^6+-808*a^4*b^2+912*a^2*b^4)*Elliptic.F((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1)+8//3465*a*b^-5*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^-1//2*(a+b*sin(c+d*x))^(1/2)*(32*a^4+93*b^4+-93*a^2*b^2)*Elliptic.E((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*sin(c+d*x))^3//2*cos(c+d*x)^4*sin(c+d*x)^2, x) == :(-2//15*b^-1*d^-1*(a+b*sin(c+d*x))^5//2*sin(c+d*x)^4*cos(c+d*x)+-1//45045*b^-5*d^-1*(a+b*sin(c+d*x))^5//2*(936*b^4+1280*a^4+-3000*a^2*b^2)*cos(c+d*x)+1//45045*b^-5*d^-1*(a+b*sin(c+d*x))^(1/2)*(-1560*b^6+512*a^6+-1392*a^4*b^2+648*a^2*b^4)*cos(c+d*x)+-1//2145*b^-3*d^-1*(a+b*sin(c+d*x))^5//2*sin(c+d*x)^2*(-442*b^2+160*a^2)*cos(c+d*x)+1//45045*b^-6*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^(1/2)*(a+b*sin(c+d*x))^-1//2*(512*a^8+1560*b^8+-2208*a^2*b^6+-1904*a^6*b^2+2040*a^4*b^4)*Elliptic.F((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1)+4//39*a*b^-2*d^-1*(a+b*sin(c+d*x))^5//2*sin(c+d*x)^3*cos(c+d*x)+16//45045*a*b^-5*d^-1*(a+b*sin(c+d*x))^3//2*(-27*b^4+32*a^4+-47*a^2*b^2)*cos(c+d*x)+-16//45045*a*b^-6*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^-1//2*(a+b*sin(c+d*x))^(1/2)*(-471*b^6+32*a^6+-111*a^4*b^2+102*a^2*b^4)*Elliptic.E((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1)+8//1287*a*b^-4*d^-1*(a+b*sin(c+d*x))^5//2*(-21*b^2+8*a^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^3//2*cos(c+d*x)^4*sin(c+d*x), x) == :(-2//13*d^-1*(a+b*sin(c+d*x))^3//2*cos(c+d*x)^5+-6//143*a*d^-1*(a+b*sin(c+d*x))^(1/2)*cos(c+d*x)^5+-2//3003*b^-2*d^-1*(a+b*sin(c+d*x))^(1/2)*cos(c+d*x)^3*(4*a*(-5*b^2+2*a^2)+-7*b*(a^2+11*b^2)*sin(c+d*x))+4//15015*b^-4*d^-1*(a+b*sin(c+d*x))^(1/2)*(a*(32*a^4+177*b^4+-113*a^2*b^2)+-3*b*(-77*b^4+8*a^4+-27*a^2*b^2)*sin(c+d*x))*cos(c+d*x)+1//15015*b^-5*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^-1//2*(a+b*sin(c+d*x))^(1/2)*(256*a^6+1848*b^6+-1096*a^4*b^2+2064*a^2*b^4)*Elliptic.E((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1)+-8//15015*a*b^-5*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^(1/2)*(a+b*sin(c+d*x))^-1//2*(-177*b^6+32*a^6+-145*a^4*b^2+290*a^2*b^4)*Elliptic.F((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*sin(c+d*x))^5//2*cos(c+d*x)^4*sin(c+d*x), x) == :(-2//15*d^-1*(a+b*sin(c+d*x))^5//2*cos(c+d*x)^5+-2//39*a*d^-1*(a+b*sin(c+d*x))^3//2*cos(c+d*x)^5+1//429*d^-1*(a+b*sin(c+d*x))^(1/2)*cos(c+d*x)^5*(-26*b^2+-6*a^2)+-2//9009*b^-2*d^-1*(a+b*sin(c+d*x))^(1/2)*cos(c+d*x)^3*(-39*b^4+8*a^4+-33*a^2*b^2+-7*a*b*(a^2+63*b^2)*sin(c+d*x))+4//45045*b^-4*d^-1*(a+b*sin(c+d*x))^(1/2)*(32*a^6+195*b^6+-165*a^4*b^2+450*a^2*b^4+-24*a*b*(a^4+-60*b^4+-5*a^2*b^2)*sin(c+d*x))*cos(c+d*x)+-1//45045*b^-5*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^(1/2)*(a+b*sin(c+d*x))^-1//2*(-1560*b^8+256*a^8+-2040*a^2*b^6+-1576*a^6*b^2+4920*a^4*b^4)*Elliptic.F((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1)+8//45045*a*b^-5*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^-1//2*(a+b*sin(c+d*x))^(1/2)*(32*a^6+1635*b^6+-189*a^4*b^2+570*a^2*b^4)*Elliptic.E((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*sin(c+d*x))^-1//2*cos(c+d*x)^4*sin(c+d*x)^3, x) == :(-2//13*b^-1*d^-1*(a+b*sin(c+d*x))^(1/2)*sin(c+d*x)^5*cos(c+d*x)+-1//429*b^-3*d^-1*(a+b*sin(c+d*x))^(1/2)*sin(c+d*x)^3*(-110*b^2+80*a^2)*cos(c+d*x)+-1//15015*b^-5*d^-1*(a+b*sin(c+d*x))^(1/2)*(616*b^4+3840*a^4+-5464*a^2*b^2)*cos(c+d*x)*sin(c+d*x)+1//15015*b^-7*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^-1//2*(a+b*sin(c+d*x))^(1/2)*(1848*b^6+10240*a^6+-16384*a^4*b^2+3624*a^2*b^4)*Elliptic.E((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1)+24//143*a*b^-2*d^-1*(a+b*sin(c+d*x))^(1/2)*sin(c+d*x)^4*cos(c+d*x)+64//15015*a*b^-6*d^-1*(a+b*sin(c+d*x))^(1/2)*(17*b^4+80*a^4+-118*a^2*b^2)*cos(c+d*x)+-8//15015*a*b^-7*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^(1/2)*(a+b*sin(c+d*x))^-1//2*(213*b^6+1280*a^6+-2368*a^4*b^2+875*a^2*b^4)*Elliptic.F((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1)+4//3003*a*b^-4*d^-1*(a+b*sin(c+d*x))^(1/2)*sin(c+d*x)^2*(-223*b^2+160*a^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-1//2*cos(c+d*x)^4*sin(c+d*x)^2, x) == :(-2//11*b^-1*d^-1*(a+b*sin(c+d*x))^(1/2)*sin(c+d*x)^4*cos(c+d*x)+1//3465*b^-5*d^-1*(a+b*sin(c+d*x))^(1/2)*(-1280*a^4+-360*b^4+1976*a^2*b^2)*cos(c+d*x)+-1//693*b^-3*d^-1*(a+b*sin(c+d*x))^(1/2)*sin(c+d*x)^2*(-234*b^2+160*a^2)*cos(c+d*x)+1//3465*b^-6*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^(1/2)*(a+b*sin(c+d*x))^-1//2*(360*b^6+2560*a^6+-4912*a^4*b^2+1992*a^2*b^4)*Elliptic.F((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1)+20//99*a*b^-2*d^-1*(a+b*sin(c+d*x))^(1/2)*sin(c+d*x)^3*cos(c+d*x)+-16//3465*a*b^-6*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^-1//2*(a+b*sin(c+d*x))^(1/2)*(69*b^4+160*a^4+-267*a^2*b^2)*Elliptic.E((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1)+8//3465*a*b^-4*d^-1*(a+b*sin(c+d*x))^(1/2)*(-179*b^2+120*a^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^-1//2*cos(c+d*x)^4*sin(c+d*x), x) == :(-2//63*b^-2*d^-1*(a+b*sin(c+d*x))^(1/2)*cos(c+d*x)^3*(8a+-7*b*sin(c+d*x))+4//315*b^-4*d^-1*(a+b*sin(c+d*x))^(1/2)*(a*(-33*b^2+32*a^2)+-3*b*(-7*b^2+8*a^2)*sin(c+d*x))*cos(c+d*x)+1//315*b^-5*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^-1//2*(a+b*sin(c+d*x))^(1/2)*(168*b^4+256*a^4+-456*a^2*b^2)*Elliptic.E((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1)+-8//315*a*b^-5*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^(1/2)*(a+b*sin(c+d*x))^-1//2*(32*a^4+33*b^4+-65*a^2*b^2)*Elliptic.F((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*sin(c+d*x))^-3//2*cos(c+d*x)^4*sin(c+d*x)^3, x) == :(-2//11*b^-2*d^-1*(a+b*sin(c+d*x))^(1/2)*sin(c+d*x)^4*cos(c+d*x)+-1//1155*b^-6*d^-1*(a+b*sin(c+d*x))^(1/2)*(120*b^4+5120*a^4+-4736*a^2*b^2)*cos(c+d*x)+-1//231*b^-4*d^-1*(a+b*sin(c+d*x))^(1/2)*sin(c+d*x)^2*(-540*b^2+640*a^2)*cos(c+d*x)+1//1155*b^-7*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^(1/2)*(a+b*sin(c+d*x))^-1//2*(120*b^6+10240*a^6+-13312*a^4*b^2+2952*a^2*b^4)*Elliptic.F((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1)+a^-1*b^-2*d^-1*(a+b*sin(c+d*x))^-1//2*sin(c+d*x)^4*(-2*a^2+2*b^2)*cos(c+d*x)+-8//1155*a*b^-7*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^-1//2*(a+b*sin(c+d*x))^(1/2)*(123*b^4+1280*a^4+-1344*a^2*b^2)*Elliptic.E((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1)+1//33*a^-1*b^-3*d^-1*(a+b*sin(c+d*x))^(1/2)*sin(c+d*x)^3*(-66*b^2+80*a^2)*cos(c+d*x)+8//1155*a*b^-5*d^-1*(a+b*sin(c+d*x))^(1/2)*(-419*b^2+480*a^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^-3//2*cos(c+d*x)^4*sin(c+d*x)^2, x) == :(-2//9*b^-2*d^-1*(a+b*sin(c+d*x))^(1/2)*sin(c+d*x)^3*cos(c+d*x)+-1//315*b^-4*d^-1*(a+b*sin(c+d*x))^(1/2)*(-784*b^2+960*a^2)*cos(c+d*x)*sin(c+d*x)+1//315*b^-6*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^-1//2*(a+b*sin(c+d*x))^(1/2)*(168*b^4+2560*a^4+-2544*a^2*b^2)*Elliptic.E((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1)+8//315*a*b^-5*d^-1*(a+b*sin(c+d*x))^(1/2)*(-139*b^2+160*a^2)*cos(c+d*x)+a^-1*b^-2*d^-1*(a+b*sin(c+d*x))^-1//2*sin(c+d*x)^3*(-2*a^2+2*b^2)*cos(c+d*x)+-16//315*a*b^-6*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^(1/2)*(a+b*sin(c+d*x))^-1//2*(39*b^4+160*a^4+-199*a^2*b^2)*Elliptic.F((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1)+1//63*a^-1*b^-3*d^-1*(a+b*sin(c+d*x))^(1/2)*sin(c+d*x)^2*(-126*b^2+160*a^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-3//2*cos(c+d*x)^4*sin(c+d*x), x) == :(-4//35*b^-4*d^-1*(a+b*sin(c+d*x))^(1/2)*(-5*b^2+32*a^2+-24*a*b*sin(c+d*x))*cos(c+d*x)+2//7*b^-2*d^-1*(a+b*sin(c+d*x))^-1//2*cos(c+d*x)^3*(8a+b*sin(c+d*x))+1//35*b^-5*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^(1/2)*(a+b*sin(c+d*x))^-1//2*(40*b^4+256*a^4+-296*a^2*b^2)*Elliptic.F((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1)+-8//35*a*b^-5*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^-1//2*(a+b*sin(c+d*x))^(1/2)*(-29*b^2+32*a^2)*Elliptic.E((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((a+b*sin(c+d*x))^-5//2*cos(c+d*x)^4*sin(c+d*x)^3, x) == :(-1//315*b^-5*d^-1*(a+b*sin(c+d*x))^(1/2)*(-1624*b^2+3840*a^2)*cos(c+d*x)*sin(c+d*x)+1//315*b^-7*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^-1//2*(a+b*sin(c+d*x))^(1/2)*(168*b^4+10240*a^4+-6144*a^2*b^2)*Elliptic.E((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1)+128//315*a*b^-6*d^-1*(a+b*sin(c+d*x))^(1/2)*(-19*b^2+40*a^2)*cos(c+d*x)+-8//315*a*b^-7*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^(1/2)*(a+b*sin(c+d*x))^-1//2*(123*b^4+1280*a^4+-1088*a^2*b^2)*Elliptic.F((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1)+-1//9*a^-2*b^-3*d^-1*(a+b*sin(c+d*x))^(1/2)*sin(c+d*x)^3*(-30*b^2+80*a^2)*cos(c+d*x)+1//3*a^-1*b^-2*d^-1*(a+b*sin(c+d*x))^-3//2*sin(c+d*x)^4*(-2*a^2+2*b^2)*cos(c+d*x)+1//3*a^-2*b^-2*d^-1*(a+b*sin(c+d*x))^-1//2*sin(c+d*x)^4*(-10*b^2+26*a^2)*cos(c+d*x)+1//63*a^-1*b^-4*d^-1*(a+b*sin(c+d*x))^(1/2)*sin(c+d*x)^2*(-252*b^2+640*a^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-5//2*cos(c+d*x)^4*sin(c+d*x)^2, x) == :(-1//21*b^-5*d^-1*(a+b*sin(c+d*x))^(1/2)*(-88*b^2+256*a^2)*cos(c+d*x)+1//21*b^-6*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^(1/2)*(a+b*sin(c+d*x))^-1//2*(24*b^4+512*a^4+-368*a^2*b^2)*Elliptic.F((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1)+-16//21*a*b^-6*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^-1//2*(a+b*sin(c+d*x))^(1/2)*(-15*b^2+32*a^2)*Elliptic.E((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1)+-1//21*a^-2*b^-3*d^-1*(a+b*sin(c+d*x))^(1/2)*sin(c+d*x)^2*(-42*b^2+160*a^2)*cos(c+d*x)+1//3*a^-1*b^-2*d^-1*(a+b*sin(c+d*x))^-3//2*sin(c+d*x)^3*(-2*a^2+2*b^2)*cos(c+d*x)+1//3*a^-2*b^-2*d^-1*(a+b*sin(c+d*x))^-1//2*sin(c+d*x)^3*(-6*b^2+22*a^2)*cos(c+d*x)+1//21*a^-1*b^-4*d^-1*(a+b*sin(c+d*x))^(1/2)*(-56*b^2+192*a^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^-5//2*cos(c+d*x)^4*sin(c+d*x), x) == :(2//15*b^-2*d^-1*(a+b*sin(c+d*x))^-3//2*cos(c+d*x)^3*(8a+3*b*sin(c+d*x))+4//15*b^-4*d^-1*(a+b*sin(c+d*x))^-1//2*(-9*b^2+32*a^2+8*a*b*sin(c+d*x))*cos(c+d*x)+1//15*b^-5*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^-1//2*(a+b*sin(c+d*x))^(1/2)*(-72*b^2+256*a^2)*Elliptic.E((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1)+-8//15*a*b^-5*d^-1*((a+b)^-1*(a+b*sin(c+d*x)))^(1/2)*(a+b*sin(c+d*x))^-1//2*(-17*b^2+32*a^2)*Elliptic.F((1/2)*c+-1//4*pi+(1/2)*d*x,2*b*(a+b)^-1))
@test integrate((d*sin(e+f*x))^-1//2*(a+b*sin(e+f*x))^-9//2*cos(e+f*x)^4, x) == :(2//7*a^-1*d^-1*f^-1*(d*sin(e+f*x))^(1/2)*(a+b*sin(e+f*x))^-7//2*cos(e+f*x)^3+12//35*a^-2*d^-1*f^-1*(d*sin(e+f*x))^(1/2)*(a+b*sin(e+f*x))^-5//2*cos(e+f*x)+1//35*a^-3*d^-1*f^-1*(d*sin(e+f*x))^(1/2)*(a+b*sin(e+f*x))^-3//2*(a^2+-1*b^2)^-1*(-16*b^2+8*a^2)*cos(e+f*x)+32//35*b*a^-3*f^-1*(d*sin(e+f*x))^-1//2*(a+b*sin(e+f*x))^-1//2*(a^2+-1*b^2)^-2*(-1*b^2+2*a^2)*cos(e+f*x)+-1//35*a^-4*d^-1//2*f^-1*(a*(a+b)^-1*(1+-1*csc(e+f*x)))^(1/2)*(a*(a+-1b)^-1*(1+csc(e+f*x)))^(1/2)*(a+b)^-3//2*(a+-1b)^-1*(-32*b^2+40*a^2+-24*a*b)*Elliptic.F(arcsin(d^(1/2)*(d*sin(e+f*x))^-1//2*(a+b)^-1//2*(a+b*sin(e+f*x))^(1/2)),-1*(a+-1b)^-1*(a+b))*tan(e+f*x)+-32//35*b*a^-5*d^-1//2*f^-1*(a*(a+b)^-1*(1+-1*csc(e+f*x)))^(1/2)*(a*(a+-1b)^-1*(1+csc(e+f*x)))^(1/2)*(a+b)^-3//2*(a+-1b)^-1*(-1*b^2+2*a^2)*Elliptic.E(arcsin(d^(1/2)*(d*sin(e+f*x))^-1//2*(a+b)^-1//2*(a+b*sin(e+f*x))^(1/2)),-1*(a+-1b)^-1*(a+b))*tan(e+f*x))
@test integrate(cos(c+d*x)^5*sin(c+d*x)^5*(a+b*sin(c+d*x)), x) == :(-2//9*b*d^-1*sin(c+d*x)^9+-1//4*a*d^-1*sin(c+d*x)^8+1//6*a*d^-1*sin(c+d*x)^6+1//7*b*d^-1*sin(c+d*x)^7+1//10*a*d^-1*sin(c+d*x)^10+1//11*b*d^-1*sin(c+d*x)^11)
@test integrate(cos(c+d*x)^5*sin(c+d*x)^4*(a+b*sin(c+d*x)), x) == :(-2//7*a*d^-1*sin(c+d*x)^7+-1//4*b*d^-1*sin(c+d*x)^8+1//5*a*d^-1*sin(c+d*x)^5+1//6*b*d^-1*sin(c+d*x)^6+1//9*a*d^-1*sin(c+d*x)^9+1//10*b*d^-1*sin(c+d*x)^10)
@test integrate(cos(c+d*x)^5*sin(c+d*x)^3*(a+b*sin(c+d*x)), x) == :(-2//7*b*d^-1*sin(c+d*x)^7+-1//6*a*d^-1*cos(c+d*x)^6+1//5*b*d^-1*sin(c+d*x)^5+1//8*a*d^-1*cos(c+d*x)^8+1//9*b*d^-1*sin(c+d*x)^9)
@test integrate(cos(c+d*x)^5*sin(c+d*x)^2*(a+b*sin(c+d*x)), x) == :(-2//5*a*d^-1*sin(c+d*x)^5+-1//6*b*d^-1*cos(c+d*x)^6+1//3*a*d^-1*sin(c+d*x)^3+1//7*a*d^-1*sin(c+d*x)^7+1//8*b*d^-1*cos(c+d*x)^8)
@test integrate(cos(c+d*x)^5*(a+b*sin(c+d*x))*sin(c+d*x), x) == :(-2//5*b*d^-1*sin(c+d*x)^5+-1//6*a*d^-1*cos(c+d*x)^6+1//3*b*d^-1*sin(c+d*x)^3+1//7*b*d^-1*sin(c+d*x)^7)
@test integrate(cos(c+d*x)^5*(a+b*sin(c+d*x))*csc(c+d*x), x) == :(a*d^-1*log(sin(c+d*x))+b*d^-1*sin(c+d*x)+-1*a*d^-1*sin(c+d*x)^2+-2//3*b*d^-1*sin(c+d*x)^3+1//4*a*d^-1*sin(c+d*x)^4+1//5*b*d^-1*sin(c+d*x)^5)
@test integrate(cos(c+d*x)^5*csc(c+d*x)^2*(a+b*sin(c+d*x)), x) == :(b*d^-1*log(sin(c+d*x))+-1*a*d^-1*csc(c+d*x)+-1*b*d^-1*sin(c+d*x)^2+-2*a*d^-1*sin(c+d*x)+1//3*a*d^-1*sin(c+d*x)^3+1//4*b*d^-1*sin(c+d*x)^4)
@test integrate(cos(c+d*x)^5*csc(c+d*x)^3*(a+b*sin(c+d*x)), x) == :((1/2)*a*d^-1*sin(c+d*x)^2+-1*b*d^-1*csc(c+d*x)+-2*a*d^-1*log(sin(c+d*x))+-2*b*d^-1*sin(c+d*x)+-1//2*a*d^-1*csc(c+d*x)^2+1//3*b*d^-1*sin(c+d*x)^3)
@test integrate(cos(c+d*x)^5*csc(c+d*x)^4*(a+b*sin(c+d*x)), x) == :(a*d^-1*sin(c+d*x)+(1/2)*b*d^-1*sin(c+d*x)^2+-2*b*d^-1*log(sin(c+d*x))+2*a*d^-1*csc(c+d*x)+-1//2*b*d^-1*csc(c+d*x)^2+-1//3*a*d^-1*csc(c+d*x)^3)
@test integrate(cos(c+d*x)^5*csc(c+d*x)^5*(a+b*sin(c+d*x)), x) == :(a*d^-1*csc(c+d*x)^2+a*d^-1*log(sin(c+d*x))+b*d^-1*sin(c+d*x)+2*b*d^-1*csc(c+d*x)+-1//3*b*d^-1*csc(c+d*x)^3+-1//4*a*d^-1*csc(c+d*x)^4)
@test integrate(cos(c+d*x)^5*csc(c+d*x)^6*(a+b*sin(c+d*x)), x) == :(b*d^-1*csc(c+d*x)^2+b*d^-1*log(sin(c+d*x))+-1*a*d^-1*csc(c+d*x)+-1//4*b*d^-1*csc(c+d*x)^4+-1//5*a*d^-1*csc(c+d*x)^5+2//3*a*d^-1*csc(c+d*x)^3)
@test integrate(cos(c+d*x)^5*csc(c+d*x)^7*(a+b*sin(c+d*x)), x) == :(-1*b*d^-1*csc(c+d*x)+-1//5*b*d^-1*csc(c+d*x)^5+-1//6*a*d^-1*cot(c+d*x)^6+2//3*b*d^-1*csc(c+d*x)^3)
@test integrate(cos(c+d*x)^5*csc(c+d*x)^8*(a+b*sin(c+d*x)), x) == :(-1//3*a*d^-1*csc(c+d*x)^3+-1//6*b*d^-1*cot(c+d*x)^6+-1//7*a*d^-1*csc(c+d*x)^7+2//5*a*d^-1*csc(c+d*x)^5)
@test integrate(cos(c+d*x)^5*csc(c+d*x)^9*(a+b*sin(c+d*x)), x) == :(-1//3*b*d^-1*csc(c+d*x)^3+-1//6*a*d^-1*cot(c+d*x)^6+-1//7*b*d^-1*csc(c+d*x)^7+-1//8*a*d^-1*cot(c+d*x)^8+2//5*b*d^-1*csc(c+d*x)^5)
@test integrate(cos(c+d*x)^5*csc(c+d*x)^10*(a+b*sin(c+d*x)), x) == :(-1//5*a*d^-1*csc(c+d*x)^5+-1//6*b*d^-1*cot(c+d*x)^6+-1//8*b*d^-1*cot(c+d*x)^8+-1//9*a*d^-1*csc(c+d*x)^9+2//7*a*d^-1*csc(c+d*x)^7)
@test integrate(cos(c+d*x)^5*csc(c+d*x)^11*(a+b*sin(c+d*x)), x) == :(-1//5*b*d^-1*csc(c+d*x)^5+-1//6*a*d^-1*csc(c+d*x)^6+-1//9*b*d^-1*csc(c+d*x)^9+-1//10*a*d^-1*csc(c+d*x)^10+1//4*a*d^-1*csc(c+d*x)^8+2//7*b*d^-1*csc(c+d*x)^7)
@test integrate(cos(c+d*x)^5*csc(c+d*x)^12*(a+b*sin(c+d*x)), x) == :(-1//6*b*d^-1*csc(c+d*x)^6+-1//7*a*d^-1*csc(c+d*x)^7+-1//10*b*d^-1*csc(c+d*x)^10+-1//11*a*d^-1*csc(c+d*x)^11+1//4*b*d^-1*csc(c+d*x)^8+2//9*a*d^-1*csc(c+d*x)^9)
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^5*sin(c+d*x)^2, x) == :(-1//5*d^-1*sin(c+d*x)^5*(-1*b^2+2*a^2)+1//3*a^2*d^-1*sin(c+d*x)^3+1//7*d^-1*sin(c+d*x)^7*(a^2+-2*b^2)+1//9*b^2*d^-1*sin(c+d*x)^9+(1/2)*a*b*d^-1*sin(c+d*x)^4+-2//3*a*b*d^-1*sin(c+d*x)^6+1//4*a*b*d^-1*sin(c+d*x)^8)
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^5*sin(c+d*x), x) == :((1/2)*a^2*d^-1*sin(c+d*x)^2+-1//4*d^-1*sin(c+d*x)^4*(-1*b^2+2*a^2)+1//6*d^-1*sin(c+d*x)^6*(a^2+-2*b^2)+1//8*b^2*d^-1*sin(c+d*x)^8+-4//5*a*b*d^-1*sin(c+d*x)^5+2//3*a*b*d^-1*sin(c+d*x)^3+2//7*a*b*d^-1*sin(c+d*x)^7)
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^5*csc(c+d*x), x) == :(a^2*d^-1*log(sin(c+d*x))+-1//2*d^-1*sin(c+d*x)^2*(-1*b^2+2*a^2)+1//4*d^-1*sin(c+d*x)^4*(a^2+-2*b^2)+1//6*b^2*d^-1*sin(c+d*x)^6+2*a*b*d^-1*sin(c+d*x)+-4//3*a*b*d^-1*sin(c+d*x)^3+2//5*a*b*d^-1*sin(c+d*x)^5)
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^5*csc(c+d*x)^2, x) == :(-1*a^2*d^-1*csc(c+d*x)+-1*d^-1*(-1*b^2+2*a^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+(1/2)*a*b*d^-1*sin(c+d*x)^4+-2*a*b*d^-1*sin(c+d*x)^2+2*a*b*d^-1*log(sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^5*csc(c+d*x)^3, x) == :((1/2)*d^-1*sin(c+d*x)^2*(a^2+-2*b^2)+-1*d^-1*(-1*b^2+2*a^2)*log(sin(c+d*x))+-1//2*a^2*d^-1*csc(c+d*x)^2+1//4*b^2*d^-1*sin(c+d*x)^4+-4*a*b*d^-1*sin(c+d*x)+-2*a*b*d^-1*csc(c+d*x)+2//3*a*b*d^-1*sin(c+d*x)^3)
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^5*csc(c+d*x)^4, x) == :(d^-1*(a^2+-2*b^2)*sin(c+d*x)+d^-1*(-1*b^2+2*a^2)*csc(c+d*x)+-1//3*a^2*d^-1*csc(c+d*x)^3+1//3*b^2*d^-1*sin(c+d*x)^3+a*b*d^-1*sin(c+d*x)^2+-1*a*b*d^-1*csc(c+d*x)^2+-4*a*b*d^-1*log(sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^5*csc(c+d*x)^5, x) == :(d^-1*(a^2+-2*b^2)*log(sin(c+d*x))+(1/2)*b^2*d^-1*sin(c+d*x)^2+(1/2)*d^-1*csc(c+d*x)^2*(-1*b^2+2*a^2)+-1//4*a^2*d^-1*csc(c+d*x)^4+2*a*b*d^-1*sin(c+d*x)+4*a*b*d^-1*csc(c+d*x)+-2//3*a*b*d^-1*csc(c+d*x)^3)
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^5*csc(c+d*x)^6, x) == :(b^2*d^-1*sin(c+d*x)+-1*d^-1*(a^2+-2*b^2)*csc(c+d*x)+-1//5*a^2*d^-1*csc(c+d*x)^5+1//3*d^-1*csc(c+d*x)^3*(-1*b^2+2*a^2)+2*a*b*d^-1*csc(c+d*x)^2+2*a*b*d^-1*log(sin(c+d*x))+-1//2*a*b*d^-1*csc(c+d*x)^4)
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^5*csc(c+d*x)^7, x) == :(b^2*d^-1*log(sin(c+d*x))+-1//2*d^-1*csc(c+d*x)^2*(a^2+-2*b^2)+-1//6*a^2*d^-1*csc(c+d*x)^6+1//4*d^-1*csc(c+d*x)^4*(-1*b^2+2*a^2)+-2*a*b*d^-1*csc(c+d*x)+-2//5*a*b*d^-1*csc(c+d*x)^5+4//3*a*b*d^-1*csc(c+d*x)^3)
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^5*csc(c+d*x)^8, x) == :(-1*b^2*d^-1*csc(c+d*x)+-1//3*d^-1*csc(c+d*x)^3*(a^2+-2*b^2)+-1//7*a^2*d^-1*csc(c+d*x)^7+1//5*d^-1*csc(c+d*x)^5*(-1*b^2+2*a^2)+a*b*d^-1*csc(c+d*x)^4+-1*a*b*d^-1*csc(c+d*x)^2+-1//3*a*b*d^-1*csc(c+d*x)^6)
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^5*csc(c+d*x)^9, x) == :(-1//2*b^2*d^-1*csc(c+d*x)^2+-1//4*d^-1*csc(c+d*x)^4*(a^2+-2*b^2)+-1//8*a^2*d^-1*csc(c+d*x)^8+1//6*d^-1*csc(c+d*x)^6*(-1*b^2+2*a^2)+-2//3*a*b*d^-1*csc(c+d*x)^3+-2//7*a*b*d^-1*csc(c+d*x)^7+4//5*a*b*d^-1*csc(c+d*x)^5)
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^5*sin(c+d*x)^3, x) == :(1//6*b^-2*d^-1*sin(c+d*x)^6+(1/2)*b^-6*d^-1*sin(c+d*x)^2*(b^4+5*a^4+-6*a^2*b^2)+-2//5*a*b^-3*d^-1*sin(c+d*x)^5+1//4*b^-4*d^-1*sin(c+d*x)^4*(-2*b^2+3*a^2)+a^2*b^-8*d^-1*(3*b^4+7*a^4+-10*a^2*b^2)*log(a+b*sin(c+d*x))+a^3*b^-8*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^2+-2*a*b^-7*d^-1*(b^4+3*a^4+-4*a^2*b^2)*sin(c+d*x)+-4//3*a*b^-5*d^-1*sin(c+d*x)^3*(a^2+-1*b^2))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^5*sin(c+d*x)^2, x) == :(1//5*b^-2*d^-1*sin(c+d*x)^5+b^-6*d^-1*(b^4+5*a^4+-6*a^2*b^2)*sin(c+d*x)+-1//2*a*b^-3*d^-1*sin(c+d*x)^4+-1//3*b^-2*d^-1*sin(c+d*x)^3*(2+-3*a^2*b^-2)+-1*a^2*b^-7*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^2+-2*a*b^-7*d^-1*(b^4+3*a^4+-4*a^2*b^2)*log(a+b*sin(c+d*x))+-2*a*b^-5*d^-1*sin(c+d*x)^2*(a^2+-1*b^2))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^5*sin(c+d*x), x) == :(1//4*b^-2*d^-1*sin(c+d*x)^4+b^-6*d^-1*(b^4+5*a^4+-6*a^2*b^2)*log(a+b*sin(c+d*x))+(1/2)*b^-4*d^-1*sin(c+d*x)^2*(-2*b^2+3*a^2)+-2//3*a*b^-3*d^-1*sin(c+d*x)^3+a*b^-6*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^2+-4*a*b^-5*d^-1*(a^2+-1*b^2)*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^5*csc(c+d*x), x) == :(a^-2*d^-1*log(sin(c+d*x))+(1/2)*b^-2*d^-1*sin(c+d*x)^2+-2*a*b^-3*d^-1*sin(c+d*x)+a^-1*b^-4*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^2+a^-2*b^-4*d^-1*(a^2+-1*b^2)*(b^2+3*a^2)*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^5*csc(c+d*x)^2, x) == :(b^-2*d^-1*sin(c+d*x)+-1*a^-2*d^-1*csc(c+d*x)+-2*b*a^-3*d^-1*log(sin(c+d*x))+-1*a^-3*b^-3*d^-1*(-2*b^4+2*a^4)*log(a+b*sin(c+d*x))+-1*a^-2*b^-3*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^2)
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^5*csc(c+d*x)^3, x) == :(-1//2*a^-2*d^-1*csc(c+d*x)^2+-1*a^-4*d^-1*(-3*b^2+2*a^2)*log(sin(c+d*x))+2*b*a^-3*d^-1*csc(c+d*x)+a^-4*b^-2*d^-1*(a^4+-3*b^4+2*a^2*b^2)*log(a+b*sin(c+d*x))+a^-3*b^-2*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^2)
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^5*csc(c+d*x)^4, x) == :(-1//3*a^-2*d^-1*csc(c+d*x)^3+b*a^-3*d^-1*csc(c+d*x)^2+a^-4*d^-1*(-3*b^2+2*a^2)*csc(c+d*x)+-1*a^-4*b^-1*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^2+-4*b*a^-5*d^-1*(a^2+-1*b^2)*log(a+b*sin(c+d*x))+4*b*a^-5*d^-1*(a^2+-1*b^2)*log(sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^5*csc(c+d*x)^5, x) == :(-1//4*a^-2*d^-1*csc(c+d*x)^4+a^-6*d^-1*(a^4+5*b^4+-6*a^2*b^2)*log(sin(c+d*x))+a^-5*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^2+(1/2)*a^-4*d^-1*csc(c+d*x)^2*(-3*b^2+2*a^2)+-1*a^-6*d^-1*(a^4+5*b^4+-6*a^2*b^2)*log(a+b*sin(c+d*x))+2//3*b*a^-3*d^-1*csc(c+d*x)^3+-4*b*a^-5*d^-1*(a^2+-1*b^2)*csc(c+d*x))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^5*csc(c+d*x)^6, x) == :(-1//5*a^-2*d^-1*csc(c+d*x)^5+(1/2)*b*a^-3*d^-1*csc(c+d*x)^4+-1*a^-6*d^-1*(a^4+5*b^4+-6*a^2*b^2)*csc(c+d*x)+1//3*a^-4*d^-1*csc(c+d*x)^3*(-3*b^2+2*a^2)+-1*b*a^-6*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^2+-2*b*a^-7*d^-1*(a^4+3*b^4+-4*a^2*b^2)*log(sin(c+d*x))+-2*b*a^-5*d^-1*csc(c+d*x)^2*(a^2+-1*b^2)+2*b*a^-7*d^-1*(a^4+3*b^4+-4*a^2*b^2)*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^5*sin(c+d*x)^n, x) == :(a^2*d^-1*(1+n)^-1*sin(c+d*x)^(1+n)+b^2*d^-1*(7+n)^-1*sin(c+d*x)^(7+n)+d^-1*(5+n)^-1*sin(c+d*x)^(5+n)*(a^2+-2*b^2)+-1*d^-1*(3+n)^-1*sin(c+d*x)^(3+n)*(-1*b^2+2*a^2)+-4*a*b*d^-1*(4+n)^-1*sin(c+d*x)^(4+n)+2*a*b*d^-1*(2+n)^-1*sin(c+d*x)^(2+n)+2*a*b*d^-1*(6+n)^-1*sin(c+d*x)^(6+n))
@test integrate(cos(c+d*x)^5*sin(c+d*x)^n*(a+b*sin(c+d*x)), x) == :(a*d^-1*(1+n)^-1*sin(c+d*x)^(1+n)+a*d^-1*(5+n)^-1*sin(c+d*x)^(5+n)+b*d^-1*(2+n)^-1*sin(c+d*x)^(2+n)+b*d^-1*(6+n)^-1*sin(c+d*x)^(6+n)+-2*a*d^-1*(3+n)^-1*sin(c+d*x)^(3+n)+-2*b*d^-1*(4+n)^-1*sin(c+d*x)^(4+n))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^6*sin(c+d*x)^5, x) == :(-1//7*d^-1*cos(c+d*x)^7*(a^2+b^2)+-1//11*d^-1*cos(c+d*x)^11*(a^2+3*b^2)+1//9*d^-1*cos(c+d*x)^9*(2*a^2+3*b^2)+1//13*b^2*d^-1*cos(c+d*x)^13+5//512*a*b*x+-1//6*a*b*d^-1*cos(c+d*x)^7*sin(c+d*x)^5+-1//12*a*b*d^-1*cos(c+d*x)^7*sin(c+d*x)^3+-1//32*a*b*d^-1*cos(c+d*x)^7*sin(c+d*x)+1//192*a*b*d^-1*cos(c+d*x)^5*sin(c+d*x)+5//512*a*b*d^-1*cos(c+d*x)*sin(c+d*x)+5//768*a*b*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^6*sin(c+d*x)^4, x) == :(1//1024*x*(5*b^2+12*a^2)+-2//7*a*b*d^-1*cos(c+d*x)^7+-2//11*a*b*d^-1*cos(c+d*x)^11+-1//12*b^2*d^-1*cos(c+d*x)^11*sin(c+d*x)+-1//320*d^-1*cos(c+d*x)^7*(44*a^2+45*b^2)*sin(c+d*x)+1//120*d^-1*cos(c+d*x)^9*(12*a^2+25*b^2)*sin(c+d*x)+1//1024*d^-1*(5*b^2+12*a^2)*cos(c+d*x)*sin(c+d*x)+1//1536*d^-1*cos(c+d*x)^3*(5*b^2+12*a^2)*sin(c+d*x)+1//1920*d^-1*cos(c+d*x)^5*(5*b^2+12*a^2)*sin(c+d*x)+4//9*a*b*d^-1*cos(c+d*x)^9)
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^6*sin(c+d*x)^3, x) == :(-1//7*d^-1*cos(c+d*x)^7*(a^2+b^2)+-1//11*b^2*d^-1*cos(c+d*x)^11+1//9*d^-1*cos(c+d*x)^9*(a^2+2*b^2)+3//128*a*b*x+-3//40*a*b*d^-1*cos(c+d*x)^7*sin(c+d*x)+-1//5*a*b*d^-1*cos(c+d*x)^7*sin(c+d*x)^3+1//64*a*b*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//80*a*b*d^-1*cos(c+d*x)^5*sin(c+d*x)+3//128*a*b*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^6*sin(c+d*x)^2, x) == :(x*(3//256*b^2+5//128*a^2)+-2//7*a*b*d^-1*cos(c+d*x)^7+-1//80*d^-1*cos(c+d*x)^7*(10*a^2+11*b^2)*sin(c+d*x)+1//10*b^2*d^-1*cos(c+d*x)^9*sin(c+d*x)+1//256*d^-1*(3*b^2+10*a^2)*cos(c+d*x)*sin(c+d*x)+1//384*d^-1*cos(c+d*x)^3*(3*b^2+10*a^2)*sin(c+d*x)+1//480*d^-1*cos(c+d*x)^5*(3*b^2+10*a^2)*sin(c+d*x)+2//9*a*b*d^-1*cos(c+d*x)^9)
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^6*sin(c+d*x), x) == :(-1//9*d^-1*(a+b*sin(c+d*x))^2*cos(c+d*x)^7+-1//252*d^-1*cos(c+d*x)^7*(a^2+8*b^2)+5//64*a*b*x+-1//36*a*d^-1*cos(c+d*x)^7*(a+b*sin(c+d*x))+1//24*a*b*d^-1*cos(c+d*x)^5*sin(c+d*x)+5//64*a*b*d^-1*cos(c+d*x)*sin(c+d*x)+5//96*a*b*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^6*csc(c+d*x), x) == :(a^2*d^-1*cos(c+d*x)+-1*a^2*d^-1*arctanh(cos(c+d*x))+-1//7*b^2*d^-1*cos(c+d*x)^7+1//3*a^2*d^-1*cos(c+d*x)^3+1//5*a^2*d^-1*cos(c+d*x)^5+5//8*a*b*x+1//3*a*b*d^-1*cos(c+d*x)^5*sin(c+d*x)+5//8*a*b*d^-1*cos(c+d*x)*sin(c+d*x)+5//12*a*b*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^6*csc(c+d*x)^2, x) == :(x*(-15//8*a^2+5//16*b^2)+-1*a^2*d^-1*cot(c+d*x)+-2*a*b*d^-1*arctanh(cos(c+d*x))+2*a*b*d^-1*cos(c+d*x)+-1//16*d^-1*(-5*b^2+14*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)+1//6*b^2*d^-1*cos(c+d*x)^5*sin(c+d*x)+2//3*a*b*d^-1*cos(c+d*x)^3+2//5*a*b*d^-1*cos(c+d*x)^5)
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^6*csc(c+d*x)^3, x) == :((1/2)*d^-1*(-2*b^2+5*a^2)*arctanh(cos(c+d*x))+-1*d^-1*(-1*b^2+2*a^2)*cos(c+d*x)+-15//4*a*b*x+-1//3*d^-1*cos(c+d*x)^3*(a^2+-1*b^2)+1//5*b^2*d^-1*cos(c+d*x)^5+-15//4*a*b*d^-1*cot(c+d*x)+-1//2*a^2*d^-1*cot(c+d*x)*csc(c+d*x)+(1/2)*a*b*d^-1*cos(c+d*x)^4*cot(c+d*x)+5//4*a*b*d^-1*cos(c+d*x)^2*cot(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^6*csc(c+d*x)^4, x) == :(x*(-15//8*b^2+5//2*a^2)+d^-1*(-1*b^2+2*a^2)*cot(c+d*x)+-1//3*a^2*d^-1*cot(c+d*x)^3+-5*a*b*d^-1*cos(c+d*x)+5*a*b*d^-1*arctanh(cos(c+d*x))+-5//3*a*b*d^-1*cos(c+d*x)^3+-1//4*b^2*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//8*d^-1*(-7*b^2+4*a^2)*cos(c+d*x)*sin(c+d*x)+-1*a*b*d^-1*cos(c+d*x)^3*cot(c+d*x)^2)
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^6*csc(c+d*x)^5, x) == :(d^-1*(a^2+-2*b^2)*cos(c+d*x)+5*a*b*x+-1//3*b^2*d^-1*cos(c+d*x)^3+-1//8*d^-1*(-20*b^2+15*a^2)*arctanh(cos(c+d*x))+5*a*b*d^-1*cot(c+d*x)+-5//3*a*b*d^-1*cot(c+d*x)^3+-1//4*a^2*d^-1*csc(c+d*x)^3*cot(c+d*x)+1//8*d^-1*(-4*b^2+9*a^2)*cot(c+d*x)*csc(c+d*x)+a*b*d^-1*cos(c+d*x)^2*cot(c+d*x)^3)
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^6*csc(c+d*x)^6, x) == :(-1*x*a^2+5//2*x*b^2+-1*a^2*d^-1*cot(c+d*x)+-5//6*b^2*d^-1*cot(c+d*x)^3+-1//5*a^2*d^-1*cot(c+d*x)^5+1//3*a^2*d^-1*cot(c+d*x)^3+5//2*b^2*d^-1*cot(c+d*x)+(1/2)*b^2*d^-1*cos(c+d*x)^2*cot(c+d*x)^3+-15//4*a*b*d^-1*arctanh(cos(c+d*x))+15//4*a*b*d^-1*cos(c+d*x)+-1//2*a*b*d^-1*cot(c+d*x)^4*cos(c+d*x)+5//4*a*b*d^-1*cot(c+d*x)^2*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^6*csc(c+d*x)^7, x) == :(b^2*d^-1*cos(c+d*x)+-2*a*b*x+1//16*d^-1*(-30*b^2+5*a^2)*arctanh(cos(c+d*x))+-2*a*b*d^-1*cot(c+d*x)+-2//5*a*b*d^-1*cot(c+d*x)^5+-1//6*a^2*d^-1*csc(c+d*x)^5*cot(c+d*x)+-1//16*d^-1*(-18*b^2+11*a^2)*cot(c+d*x)*csc(c+d*x)+1//24*d^-1*csc(c+d*x)^3*(-6*b^2+13*a^2)*cot(c+d*x)+2//3*a*b*d^-1*cot(c+d*x)^3)
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^6*csc(c+d*x)^8, x) == :(-1*x*b^2+-1*b^2*d^-1*cot(c+d*x)+-1//5*b^2*d^-1*cot(c+d*x)^5+-1//7*a^2*d^-1*cot(c+d*x)^7+1//3*b^2*d^-1*cot(c+d*x)^3+5//8*a*b*d^-1*arctanh(cos(c+d*x))+-5//8*a*b*d^-1*cot(c+d*x)*csc(c+d*x)+-1//3*a*b*d^-1*cot(c+d*x)^5*csc(c+d*x)+5//12*a*b*d^-1*cot(c+d*x)^3*csc(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^6*csc(c+d*x)^9, x) == :(1//128*d^-1*(5*a^2+40*b^2)*arctanh(cos(c+d*x))+-2//7*a*b*d^-1*cot(c+d*x)^7+-1//8*a^2*d^-1*csc(c+d*x)^7*cot(c+d*x)+-1//192*d^-1*csc(c+d*x)^3*(-104*b^2+59*a^2)*cot(c+d*x)+1//48*d^-1*csc(c+d*x)^5*(-8*b^2+17*a^2)*cot(c+d*x)+1//128*d^-1*(-88*b^2+5*a^2)*cot(c+d*x)*csc(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^6*csc(c+d*x)^10, x) == :(-1//7*d^-1*cot(c+d*x)^7*(a^2+b^2)+-1//9*a^2*d^-1*cot(c+d*x)^9+5//64*a*b*d^-1*arctanh(cos(c+d*x))+-5//32*a*b*d^-1*csc(c+d*x)^3*cot(c+d*x)+-1//4*a*b*d^-1*cot(c+d*x)^5*csc(c+d*x)^3+5//24*a*b*d^-1*cot(c+d*x)^3*csc(c+d*x)^3+5//64*a*b*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^6*csc(c+d*x)^11, x) == :(1//256*d^-1*(3*a^2+10*b^2)*arctanh(cos(c+d*x))+-2//7*a*b*d^-1*cot(c+d*x)^7+-2//9*a*b*d^-1*cot(c+d*x)^9+-1//10*a^2*d^-1*csc(c+d*x)^9*cot(c+d*x)+-1//480*d^-1*csc(c+d*x)^5*(-170*b^2+93*a^2)*cot(c+d*x)+1//80*d^-1*csc(c+d*x)^7*(-10*b^2+21*a^2)*cot(c+d*x)+1//256*d^-1*(3*a^2+10*b^2)*cot(c+d*x)*csc(c+d*x)+1//384*d^-1*csc(c+d*x)^3*(-118*b^2+3*a^2)*cot(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^6*csc(c+d*x)^12, x) == :(-1//7*d^-1*cot(c+d*x)^7*(a^2+b^2)+-1//9*d^-1*cot(c+d*x)^9*(b^2+2*a^2)+-1//11*a^2*d^-1*cot(c+d*x)^11+3//128*a*b*d^-1*arctanh(cos(c+d*x))+-1//5*a*b*d^-1*cot(c+d*x)^5*csc(c+d*x)^5+-1//16*a*b*d^-1*csc(c+d*x)^5*cot(c+d*x)+1//8*a*b*d^-1*cot(c+d*x)^3*csc(c+d*x)^5+1//64*a*b*d^-1*csc(c+d*x)^3*cot(c+d*x)+3//128*a*b*d^-1*cot(c+d*x)*csc(c+d*x))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^6*sin(c+d*x)^3, x) == :(1//8*a*x*b^-9*(-5*b^6+64*a^6+-120*a^4*b^2+60*a^2*b^4)+1//105*b^-8*d^-1*(-15*b^6+840*a^6+-1435*a^4*b^2+588*a^2*b^4)*cos(c+d*x)+1//4*a^-1*d^-1*(a+b*sin(c+d*x))^-1*sin(c+d*x)^4*cos(c+d*x)+1//7*b^-1*d^-1*(a+b*sin(c+d*x))^-1*sin(c+d*x)^7*cos(c+d*x)+1//105*b^-6*d^-1*sin(c+d*x)^2*(150*b^4+280*a^4+-441*a^2*b^2)*cos(c+d*x)+-2*a^2*b^-9*d^-1*(a^2+-1*b^2)^3//2*(-3*b^2+8*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-4//21*a*b^-2*d^-1*(a+b*sin(c+d*x))^-1*sin(c+d*x)^6*cos(c+d*x)+-3//20*b*a^-2*d^-1*(a+b*sin(c+d*x))^-1*sin(c+d*x)^5*cos(c+d*x)+-1//8*a*b^-7*d^-1*(19*b^4+32*a^4+-52*a^2*b^2)*cos(c+d*x)*sin(c+d*x)+-1//12*a^-1*b^-5*d^-1*sin(c+d*x)^3*(12*b^4+24*a^4+-37*a^2*b^2)*cos(c+d*x)+1//140*a^-2*b^-4*d^-1*sin(c+d*x)^4*(105*b^4+224*a^4+-340*a^2*b^2)*cos(c+d*x)+-1//15*a^-2*b^-3*d^-1*(a+b*sin(c+d*x))^-1*sin(c+d*x)^5*(9*b^4+20*a^4+-30*a^2*b^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^6*sin(c+d*x)^2, x) == :(-1//16*x*b^-8*(-5*b^6+112*a^6+-200*a^4*b^2+90*a^2*b^4)+-1//15*a*b^-7*d^-1*(61*b^4+105*a^4+-170*a^2*b^2)*cos(c+d*x)+1//3*a^-1*d^-1*(a+b*sin(c+d*x))^-1*sin(c+d*x)^3*cos(c+d*x)+1//6*b^-1*d^-1*(a+b*sin(c+d*x))^-1*sin(c+d*x)^6*cos(c+d*x)+1//16*b^-6*d^-1*(27*b^4+56*a^4+-86*a^2*b^2)*cos(c+d*x)*sin(c+d*x)+2*a*b^-8*d^-1*(a^2+-1*b^2)^3//2*(-2*b^2+7*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-7//30*a*b^-2*d^-1*(a+b*sin(c+d*x))^-1*sin(c+d*x)^5*cos(c+d*x)+-1//6*b*a^-2*d^-1*(a+b*sin(c+d*x))^-1*sin(c+d*x)^4*cos(c+d*x)+-1//15*a^-1*b^-5*d^-1*sin(c+d*x)^2*(15*b^4+35*a^4+-52*a^2*b^2)*cos(c+d*x)+1//24*a^-2*b^-4*d^-1*sin(c+d*x)^3*(16*b^4+42*a^4+-61*a^2*b^2)*cos(c+d*x)+-1//10*a^-2*b^-3*d^-1*(a+b*sin(c+d*x))^-1*sin(c+d*x)^4*(5*b^4+14*a^4+-20*a^2*b^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^6*sin(c+d*x), x) == :(-1//6*b^-4*d^-1*cos(c+d*x)^3*(-2*b^2+12*a^2+-9*a*b*sin(c+d*x))+1//4*a*x*b^-7*(15*b^4+24*a^4+-40*a^2*b^2)+1//4*b^-6*d^-1*(4*b^4+24*a^4+-28*a^2*b^2+-1*a*b*(-11*b^2+12*a^2)*sin(c+d*x))*cos(c+d*x)+-2*b^-7*d^-1*(a^2+-1*b^2)^3//2*(-1*b^2+6*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+1//5*b^-2*d^-1*(a+b*sin(c+d*x))^-1*cos(c+d*x)^5*(6a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^6*csc(c+d*x), x) == :(a*x*b^-3+b^-2*d^-1*cos(c+d*x)+-1*a^-2*d^-1*arctanh(cos(c+d*x))+-1//3*b^-2*d^-1*cos(c+d*x)^3+b^-4*d^-1*(-3*b^2+3*a^2)*cos(c+d*x)+2*a*x*b^-5*(-3*b^2+2*a^2)+2*b^-5*d^-1*(a^2+-1*b^2)^3//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1*a*b^-3*d^-1*cos(c+d*x)*sin(c+d*x)+a^-1*b^-4*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^2*cos(c+d*x)+-2*a^-2*b^-5*d^-1*(a^2+-1*b^2)^3//2*(b^2+5*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^6*csc(c+d*x)^2, x) == :(-1//2*x*b^-2+-1*x*b^-4*(-3*b^2+3*a^2)+-1*a^-2*d^-1*cot(c+d*x)+(1/2)*b^-2*d^-1*cos(c+d*x)*sin(c+d*x)+-2*a*b^-3*d^-1*cos(c+d*x)+2*b*a^-3*d^-1*arctanh(cos(c+d*x))+-2*a^-1*b^-4*d^-1*(a^2+-1*b^2)^3//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+a^-3*b^-4*d^-1*(a^2+-1*b^2)^-1//2*(4*b^6+8*a^6+-12*a^4*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1*a^-2*b^-3*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^2*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^6*csc(c+d*x)^3, x) == :(b^-2*d^-1*cos(c+d*x)+2*a*x*b^-3+-1//2*a^-2*d^-1*arctanh(cos(c+d*x))+a^-4*d^-1*(-3*b^2+3*a^2)*arctanh(cos(c+d*x))+2*b*a^-3*d^-1*cot(c+d*x)+-1//2*a^-2*d^-1*cot(c+d*x)*csc(c+d*x)+2*a^-2*b^-3*d^-1*(a^2+-1*b^2)^3//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+a^-3*b^-2*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^2*cos(c+d*x)+-6*a^-4*b^-3*d^-1*(a^2+-1*b^2)^3//2*(a^2+b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^6*csc(c+d*x)^4, x) == :(-1*x*b^-2+-1*a^-2*d^-1*cot(c+d*x)+-1//3*a^-2*d^-1*cot(c+d*x)^3+b*a^-3*d^-1*arctanh(cos(c+d*x))+a^-4*d^-1*(-3*b^2+3*a^2)*cot(c+d*x)+b*a^-3*d^-1*cot(c+d*x)*csc(c+d*x)+-2*b*a^-5*d^-1*(-2*b^2+3*a^2)*arctanh(cos(c+d*x))+-2*a^-3*b^-2*d^-1*(a^2+-1*b^2)^3//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+a^-5*b^-2*d^-1*(a^2+-1*b^2)^-1//2*(4*a^6+8*b^6+-12*a^2*b^4)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1*a^-4*b^-1*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^2*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^6*csc(c+d*x)^5, x) == :(-1*b^-1*d^-1*(a+b*sin(c+d*x))^-1*cot(c+d*x)+-1//8*a^-6*d^-1*(15*a^4+40*b^4+-60*a^2*b^2)*arctanh(cos(c+d*x))+-10*b*a^-6*d^-1*(a^2+-1*b^2)^3//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//4*a^-1*d^-1*(a+b*sin(c+d*x))^-1*csc(c+d*x)^3*cot(c+d*x)+1//3*a^-5*b^-1*d^-1*(3*a^4+15*b^4+-20*a^2*b^2)*cot(c+d*x)+1//8*a^-4*d^-1*(-20*b^2+25*a^2)*cot(c+d*x)*csc(c+d*x)+-1//3*a^-3*d^-1*(a+b*sin(c+d*x))^-1*(-5*b^2+6*a^2)*cot(c+d*x)*csc(c+d*x)+5//12*b*a^-2*d^-1*(a+b*sin(c+d*x))^-1*csc(c+d*x)^2*cot(c+d*x))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^6*csc(c+d*x)^6, x) == :(-1//15*a^-6*d^-1*(38*a^4+90*b^4+-135*a^2*b^2)*cot(c+d*x)+-1*a^-7*d^-1*(a^2+-1*b^2)^3//2*(-12*b^2+2*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//2*b^-1*d^-1*(a+b*sin(c+d*x))^-1*cot(c+d*x)*csc(c+d*x)+-1//5*a^-1*d^-1*(a+b*sin(c+d*x))^-1*csc(c+d*x)^4*cot(c+d*x)+1//4*b*a^-7*d^-1*(15*a^4+24*b^4+-40*a^2*b^2)*arctanh(cos(c+d*x))+-1//30*a^-4*b^-2*d^-1*csc(c+d*x)^2*(15*a^4+60*b^4+-82*a^2*b^2)*cot(c+d*x)+1//4*a^-5*b^-1*d^-1*(4*a^4+12*b^4+-17*a^2*b^2)*cot(c+d*x)*csc(c+d*x)+1//6*a*b^-2*d^-1*(a+b*sin(c+d*x))^-1*csc(c+d*x)^2*cot(c+d*x)+3//10*b*a^-2*d^-1*(a+b*sin(c+d*x))^-1*csc(c+d*x)^3*cot(c+d*x)+1//6*a^-3*b^-2*d^-1*(a+b*sin(c+d*x))^-1*csc(c+d*x)^2*(2*a^4+9*b^4+-12*a^2*b^2)*cot(c+d*x))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^6*csc(c+d*x)^7, x) == :(1//16*a^-8*d^-1*(-112*b^6+5*a^6+-90*a^4*b^2+200*a^2*b^4)*arctanh(cos(c+d*x))+-1//3*b^-1*d^-1*(a+b*sin(c+d*x))^-1*csc(c+d*x)^2*cot(c+d*x)+-1//6*a^-1*d^-1*(a+b*sin(c+d*x))^-1*csc(c+d*x)^5*cot(c+d*x)+-1//16*a^-6*d^-1*(27*a^4+56*b^4+-86*a^2*b^2)*cot(c+d*x)*csc(c+d*x)+1//15*b*a^-7*d^-1*(61*a^4+105*b^4+-170*a^2*b^2)*cot(c+d*x)+2*b*a^-8*d^-1*(a^2+-1*b^2)^3//2*(-7*b^2+2*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//24*a^-4*b^-2*d^-1*csc(c+d*x)^3*(16*a^4+42*b^4+-61*a^2*b^2)*cot(c+d*x)+1//6*a*b^-2*d^-1*(a+b*sin(c+d*x))^-1*csc(c+d*x)^3*cot(c+d*x)+1//15*a^-5*b^-1*d^-1*csc(c+d*x)^2*(15*a^4+35*b^4+-52*a^2*b^2)*cot(c+d*x)+7//30*b*a^-2*d^-1*(a+b*sin(c+d*x))^-1*csc(c+d*x)^4*cot(c+d*x)+1//10*a^-3*b^-2*d^-1*(a+b*sin(c+d*x))^-1*csc(c+d*x)^3*(5*a^4+14*b^4+-20*a^2*b^2)*cot(c+d*x))
@test integrate((a+b*sin(c+d*x))^-3*cos(c+d*x)^6*sin(c+d*x)^3, x) == :(-1//16*x*b^-9*(-5*b^6+448*a^6+-600*a^4*b^2+180*a^2*b^4)+-1//30*a*b^-8*d^-1*(213*b^4+840*a^4+-985*a^2*b^2)*cos(c+d*x)+1//4*a^-1*d^-1*(a+b*sin(c+d*x))^-2*sin(c+d*x)^4*cos(c+d*x)+1//6*b^-1*d^-1*(a+b*sin(c+d*x))^-2*sin(c+d*x)^7*cos(c+d*x)+1//16*b^-7*d^-1*(43*b^4+224*a^4+-244*a^2*b^2)*cos(c+d*x)*sin(c+d*x)+a*b^-9*d^-1*(a^2+-1*b^2)^(1/2)*(6*b^4+56*a^4+-47*a^2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-4//15*a*b^-2*d^-1*(a+b*sin(c+d*x))^-2*sin(c+d*x)^6*cos(c+d*x)+-1//10*b*a^-2*d^-1*(a+b*sin(c+d*x))^-2*sin(c+d*x)^5*cos(c+d*x)+-1//30*a^-1*b^-6*d^-1*sin(c+d*x)^2*(45*b^4+280*a^4+-291*a^2*b^2)*cos(c+d*x)+1//24*a^-2*b^-5*d^-1*sin(c+d*x)^3*(24*b^4+168*a^4+-169*a^2*b^2)*cos(c+d*x)+-1//20*a^-2*b^-4*d^-1*(a+b*sin(c+d*x))^-1*sin(c+d*x)^4*(15*b^4+112*a^4+-110*a^2*b^2)*cos(c+d*x)+-1//60*a^-2*b^-3*d^-1*(a+b*sin(c+d*x))^-2*sin(c+d*x)^5*(9*b^4+56*a^4+-60*a^2*b^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-3*cos(c+d*x)^6*sin(c+d*x)^2, x) == :(1//8*a*x*b^-8*(45*b^4+168*a^4+-200*a^2*b^2)+1//30*b^-7*d^-1*(91*b^4+630*a^4+-645*a^2*b^2)*cos(c+d*x)+-1*b^-8*d^-1*(a^2+-1*b^2)^(1/2)*(2*b^4+42*a^4+-29*a^2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+1//3*a^-1*d^-1*(a+b*sin(c+d*x))^-2*sin(c+d*x)^3*cos(c+d*x)+1//5*b^-1*d^-1*(a+b*sin(c+d*x))^-2*sin(c+d*x)^6*cos(c+d*x)+-7//20*a*b^-2*d^-1*(a+b*sin(c+d*x))^-2*sin(c+d*x)^5*cos(c+d*x)+-1//8*a^-1*b^-6*d^-1*(8*b^4+84*a^4+-79*a^2*b^2)*cos(c+d*x)*sin(c+d*x)+-1//12*b*a^-2*d^-1*(a+b*sin(c+d*x))^-2*sin(c+d*x)^4*cos(c+d*x)+1//30*a^-2*b^-5*d^-1*sin(c+d*x)^2*(15*b^4+210*a^4+-187*a^2*b^2)*cos(c+d*x)+-1//12*a^-2*b^-4*d^-1*(a+b*sin(c+d*x))^-1*sin(c+d*x)^3*(4*b^4+63*a^4+-54*a^2*b^2)*cos(c+d*x)+-1//60*a^-2*b^-3*d^-1*(a+b*sin(c+d*x))^-2*sin(c+d*x)^4*(5*b^4+63*a^4+-60*a^2*b^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-3*cos(c+d*x)^6*sin(c+d*x), x) == :(-1//8*x*b^-7*(15*b^4+120*a^4+-120*a^2*b^2)+-15//8*b^-6*d^-1*(4*a*(-1*b^2+2*a^2)+-1*b*(-1*b^2+4*a^2)*sin(c+d*x))*cos(c+d*x)+1//4*b^-2*d^-1*(a+b*sin(c+d*x))^-2*cos(c+d*x)^5*(3a+b*sin(c+d*x))+5//4*b^-4*d^-1*(a+b*sin(c+d*x))^-1*cos(c+d*x)^3*(-1*b^2+4*a^2+a*b*sin(c+d*x))+15*a*b^-7*d^-1*(a^2+-1*b^2)^-1//2*(b^4+2*a^4+-3*a^2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-3*cos(c+d*x)^6*csc(c+d*x), x) == :(-1//2*x*b^-3+-1*x*b^-5*(-3*b^2+6*a^2)+-1*a^-3*d^-1*arctanh(cos(c+d*x))+(1/2)*b^-3*d^-1*cos(c+d*x)*sin(c+d*x)+-3*a*b^-4*d^-1*cos(c+d*x)+(1/2)*b^-4*d^-1*(a+b*sin(c+d*x))^-1*(-3*b^2+3*a^2)*cos(c+d*x)+a^-1*b^-5*d^-1*(a^2+-1*b^2)^(1/2)*(b^2+2*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+a^-3*b^-5*d^-1*(a^2+-1*b^2)^-1//2*(-2*b^6+20*a^6+-18*a^4*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+(1/2)*a^-1*b^-4*d^-1*(a+b*sin(c+d*x))^-2*(a^2+-1*b^2)^2*cos(c+d*x)+-2*a^-1*b^-5*d^-1*(a^2+-1*b^2)^(1/2)*(b^2+5*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1*a^-2*b^-4*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)*(b^2+5*a^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-3*cos(c+d*x)^6*csc(c+d*x)^2, x) == :(b^-3*d^-1*cos(c+d*x)+-1*a^-3*d^-1*cot(c+d*x)+3*a*x*b^-4+3*b*a^-4*d^-1*arctanh(cos(c+d*x))+-1*a^-4*b^-4*d^-1*(a^2+-1*b^2)^-1//2*(-6*b^6+12*a^6+-6*a^4*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+3*a^-2*b^-4*d^-1*(a^2+-1*b^2)^(1/2)*(b^2+2*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//2*a^-1*b^-3*d^-1*(a+b*sin(c+d*x))^-1*(-3*b^2+3*a^2)*cos(c+d*x)+-1//2*a^-2*b^-3*d^-1*(a+b*sin(c+d*x))^-2*(a^2+-1*b^2)^2*cos(c+d*x)+a^-3*b^-3*d^-1*(a+b*sin(c+d*x))^-1*(b^2+2*a^2)*(-2*b^2+2*a^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-3*cos(c+d*x)^6*csc(c+d*x)^3, x) == :(-1*x*b^-3+-1//2*a^-3*d^-1*arctanh(cos(c+d*x))+a^-5*d^-1*(-6*b^2+3*a^2)*arctanh(cos(c+d*x))+3*b*a^-4*d^-1*cot(c+d*x)+-1//2*a^-3*d^-1*cot(c+d*x)*csc(c+d*x)+a^-5*b^-3*d^-1*(a^2+-1*b^2)^-1//2*(-12*b^6+6*a^6+6*a^2*b^4)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+a^-3*b^-3*d^-1*(a^2+-1*b^2)^(1/2)*(b^2+2*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+(1/2)*a^-3*b^-2*d^-1*(a+b*sin(c+d*x))^-2*(a^2+-1*b^2)^2*cos(c+d*x)+(1/2)*a^-2*b^-2*d^-1*(a+b*sin(c+d*x))^-1*(-3*b^2+3*a^2)*cos(c+d*x)+-1*a^-4*b^-2*d^-1*(a+b*sin(c+d*x))^-1*(-3*b^4+3*a^4)*cos(c+d*x)+-6*a^-3*b^-3*d^-1*(a^2+-1*b^2)^(1/2)*(a^2+b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-3*cos(c+d*x)^6*csc(c+d*x)^4, x) == :(-1*b^-1*d^-1*(a+b*sin(c+d*x))^-2*cos(c+d*x)+a^-6*d^-1*(a^2+-1*b^2)^(1/2)*(-20*b^2+5*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-5//2*b*a^-6*d^-1*(-4*b^2+3*a^2)*arctanh(cos(c+d*x))+-1//2*a*b^-2*d^-1*(a+b*sin(c+d*x))^-2*cot(c+d*x)+-1//2*a^-4*d^-1*(a+b*sin(c+d*x))^-1*(-10*b^2+5*a^2)*cot(c+d*x)+-1//3*a^-1*d^-1*(a+b*sin(c+d*x))^-2*csc(c+d*x)^2*cot(c+d*x)+-1//3*a^-3*d^-1*(a+b*sin(c+d*x))^-2*(-5*b^2+3*a^2)*cot(c+d*x)+1//6*a^-5*b^-2*d^-1*(-60*b^4+3*a^4+35*a^2*b^2)*cot(c+d*x)+5//6*b*a^-2*d^-1*(a+b*sin(c+d*x))^-2*cot(c+d*x)*csc(c+d*x))
@test integrate((a+b*sin(c+d*x))^-3*cos(c+d*x)^6*csc(c+d*x)^5, x) == :(-1//2*b^-1*d^-1*(a+b*sin(c+d*x))^-2*cot(c+d*x)+-1//8*a^-7*d^-1*(15*a^4+120*b^4+-120*a^2*b^2)*arctanh(cos(c+d*x))+(1/2)*a^-6*b^-1*d^-1*(a^4+30*b^4+-25*a^2*b^2)*cot(c+d*x)+-1//4*a^-1*d^-1*(a+b*sin(c+d*x))^-2*csc(c+d*x)^3*cot(c+d*x)+1//8*a^-5*d^-1*(-60*b^2+45*a^2)*cot(c+d*x)*csc(c+d*x)+(1/2)*b*a^-2*d^-1*(a+b*sin(c+d*x))^-2*csc(c+d*x)^2*cot(c+d*x)+-15*b*a^-7*d^-1*(a^2+-1*b^2)^(1/2)*(a^2+-2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//2*a^-4*d^-1*(a+b*sin(c+d*x))^-1*(-10*b^2+7*a^2)*cot(c+d*x)*csc(c+d*x)+-1//4*a^-3*d^-1*(a+b*sin(c+d*x))^-2*(-5*b^2+4*a^2)*cot(c+d*x)*csc(c+d*x))
@test integrate((a+b*sin(c+d*x))^-3*cos(c+d*x)^6*csc(c+d*x)^6, x) == :(-1//30*a^-7*d^-1*(91*a^4+630*b^4+-645*a^2*b^2)*cot(c+d*x)+-1*a^-8*d^-1*(a^2+-1*b^2)^(1/2)*(2*a^4+42*b^4+-29*a^2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//3*b^-1*d^-1*(a+b*sin(c+d*x))^-2*cot(c+d*x)*csc(c+d*x)+-1//5*a^-1*d^-1*(a+b*sin(c+d*x))^-2*csc(c+d*x)^4*cot(c+d*x)+1//8*b*a^-8*d^-1*(45*a^4+168*b^4+-200*a^2*b^2)*arctanh(cos(c+d*x))+-1//30*a^-5*b^-2*d^-1*csc(c+d*x)^2*(15*a^4+210*b^4+-187*a^2*b^2)*cot(c+d*x)+1//8*a^-6*b^-1*d^-1*(8*a^4+84*b^4+-79*a^2*b^2)*cot(c+d*x)*csc(c+d*x)+1//12*a*b^-2*d^-1*(a+b*sin(c+d*x))^-2*csc(c+d*x)^2*cot(c+d*x)+7//20*b*a^-2*d^-1*(a+b*sin(c+d*x))^-2*csc(c+d*x)^3*cot(c+d*x)+1//12*a^-4*b^-2*d^-1*(a+b*sin(c+d*x))^-1*csc(c+d*x)^2*(4*a^4+63*b^4+-54*a^2*b^2)*cot(c+d*x)+1//60*a^-3*b^-2*d^-1*(a+b*sin(c+d*x))^-2*csc(c+d*x)^2*(5*a^4+63*b^4+-60*a^2*b^2)*cot(c+d*x))
@test integrate((a+b*sin(c+d*x))^-3*cos(c+d*x)^6*csc(c+d*x)^8, x) == :(1//70*a^-9*d^-1*(-2520*b^6+10*a^6+-889*a^4*b^2+3255*a^2*b^4)*cot(c+d*x)+-3//16*b*a^-10*d^-1*(-192*b^6+5*a^6+-100*a^4*b^2+280*a^2*b^4)*arctanh(cos(c+d*x))+-1//5*b^-1*d^-1*(a+b*sin(c+d*x))^-2*csc(c+d*x)^3*cot(c+d*x)+-1//7*a^-1*d^-1*(a+b*sin(c+d*x))^-2*csc(c+d*x)^6*cot(c+d*x)+-1//70*a^-7*d^-1*csc(c+d*x)^2*(205*a^4+840*b^4+-973*a^2*b^2)*cot(c+d*x)+-3*a^-10*b^2*d^-1*(a^2+-1*b^2)^(1/2)*(4*a^4+24*b^4+-23*a^2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//70*a^-5*b^-2*d^-1*csc(c+d*x)^4*(105*a^4+504*b^4+-555*a^2*b^2)*cot(c+d*x)+1//8*a^-6*b^-1*d^-1*csc(c+d*x)^3*(16*a^4+72*b^4+-81*a^2*b^2)*cot(c+d*x)+1//10*a*b^-2*d^-1*(a+b*sin(c+d*x))^-2*csc(c+d*x)^4*cot(c+d*x)+3//14*b*a^-2*d^-1*(a+b*sin(c+d*x))^-2*csc(c+d*x)^5*cot(c+d*x)+3//16*b*a^-8*d^-1*(27*a^4+96*b^4+-116*a^2*b^2)*cot(c+d*x)*csc(c+d*x)+1//10*a^-4*b^-2*d^-1*(a+b*sin(c+d*x))^-1*csc(c+d*x)^4*(12*a^4+60*b^4+-65*a^2*b^2)*cot(c+d*x)+1//35*a^-3*b^-2*d^-1*(a+b*sin(c+d*x))^-2*csc(c+d*x)^4*(7*a^4+30*b^4+-35*a^2*b^2)*cot(c+d*x))
@test integrate((d*sin(e+f*x))^-1//2*(a+b*sin(e+f*x))^-13//2*cos(e+f*x)^6, x) == :(2//11*a^-1*d^-1*f^-1*(d*sin(e+f*x))^(1/2)*(a+b*sin(e+f*x))^-11//2*cos(e+f*x)^5+-1//99*a^-2*b^-2*d^-1*f^-1*(d*sin(e+f*x))^(1/2)*(a+b*sin(e+f*x))^-9//2*(-20*b^2+20*a^2)*cos(e+f*x)+1//693*a^-3*b^-2*d^-1*f^-1*(d*sin(e+f*x))^(1/2)*(a+b*sin(e+f*x))^-7//2*(160*b^2+240*a^2)*cos(e+f*x)+16//693*b*a^-5*f^-1*(d*sin(e+f*x))^-1//2*(a+b*sin(e+f*x))^-1//2*(a^2+-1*b^2)^-3*(32*b^4+93*a^4+-93*a^2*b^2)*cos(e+f*x)+-1//231*a^-4*b^-2*d^-1*f^-1*(d*sin(e+f*x))^(1/2)*(a+b*sin(e+f*x))^-5//2*(a^2+-1*b^2)^-1*(20*a^4+64*b^4+-68*a^2*b^2)*cos(e+f*x)+-1//693*a^-5*b^-2*d^-1*f^-1*(d*sin(e+f*x))^(1/2)*(a+b*sin(e+f*x))^-3//2*(a^2+-1*b^2)^-2*(-256*b^6+40*a^6+-176*a^4*b^2+520*a^2*b^4)*cos(e+f*x)+-1//693*a^-6*d^-1//2*f^-1*(a*(a+b)^-1*(1+-1*csc(e+f*x)))^(1/2)*(a*(a+-1b)^-1*(1+csc(e+f*x)))^(1/2)*(a+b)^-5//2*(a+-1b)^-2*(512*b^4+720*a^4+-1104*a^2*b^2+-768*b*a^3+384*a*b^3)*Elliptic.F(arcsin(d^(1/2)*(d*sin(e+f*x))^-1//2*(a+b)^-1//2*(a+b*sin(e+f*x))^(1/2)),-1*(a+-1b)^-1*(a+b))*tan(e+f*x)+-16//693*b*a^-7*d^-1//2*f^-1*(a*(a+b)^-1*(1+-1*csc(e+f*x)))^(1/2)*(a*(a+-1b)^-1*(1+csc(e+f*x)))^(1/2)*(a+b)^-5//2*(a+-1b)^-2*(32*b^4+93*a^4+-93*a^2*b^2)*Elliptic.E(arcsin(d^(1/2)*(d*sin(e+f*x))^-1//2*(a+b)^-1//2*(a+b*sin(e+f*x))^(1/2)),-1*(a+-1b)^-1*(a+b))*tan(e+f*x))
@test integrate((d*sin(e+f*x))^-1//2*(g*cos(e+f*x))^-7//2*(a+b*sin(e+f*x))^2, x) == :(2//5*d^-1*f^-1*g^-1*(d*sin(e+f*x))^(1/2)*(g*cos(e+f*x))^-5//2*(a+b*sin(e+f*x))^2+8//5*a^2*d^-1*f^-1*g^-3*(d*sin(e+f*x))^(1/2)*(g*cos(e+f*x))^-1//2+8//5*a*b*d^-2*f^-1*g^-3*(d*sin(e+f*x))^3//2*(g*cos(e+f*x))^-1//2+-8//5*a*b*d^-1*f^-1*g^-4*(d*sin(e+f*x))^(1/2)*(g*cos(e+f*x))^(1/2)*sin(2*e+2*f*x)^-1//2*Elliptic.E(e+-1//4*pi+f*x,2))
@test integrate((a+b*sin(c+d*x))^-1*sin(c+d*x)^3*cos(c+d*x), x) == :(1//3*b^-1*d^-1*sin(c+d*x)^3+a^2*b^-3*d^-1*sin(c+d*x)+-1*a^3*b^-4*d^-1*log(a+b*sin(c+d*x))+-1//2*a*b^-2*d^-1*sin(c+d*x)^2)
@test integrate((a+b*sin(c+d*x))^-1*sin(c+d*x)^2*cos(c+d*x), x) == :((1/2)*b^-1*d^-1*sin(c+d*x)^2+a^2*b^-3*d^-1*log(a+b*sin(c+d*x))+-1*a*b^-2*d^-1*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)*sin(c+d*x), x) == :(b^-1*d^-1*sin(c+d*x)+-1*a*b^-2*d^-1*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)*csc(c+d*x), x) == :(a^-1*d^-1*log(sin(c+d*x))+-1*a^-1*d^-1*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*csc(c+d*x)^2*cos(c+d*x), x) == :(-1*a^-1*d^-1*csc(c+d*x)+b*a^-2*d^-1*log(a+b*sin(c+d*x))+-1*b*a^-2*d^-1*log(sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*csc(c+d*x)^3*cos(c+d*x), x) == :(-1//2*a^-1*d^-1*csc(c+d*x)^2+b*a^-2*d^-1*csc(c+d*x)+a^-3*b^2*d^-1*log(sin(c+d*x))+-1*a^-3*b^2*d^-1*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^2*sin(c+d*x)^4, x) == :(1//5*b^-1*d^-1*sin(c+d*x)^4*cos(c+d*x)+1//8*a*x*b^-6*(-1*b^4+8*a^4+-4*a^2*b^2)+1//15*b^-5*d^-1*(-2*b^4+15*a^4+-5*a^2*b^2)*cos(c+d*x)+-2*a^4*b^-6*d^-1*(a^2+-1*b^2)^(1/2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//4*a*b^-2*d^-1*sin(c+d*x)^3*cos(c+d*x)+1//15*b^-3*d^-1*sin(c+d*x)^2*(-1*b^2+5*a^2)*cos(c+d*x)+-1//8*a*b^-4*d^-1*(-1*b^2+4*a^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^2*sin(c+d*x)^3, x) == :(-1//8*x*b^-5*(-1*b^4+8*a^4+-4*a^2*b^2)+1//4*b^-1*d^-1*sin(c+d*x)^3*cos(c+d*x)+2*a^3*b^-5*d^-1*(a^2+-1*b^2)^(1/2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//3*a*b^-4*d^-1*(-1*b^2+3*a^2)*cos(c+d*x)+-1//3*a*b^-2*d^-1*sin(c+d*x)^2*cos(c+d*x)+1//8*b^-3*d^-1*(-1*b^2+4*a^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^2*sin(c+d*x)^2, x) == :((1/2)*a*x*b^-4*(-1*b^2+2*a^2)+1//3*b^-1*d^-1*sin(c+d*x)^2*cos(c+d*x)+1//3*b^-3*d^-1*(-1*b^2+3*a^2)*cos(c+d*x)+-2*a^2*b^-4*d^-1*(a^2+-1*b^2)^(1/2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//2*a*b^-2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^2*sin(c+d*x), x) == :(-1//2*x*b^-3*(-1*b^2+2*a^2)+-1//2*b^-2*d^-1*(2a+-1*b*sin(c+d*x))*cos(c+d*x)+2*a*b^-3*d^-1*(a^2+-1*b^2)^(1/2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^2*csc(c+d*x), x) == :(-1*x*b^-1+-1*a^-1*d^-1*arctanh(cos(c+d*x))+2*a^-1*b^-1*d^-1*(a^2+-1*b^2)^(1/2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^2*csc(c+d*x)^2, x) == :(-1*a^-1*d^-1*cot(c+d*x)+b*a^-2*d^-1*arctanh(cos(c+d*x))+-2*a^-2*d^-1*(a^2+-1*b^2)^(1/2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^2*csc(c+d*x)^3, x) == :(b*a^-2*d^-1*cot(c+d*x)+(1/2)*a^-3*d^-1*(a^2+-2*b^2)*arctanh(cos(c+d*x))+-1//2*a^-1*d^-1*cot(c+d*x)*csc(c+d*x)+2*b*a^-3*d^-1*(a^2+-1*b^2)^(1/2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^2*csc(c+d*x)^4, x) == :(-1//3*a^-1*d^-1*csc(c+d*x)^2*cot(c+d*x)+1//3*a^-3*d^-1*(a^2+-3*b^2)*cot(c+d*x)+(1/2)*b*a^-2*d^-1*cot(c+d*x)*csc(c+d*x)+-2*a^-4*b^2*d^-1*(a^2+-1*b^2)^(1/2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//2*b*a^-4*d^-1*(a^2+-2*b^2)*arctanh(cos(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^2*csc(c+d*x)^5, x) == :(-1//4*a^-1*d^-1*csc(c+d*x)^3*cot(c+d*x)+1//8*a^-5*d^-1*(a^4+-8*b^4+4*a^2*b^2)*arctanh(cos(c+d*x))+2*a^-5*b^3*d^-1*(a^2+-1*b^2)^(1/2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//3*b*a^-4*d^-1*(a^2+-3*b^2)*cot(c+d*x)+1//3*b*a^-2*d^-1*csc(c+d*x)^2*cot(c+d*x)+1//8*a^-3*d^-1*(a^2+-4*b^2)*cot(c+d*x)*csc(c+d*x))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^2*csc(c+d*x)^6, x) == :(-1//5*a^-1*d^-1*csc(c+d*x)^4*cot(c+d*x)+1//15*a^-5*d^-1*(-15*b^4+2*a^4+5*a^2*b^2)*cot(c+d*x)+-2*a^-6*b^4*d^-1*(a^2+-1*b^2)^(1/2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//8*b*a^-6*d^-1*(a^4+-8*b^4+4*a^2*b^2)*arctanh(cos(c+d*x))+1//4*b*a^-2*d^-1*csc(c+d*x)^3*cot(c+d*x)+1//15*a^-3*d^-1*csc(c+d*x)^2*(a^2+-5*b^2)*cot(c+d*x)+-1//8*b*a^-4*d^-1*(a^2+-4*b^2)*cot(c+d*x)*csc(c+d*x))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^3*sin(c+d*x)^3, x) == :(-1//5*b^-1*d^-1*sin(c+d*x)^5+-1//3*b^-3*d^-1*sin(c+d*x)^3*(a^2+-1*b^2)+1//4*a*b^-2*d^-1*sin(c+d*x)^4+a^3*b^-6*d^-1*(a^2+-1*b^2)*log(a+b*sin(c+d*x))+(1/2)*a*b^-4*d^-1*sin(c+d*x)^2*(a^2+-1*b^2)+-1*a^2*b^-5*d^-1*(a^2+-1*b^2)*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^3*sin(c+d*x)^2, x) == :(-1//4*b^-1*d^-1*sin(c+d*x)^4+-1//2*b^-3*d^-1*sin(c+d*x)^2*(a^2+-1*b^2)+1//3*a*b^-2*d^-1*sin(c+d*x)^3+a*b^-4*d^-1*(a^2+-1*b^2)*sin(c+d*x)+-1*a^2*b^-5*d^-1*(a^2+-1*b^2)*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^3*sin(c+d*x), x) == :(-1//3*b^-1*d^-1*sin(c+d*x)^3+(1/2)*a*b^-2*d^-1*sin(c+d*x)^2+-1*b^-3*d^-1*(a^2+-1*b^2)*sin(c+d*x)+a*b^-4*d^-1*(a^2+-1*b^2)*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^3*csc(c+d*x), x) == :(a^-1*d^-1*log(sin(c+d*x))+-1*b^-1*d^-1*sin(c+d*x)+a^-1*b^-2*d^-1*(a^2+-1*b^2)*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^3*csc(c+d*x)^2, x) == :(-1*a^-1*d^-1*csc(c+d*x)+-1*b*a^-2*d^-1*log(sin(c+d*x))+-1*b^-1*d^-1*(1+-1*a^-2*b^2)*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^3*csc(c+d*x)^3, x) == :(-1//2*a^-1*d^-1*csc(c+d*x)^2+b*a^-2*d^-1*csc(c+d*x)+a^-3*d^-1*(a^2+-1*b^2)*log(a+b*sin(c+d*x))+-1*a^-3*d^-1*(a^2+-1*b^2)*log(sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^4*sin(c+d*x)^3, x) == :(1//16*x*b^-7*(b^6+16*a^6+-24*a^4*b^2+6*a^2*b^4)+-1//6*b^-1*d^-1*sin(c+d*x)^5*cos(c+d*x)+-2*a^3*b^-7*d^-1*(a^2+-1*b^2)^3//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//16*b^-5*d^-1*(b^4+8*a^4+-10*a^2*b^2)*cos(c+d*x)*sin(c+d*x)+-1//24*b^-3*d^-1*sin(c+d*x)^3*(-7*b^2+6*a^2)*cos(c+d*x)+1//5*a*b^-2*d^-1*sin(c+d*x)^4*cos(c+d*x)+1//15*a*b^-6*d^-1*(3*b^4+15*a^4+-20*a^2*b^2)*cos(c+d*x)+1//15*a*b^-4*d^-1*sin(c+d*x)^2*(-6*b^2+5*a^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^4*sin(c+d*x)^2, x) == :(-1//5*b^-1*d^-1*sin(c+d*x)^4*cos(c+d*x)+-1//8*a*x*b^-6*(3*b^4+8*a^4+-12*a^2*b^2)+-1//15*b^-5*d^-1*(3*b^4+15*a^4+-20*a^2*b^2)*cos(c+d*x)+2*a^2*b^-6*d^-1*(a^2+-1*b^2)^3//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//15*b^-3*d^-1*sin(c+d*x)^2*(-6*b^2+5*a^2)*cos(c+d*x)+1//4*a*b^-2*d^-1*sin(c+d*x)^3*cos(c+d*x)+1//8*a*b^-4*d^-1*(-5*b^2+4*a^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^4*sin(c+d*x), x) == :(1//8*x*b^-5*(3*b^4+8*a^4+-12*a^2*b^2)+-1//12*b^-2*d^-1*cos(c+d*x)^3*(4a+-3*b*sin(c+d*x))+1//8*b^-4*d^-1*(8*a*(a^2+-1*b^2)+-1*b*(-3*b^2+4*a^2)*sin(c+d*x))*cos(c+d*x)+-2*a*b^-5*d^-1*(a^2+-1*b^2)^3//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^4*csc(c+d*x), x) == :((1/2)*x*b^-3*(-3*b^2+2*a^2)+-1*a^-1*d^-1*arctanh(cos(c+d*x))+a*b^-2*d^-1*cos(c+d*x)+-1//2*b^-1*d^-1*cos(c+d*x)*sin(c+d*x)+-2*a^-1*b^-3*d^-1*(a^2+-1*b^2)^3//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^4*csc(c+d*x)^2, x) == :(-1*a*x*b^-2+-1*a^-1*d^-1*cot(c+d*x)+-1*b^-1*d^-1*cos(c+d*x)+b*a^-2*d^-1*arctanh(cos(c+d*x))+2*a^-2*b^-2*d^-1*(a^2+-1*b^2)^3//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^4*csc(c+d*x)^3, x) == :(x*b^-1+b*a^-2*d^-1*cot(c+d*x)+(1/2)*a^-3*d^-1*(-2*b^2+3*a^2)*arctanh(cos(c+d*x))+-1//2*a^-1*d^-1*cot(c+d*x)*csc(c+d*x)+-2*a^-3*b^-1*d^-1*(a^2+-1*b^2)^3//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^4*csc(c+d*x)^4, x) == :(2*a^-4*d^-1*(a^2+-1*b^2)^3//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//3*a^-1*d^-1*csc(c+d*x)^2*cot(c+d*x)+1//3*a^-3*d^-1*(-3*b^2+4*a^2)*cot(c+d*x)+(1/2)*b*a^-2*d^-1*cot(c+d*x)*csc(c+d*x)+-1//2*b*a^-4*d^-1*(-2*b^2+3*a^2)*arctanh(cos(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^4*csc(c+d*x)^5, x) == :(-1//4*a^-1*d^-1*csc(c+d*x)^3*cot(c+d*x)+-1//8*a^-5*d^-1*(3*a^4+8*b^4+-12*a^2*b^2)*arctanh(cos(c+d*x))+-2*b*a^-5*d^-1*(a^2+-1*b^2)^3//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//3*b*a^-4*d^-1*(-3*b^2+4*a^2)*cot(c+d*x)+1//3*b*a^-2*d^-1*csc(c+d*x)^2*cot(c+d*x)+1//8*a^-3*d^-1*(-4*b^2+5*a^2)*cot(c+d*x)*csc(c+d*x))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^4*csc(c+d*x)^6, x) == :(-1//5*a^-1*d^-1*csc(c+d*x)^4*cot(c+d*x)+-1//15*a^-5*d^-1*(3*a^4+15*b^4+-20*a^2*b^2)*cot(c+d*x)+2*a^-6*b^2*d^-1*(a^2+-1*b^2)^3//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+1//4*b*a^-2*d^-1*csc(c+d*x)^3*cot(c+d*x)+1//8*b*a^-6*d^-1*(3*a^4+8*b^4+-12*a^2*b^2)*arctanh(cos(c+d*x))+1//15*a^-3*d^-1*csc(c+d*x)^2*(-5*b^2+6*a^2)*cot(c+d*x)+-1//8*b*a^-4*d^-1*(-4*b^2+5*a^2)*cot(c+d*x)*csc(c+d*x))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^5*sin(c+d*x)^3, x) == :(1//7*b^-1*d^-1*sin(c+d*x)^7+-1//6*a*b^-2*d^-1*sin(c+d*x)^6+1//3*b^-5*d^-1*(a^2+-1*b^2)^2*sin(c+d*x)^3+1//5*b^-3*d^-1*sin(c+d*x)^5*(a^2+-2*b^2)+a^2*b^-7*d^-1*(a^2+-1*b^2)^2*sin(c+d*x)+-1*a^3*b^-8*d^-1*(a^2+-1*b^2)^2*log(a+b*sin(c+d*x))+-1//2*a*b^-6*d^-1*(a^2+-1*b^2)^2*sin(c+d*x)^2+-1//4*a*b^-4*d^-1*sin(c+d*x)^4*(a^2+-2*b^2))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^5*sin(c+d*x)^2, x) == :(1//6*b^-1*d^-1*sin(c+d*x)^6+(1/2)*b^-5*d^-1*(a^2+-1*b^2)^2*sin(c+d*x)^2+-1//5*a*b^-2*d^-1*sin(c+d*x)^5+1//4*b^-3*d^-1*sin(c+d*x)^4*(a^2+-2*b^2)+a^2*b^-7*d^-1*(a^2+-1*b^2)^2*log(a+b*sin(c+d*x))+-1*a*b^-6*d^-1*(a^2+-1*b^2)^2*sin(c+d*x)+-1//3*a*b^-4*d^-1*sin(c+d*x)^3*(a^2+-2*b^2))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^5*sin(c+d*x), x) == :(1//5*b^-1*d^-1*sin(c+d*x)^5+b^-5*d^-1*(a^2+-1*b^2)^2*sin(c+d*x)+-1//4*a*b^-2*d^-1*sin(c+d*x)^4+1//3*b^-3*d^-1*sin(c+d*x)^3*(a^2+-2*b^2)+-1*a*b^-6*d^-1*(a^2+-1*b^2)^2*log(a+b*sin(c+d*x))+-1//2*a*b^-4*d^-1*sin(c+d*x)^2*(a^2+-2*b^2))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^5*csc(c+d*x), x) == :(a^-1*d^-1*log(sin(c+d*x))+1//3*b^-1*d^-1*sin(c+d*x)^3+b^-3*d^-1*(a^2+-2*b^2)*sin(c+d*x)+-1//2*a*b^-2*d^-1*sin(c+d*x)^2+-1*a^-1*b^-4*d^-1*(a^2+-1*b^2)^2*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^5*csc(c+d*x)^2, x) == :((1/2)*b^-1*d^-1*sin(c+d*x)^2+-1*a^-1*d^-1*csc(c+d*x)+-1*a*b^-2*d^-1*sin(c+d*x)+-1*b*a^-2*d^-1*log(sin(c+d*x))+a^-2*b^-3*d^-1*(a^2+-1*b^2)^2*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^5*csc(c+d*x)^3, x) == :(b^-1*d^-1*sin(c+d*x)+-1//2*a^-1*d^-1*csc(c+d*x)^2+b*a^-2*d^-1*csc(c+d*x)+-1*a^-3*d^-1*(-1*b^2+2*a^2)*log(sin(c+d*x))+-1*a^-3*b^-2*d^-1*(a^2+-1*b^2)^2*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^5*csc(c+d*x)^4, x) == :(-1//3*a^-1*d^-1*csc(c+d*x)^3+a^-3*d^-1*(-1*b^2+2*a^2)*csc(c+d*x)+(1/2)*b*a^-2*d^-1*csc(c+d*x)^2+b*a^-4*d^-1*(-1*b^2+2*a^2)*log(sin(c+d*x))+a^-4*b^-1*d^-1*(a^2+-1*b^2)^2*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^5*csc(c+d*x)^5, x) == :(-1//4*a^-1*d^-1*csc(c+d*x)^4+a^-5*d^-1*(a^2+-1*b^2)^2*log(sin(c+d*x))+(1/2)*a^-3*d^-1*csc(c+d*x)^2*(-1*b^2+2*a^2)+-1*a^-5*d^-1*(a^2+-1*b^2)^2*log(a+b*sin(c+d*x))+1//3*b*a^-2*d^-1*csc(c+d*x)^3+-1*b*a^-4*d^-1*(-1*b^2+2*a^2)*csc(c+d*x))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^5*csc(c+d*x)^6, x) == :(-1//5*a^-1*d^-1*csc(c+d*x)^5+-1*a^-5*d^-1*(a^2+-1*b^2)^2*csc(c+d*x)+1//3*a^-3*d^-1*csc(c+d*x)^3*(-1*b^2+2*a^2)+1//4*b*a^-2*d^-1*csc(c+d*x)^4+b*a^-6*d^-1*(a^2+-1*b^2)^2*log(a+b*sin(c+d*x))+-1*b*a^-6*d^-1*(a^2+-1*b^2)^2*log(sin(c+d*x))+-1//2*b*a^-4*d^-1*csc(c+d*x)^2*(-1*b^2+2*a^2))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^5*csc(c+d*x)^7, x) == :(-1//6*a^-1*d^-1*csc(c+d*x)^6+-1//2*a^-5*d^-1*(a^2+-1*b^2)^2*csc(c+d*x)^2+1//4*a^-3*d^-1*csc(c+d*x)^4*(-1*b^2+2*a^2)+1//5*b*a^-2*d^-1*csc(c+d*x)^5+b*a^-6*d^-1*(a^2+-1*b^2)^2*csc(c+d*x)+a^-7*b^2*d^-1*(a^2+-1*b^2)^2*log(sin(c+d*x))+-1*a^-7*b^2*d^-1*(a^2+-1*b^2)^2*log(a+b*sin(c+d*x))+-1//3*b*a^-4*d^-1*csc(c+d*x)^3*(-1*b^2+2*a^2))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^6*sin(c+d*x)^3, x) == :(-1//128*x*b^-9*(-5*b^8+128*a^8+-320*a^6*b^2+-40*a^2*b^6+240*a^4*b^4)+1//4*a^-1*d^-1*sin(c+d*x)^4*cos(c+d*x)+1//8*b^-1*d^-1*sin(c+d*x)^7*cos(c+d*x)+2*a^3*b^-9*d^-1*(a^2+-1*b^2)^5//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//5*b*a^-2*d^-1*sin(c+d*x)^5*cos(c+d*x)+-1//7*a*b^-2*d^-1*sin(c+d*x)^6*cos(c+d*x)+-1//105*a*b^-8*d^-1*(-15*b^6+105*a^6+-245*a^4*b^2+161*a^2*b^4)*cos(c+d*x)+1//128*b^-7*d^-1*(-5*b^6+64*a^6+-144*a^4*b^2+88*a^2*b^4)*cos(c+d*x)*sin(c+d*x)+1//192*b^-5*d^-1*sin(c+d*x)^3*(48*a^4+59*b^4+-104*a^2*b^2)*cos(c+d*x)+-1//105*a*b^-6*d^-1*sin(c+d*x)^2*(35*a^4+45*b^4+-77*a^2*b^2)*cos(c+d*x)+-1//140*a^-1*b^-4*d^-1*sin(c+d*x)^4*(28*a^4+35*b^4+-60*a^2*b^2)*cos(c+d*x)+1//240*a^-2*b^-3*d^-1*sin(c+d*x)^5*(40*a^4+48*b^4+-85*a^2*b^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^6*sin(c+d*x)^2, x) == :(1//3*a^-1*d^-1*sin(c+d*x)^3*cos(c+d*x)+1//7*b^-1*d^-1*sin(c+d*x)^6*cos(c+d*x)+1//16*a*x*b^-8*(-5*b^6+16*a^6+-40*a^4*b^2+30*a^2*b^4)+1//105*b^-7*d^-1*(-15*b^6+105*a^6+-245*a^4*b^2+161*a^2*b^4)*cos(c+d*x)+-2*a^2*b^-8*d^-1*(a^2+-1*b^2)^5//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//4*b*a^-2*d^-1*sin(c+d*x)^4*cos(c+d*x)+-1//6*a*b^-2*d^-1*sin(c+d*x)^5*cos(c+d*x)+1//105*b^-5*d^-1*sin(c+d*x)^2*(35*a^4+45*b^4+-77*a^2*b^2)*cos(c+d*x)+-1//16*a*b^-6*d^-1*(8*a^4+11*b^4+-18*a^2*b^2)*cos(c+d*x)*sin(c+d*x)+-1//24*a^-1*b^-4*d^-1*sin(c+d*x)^3*(6*a^4+8*b^4+-13*a^2*b^2)*cos(c+d*x)+1//140*a^-2*b^-3*d^-1*sin(c+d*x)^4*(28*a^4+35*b^4+-60*a^2*b^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^6*sin(c+d*x), x) == :(-1//16*x*b^-7*(-5*b^6+16*a^6+-40*a^4*b^2+30*a^2*b^4)+-1//16*b^-6*d^-1*(16*a*(a^2+-1*b^2)^2+-1*b*(5*b^4+8*a^4+-14*a^2*b^2)*sin(c+d*x))*cos(c+d*x)+-1//30*b^-2*d^-1*cos(c+d*x)^5*(6a+-5*b*sin(c+d*x))+1//24*b^-4*d^-1*cos(c+d*x)^3*(8*a*(a^2+-1*b^2)+-1*b*(-5*b^2+6*a^2)*sin(c+d*x))+2*a*b^-7*d^-1*(a^2+-1*b^2)^5//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^6*csc(c+d*x), x) == :(-3//8*x*b^-1+-1*x*b^-5*(a^4+3*b^4+-3*a^2*b^2)+-1*a^-1*d^-1*arctanh(cos(c+d*x))+-1//2*x*b^-3*(a^2+-3*b^2)+-1*a*b^-2*d^-1*cos(c+d*x)+1//3*a*b^-2*d^-1*cos(c+d*x)^3+1//4*b^-1*d^-1*sin(c+d*x)^3*cos(c+d*x)+3//8*b^-1*d^-1*cos(c+d*x)*sin(c+d*x)+(1/2)*b^-3*d^-1*(a^2+-3*b^2)*cos(c+d*x)*sin(c+d*x)+-1*a*b^-4*d^-1*(a^2+-3*b^2)*cos(c+d*x)+2*a^-1*b^-5*d^-1*(a^2+-1*b^2)^5//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^6*csc(c+d*x)^2, x) == :(b^-1*d^-1*cos(c+d*x)+(1/2)*a*x*b^-2+-1*a^-1*d^-1*cot(c+d*x)+-1//3*b^-1*d^-1*cos(c+d*x)^3+a*x*b^-4*(a^2+-3*b^2)+b*a^-2*d^-1*arctanh(cos(c+d*x))+b^-3*d^-1*(a^2+-3*b^2)*cos(c+d*x)+-2*a^-2*b^-4*d^-1*(a^2+-1*b^2)^5//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//2*a*b^-2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^6*csc(c+d*x)^3, x) == :(-1//2*x*b^-3*(-5*b^2+2*a^2)+b*a^-2*d^-1*cot(c+d*x)+(1/2)*a^-3*d^-1*(-2*b^2+5*a^2)*arctanh(cos(c+d*x))+(1/2)*b^-1*d^-1*cos(c+d*x)*sin(c+d*x)+-1*a*b^-2*d^-1*cos(c+d*x)+-1//2*a^-1*d^-1*cot(c+d*x)*csc(c+d*x)+2*a^-3*b^-3*d^-1*(a^2+-1*b^2)^5//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^6*csc(c+d*x)^4, x) == :(a*x*b^-2+b^-1*d^-1*cos(c+d*x)+-1*a^-1*d^-1*cot(c+d*x)+-1//3*a^-1*d^-1*cot(c+d*x)^3+a^-3*d^-1*(-1*b^2+3*a^2)*cot(c+d*x)+(1/2)*b*a^-2*d^-1*arctanh(cos(c+d*x))+(1/2)*b*a^-2*d^-1*cot(c+d*x)*csc(c+d*x)+-1*b*a^-4*d^-1*(-1*b^2+3*a^2)*arctanh(cos(c+d*x))+-2*a^-4*b^-2*d^-1*(a^2+-1*b^2)^5//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^6*csc(c+d*x)^7, x) == :(-1//2*b^-1*d^-1*csc(c+d*x)^2*cot(c+d*x)+-1//6*a^-1*d^-1*csc(c+d*x)^5*cot(c+d*x)+1//16*a^-7*d^-1*(-16*b^6+5*a^6+-30*a^4*b^2+40*a^2*b^4)*arctanh(cos(c+d*x))+2*b*a^-7*d^-1*(a^2+-1*b^2)^5//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//16*a^-5*d^-1*(8*b^4+11*a^4+-18*a^2*b^2)*cot(c+d*x)*csc(c+d*x)+1//3*a*b^-2*d^-1*csc(c+d*x)^3*cot(c+d*x)+1//5*b*a^-2*d^-1*csc(c+d*x)^4*cot(c+d*x)+1//15*b*a^-6*d^-1*(15*b^4+23*a^4+-35*a^2*b^2)*cot(c+d*x)+-1//24*a^-3*b^-2*d^-1*csc(c+d*x)^3*(6*b^4+8*a^4+-13*a^2*b^2)*cot(c+d*x)+1//30*a^-4*b^-1*d^-1*csc(c+d*x)^2*(10*b^4+15*a^4+-22*a^2*b^2)*cot(c+d*x))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^6*csc(c+d*x)^8, x) == :(-1//3*b^-1*d^-1*csc(c+d*x)^3*cot(c+d*x)+-1//7*a^-1*d^-1*csc(c+d*x)^6*cot(c+d*x)+1//105*a^-7*d^-1*(-105*b^6+15*a^6+-161*a^4*b^2+245*a^2*b^4)*cot(c+d*x)+-2*a^-8*b^2*d^-1*(a^2+-1*b^2)^5//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//16*b*a^-8*d^-1*(-16*b^6+5*a^6+-30*a^4*b^2+40*a^2*b^4)*arctanh(cos(c+d*x))+-1//105*a^-5*d^-1*csc(c+d*x)^2*(35*b^4+45*a^4+-77*a^2*b^2)*cot(c+d*x)+1//4*a*b^-2*d^-1*csc(c+d*x)^4*cot(c+d*x)+1//6*b*a^-2*d^-1*csc(c+d*x)^5*cot(c+d*x)+-1//140*a^-3*b^-2*d^-1*csc(c+d*x)^4*(28*b^4+35*a^4+-60*a^2*b^2)*cot(c+d*x)+1//16*b*a^-6*d^-1*(8*b^4+11*a^4+-18*a^2*b^2)*cot(c+d*x)*csc(c+d*x)+1//24*a^-4*b^-1*d^-1*csc(c+d*x)^3*(6*b^4+8*a^4+-13*a^2*b^2)*cot(c+d*x))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^6*csc(c+d*x)^9, x) == :(-1//4*b^-1*d^-1*csc(c+d*x)^4*cot(c+d*x)+-1//8*a^-1*d^-1*csc(c+d*x)^7*cot(c+d*x)+1//128*a^-9*d^-1*(-128*b^8+5*a^8+-240*a^4*b^4+40*a^6*b^2+320*a^2*b^6)*arctanh(cos(c+d*x))+2*a^-9*b^3*d^-1*(a^2+-1*b^2)^5//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//105*b*a^-8*d^-1*(-105*b^6+15*a^6+-161*a^4*b^2+245*a^2*b^4)*cot(c+d*x)+-1//192*a^-5*d^-1*csc(c+d*x)^3*(48*b^4+59*a^4+-104*a^2*b^2)*cot(c+d*x)+1//5*a*b^-2*d^-1*csc(c+d*x)^5*cot(c+d*x)+1//7*b*a^-2*d^-1*csc(c+d*x)^6*cot(c+d*x)+1//128*a^-7*d^-1*(-64*b^6+5*a^6+-88*a^4*b^2+144*a^2*b^4)*cot(c+d*x)*csc(c+d*x)+-1//240*a^-3*b^-2*d^-1*csc(c+d*x)^5*(40*b^4+48*a^4+-85*a^2*b^2)*cot(c+d*x)+1//105*b*a^-6*d^-1*csc(c+d*x)^2*(35*b^4+45*a^4+-77*a^2*b^2)*cot(c+d*x)+1//140*a^-4*b^-1*d^-1*csc(c+d*x)^4*(28*b^4+35*a^4+-60*a^2*b^2)*cot(c+d*x))
@test integrate((a+b*sin(c+d*x))^-1*sin(c+d*x)^3*sec(c+d*x), x) == :(-1*b^-1*d^-1*sin(c+d*x)+-1*d^-1*(-2b+2a)^-1*log(1+sin(c+d*x))+-1*d^-1*(2a+2b)^-1*log(1+-1*sin(c+d*x))+a^3*b^-2*d^-1*(a^2+-1*b^2)^-1*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*sin(c+d*x)^2*sec(c+d*x), x) == :(d^-1*(-2b+2a)^-1*log(1+sin(c+d*x))+-1*d^-1*(2a+2b)^-1*log(1+-1*sin(c+d*x))+-1*a^2*b^-1*d^-1*(a^2+-1*b^2)^-1*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)*sin(c+d*x), x) == :(-1*d^-1*(-2b+2a)^-1*log(1+sin(c+d*x))+-1*d^-1*(2a+2b)^-1*log(1+-1*sin(c+d*x))+a*d^-1*(a^2+-1*b^2)^-1*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*csc(c+d*x)*sec(c+d*x), x) == :(a^-1*d^-1*log(sin(c+d*x))+-1*d^-1*(-2b+2a)^-1*log(1+sin(c+d*x))+-1*d^-1*(2a+2b)^-1*log(1+-1*sin(c+d*x))+a^-1*b^2*d^-1*(a^2+-1*b^2)^-1*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*csc(c+d*x)^2*sec(c+d*x), x) == :(d^-1*(-2b+2a)^-1*log(1+sin(c+d*x))+-1*a^-1*d^-1*csc(c+d*x)+-1*d^-1*(2a+2b)^-1*log(1+-1*sin(c+d*x))+-1*b*a^-2*d^-1*log(sin(c+d*x))+-1*a^-2*b^3*d^-1*(a^2+-1*b^2)^-1*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*csc(c+d*x)^3*sec(c+d*x), x) == :(-1*d^-1*(-2b+2a)^-1*log(1+sin(c+d*x))+-1*d^-1*(2a+2b)^-1*log(1+-1*sin(c+d*x))+-1//2*a^-1*d^-1*csc(c+d*x)^2+b*a^-2*d^-1*csc(c+d*x)+a^-3*d^-1*(a^2+b^2)*log(sin(c+d*x))+a^-3*b^4*d^-1*(a^2+-1*b^2)^-1*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^2*sin(c+d*x)^5, x) == :(3*b*x*(-2*b^2+2*a^2)^-1+a*d^-1*(a^2+-1*b^2)^-1*cos(c+d*x)+a*d^-1*(a^2+-1*b^2)^-1*sec(c+d*x)+-3*b*d^-1*(-2*b^2+2*a^2)^-1*tan(c+d*x)+b*d^-1*(-2*b^2+2*a^2)^-1*sin(c+d*x)^2*tan(c+d*x)+-1*a^3*b^-2*d^-1*(a^2+-1*b^2)^-1*cos(c+d*x)+2*a^5*b^-3*d^-1*(a^2+-1*b^2)^-3//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//2*x*a^2*b^-3*(a^2+-1*b^2)^-1*(b^2+2*a^2)+(1/2)*a^2*b^-1*d^-1*(a^2+-1*b^2)^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^2*sin(c+d*x)^4, x) == :(-1*a*x*(a^2+-1*b^2)^-1+a*d^-1*(a^2+-1*b^2)^-1*tan(c+d*x)+x*a^3*b^-2*(a^2+-1*b^2)^-1+-1*b*d^-1*(a^2+-1*b^2)^-1*cos(c+d*x)+-1*b*d^-1*(a^2+-1*b^2)^-1*sec(c+d*x)+a^2*b^-1*d^-1*(a^2+-1*b^2)^-1*cos(c+d*x)+-2*a^4*b^-2*d^-1*(a^2+-1*b^2)^-3//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^2*sin(c+d*x)^3, x) == :(b*x*(a^2+-1*b^2)^-1+a*d^-1*(a^2+-1*b^2)^-1*sec(c+d*x)+-1*b*d^-1*(a^2+-1*b^2)^-1*tan(c+d*x)+-1*x*a^2*b^-1*(a^2+-1*b^2)^-1+2*a^3*b^-1*d^-1*(a^2+-1*b^2)^-3//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^2*sin(c+d*x)^2, x) == :(a*d^-1*(a^2+-1*b^2)^-1*tan(c+d*x)+-1*b*d^-1*(a^2+-1*b^2)^-1*sec(c+d*x)+-2*a^2*d^-1*(a^2+-1*b^2)^-3//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^2*sin(c+d*x), x) == :(d^-1*(a^2+-1*b^2)^-1*(a+-1*b*sin(c+d*x))*sec(c+d*x)+2*a*b*d^-1*(a^2+-1*b^2)^-3//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^2*csc(c+d*x), x) == :(a^-1*d^-1*sec(c+d*x)+-1*a^-1*d^-1*arctanh(cos(c+d*x))+2*a^-1*b^3*d^-1*(a^2+-1*b^2)^-3//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+b*a^-1*d^-1*(a^2+-1*b^2)^-1*(b+-1*a*sin(c+d*x))*sec(c+d*x))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^3*sin(c+d*x)^3, x) == :(d^-1*(-2*b^2+2*a^2)^-1*sec(c+d*x)^2*(a+-1*b*sin(c+d*x))+-1*a^3*d^-1*(a^2+-1*b^2)^-2*log(a+b*sin(c+d*x))+1//4*d^-1*(a+b)^-2*(b+2a)*log(1+-1*sin(c+d*x))+1//4*d^-1*(a+-1b)^-2*(-1b+2a)*log(1+sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^3*sin(c+d*x)^2, x) == :(-1*d^-1*(-2*b^2+2*a^2)^-1*sec(c+d*x)^2*(b+-1*a*sin(c+d*x))+-1//4*a*d^-1*(a+-1b)^-2*log(1+sin(c+d*x))+1//4*a*d^-1*(a+b)^-2*log(1+-1*sin(c+d*x))+b*a^2*d^-1*(a^2+-1*b^2)^-2*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^3*sin(c+d*x), x) == :(d^-1*(-2*b^2+2*a^2)^-1*sec(c+d*x)^2*(a+-1*b*sin(c+d*x))+-1//4*b*d^-1*(a+b)^-2*log(1+-1*sin(c+d*x))+1//4*b*d^-1*(a+-1b)^-2*log(1+sin(c+d*x))+-1*a*b^2*d^-1*(a^2+-1*b^2)^-2*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^3*csc(c+d*x), x) == :(a^-1*d^-1*log(sin(c+d*x))+d^-1*(1+-1*sin(c+d*x))^-1*(4a+4b)^-1+d^-1*(1+sin(c+d*x))^-1*(-4b+4a)^-1+-1//4*d^-1*(a+b)^-2*(2a+3b)*log(1+-1*sin(c+d*x))+-1//4*d^-1*(a+-1b)^-2*(-3b+2a)*log(1+sin(c+d*x))+-1*a^-1*b^4*d^-1*(a^2+-1*b^2)^-2*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*csc(c+d*x)^2*sec(c+d*x)^3, x) == :(d^-1*(1+-1*sin(c+d*x))^-1*(4a+4b)^-1+-1*a^-1*d^-1*csc(c+d*x)+-1*d^-1*(1+sin(c+d*x))^-1*(-4b+4a)^-1+-1*b*a^-2*d^-1*log(sin(c+d*x))+-1//4*d^-1*(a+b)^-2*(3a+4b)*log(1+-1*sin(c+d*x))+1//4*d^-1*(a+-1b)^-2*(-4b+3a)*log(1+sin(c+d*x))+a^-2*b^5*d^-1*(a^2+-1*b^2)^-2*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*csc(c+d*x)^3*sec(c+d*x)^3, x) == :(d^-1*(1+-1*sin(c+d*x))^-1*(4a+4b)^-1+d^-1*(1+sin(c+d*x))^-1*(-4b+4a)^-1+-1//2*a^-1*d^-1*csc(c+d*x)^2+b*a^-2*d^-1*csc(c+d*x)+a^-3*d^-1*(b^2+2*a^2)*log(sin(c+d*x))+-1//4*d^-1*(a+b)^-2*(4a+5b)*log(1+-1*sin(c+d*x))+-1//4*d^-1*(a+-1b)^-2*(-5b+4a)*log(1+sin(c+d*x))+-1*a^-3*b^6*d^-1*(a^2+-1*b^2)^-2*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^4*sin(c+d*x)^4, x) == :(a*d^-1*(-3*b^2+3*a^2)^-1*tan(c+d*x)^3+b*d^-1*(a^2+-1*b^2)^-1*sec(c+d*x)+-1*b*d^-1*(-3*b^2+3*a^2)^-1*sec(c+d*x)^3+-1*a^3*d^-1*(a^2+-1*b^2)^-2*tan(c+d*x)+2*a^4*d^-1*(a^2+-1*b^2)^-5//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+b*a^2*d^-1*(a^2+-1*b^2)^-2*sec(c+d*x))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^4*sin(c+d*x)^3, x) == :(a*d^-1*(-3*b^2+3*a^2)^-1*sec(c+d*x)^3+-1*b*d^-1*(-3*b^2+3*a^2)^-1*tan(c+d*x)^3+-1*a^2*d^-1*(a^2+-1*b^2)^-2*(a+-1*b*sin(c+d*x))*sec(c+d*x)+-2*b*a^3*d^-1*(a^2+-1*b^2)^-5//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^4*sin(c+d*x)^2, x) == :(a*d^-1*(a^2+-1*b^2)^-1*tan(c+d*x)+a*d^-1*(-3*b^2+3*a^2)^-1*tan(c+d*x)^3+-1*b*d^-1*(-3*b^2+3*a^2)^-1*sec(c+d*x)^3+a^2*d^-1*(a^2+-1*b^2)^-2*(b+-1*a*sin(c+d*x))*sec(c+d*x)+2*a^2*b^2*d^-1*(a^2+-1*b^2)^-5//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^4*sin(c+d*x), x) == :(d^-1*(-3*b^2+3*a^2)^-1*sec(c+d*x)^3*(a+-1*b*sin(c+d*x))+-1//3*d^-1*(a^2+-1*b^2)^-2*(3*a*b^2+-1*b*(a^2+2*b^2)*sin(c+d*x))*sec(c+d*x)+-2*a*b^3*d^-1*(a^2+-1*b^2)^-5//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^4*csc(c+d*x), x) == :(a^-1*d^-1*sec(c+d*x)+-1*a^-1*d^-1*arctanh(cos(c+d*x))+1//3*a^-1*d^-1*sec(c+d*x)^3+-2*a^-1*b^5*d^-1*(a^2+-1*b^2)^-5//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//3*b*a^-1*d^-1*(a^2+-1*b^2)^-2*(3*b^3+a*(-5*b^2+2*a^2)*sin(c+d*x))*sec(c+d*x)+1//3*b*a^-1*d^-1*(a^2+-1*b^2)^-1*sec(c+d*x)^3*(b+-1*a*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*csc(c+d*x)^3*sec(c+d*x)^4, x) == :(-5//2*a^-1*d^-1*arctanh(cos(c+d*x))+5//2*a^-1*d^-1*sec(c+d*x)+5//6*a^-1*d^-1*sec(c+d*x)^3+b*a^-2*d^-1*cot(c+d*x)+a^-3*b^2*d^-1*sec(c+d*x)+-1*a^-3*b^2*d^-1*arctanh(cos(c+d*x))+-2*b*a^-2*d^-1*tan(c+d*x)+-1//2*a^-1*d^-1*csc(c+d*x)^2*sec(c+d*x)^3+-1//3*b*a^-2*d^-1*tan(c+d*x)^3+1//3*a^-3*b^2*d^-1*sec(c+d*x)^3+-2*a^-3*b^7*d^-1*(a^2+-1*b^2)^-5//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//3*a^-3*b^3*d^-1*(a^2+-1*b^2)^-2*(3*b^3+a*(-5*b^2+2*a^2)*sin(c+d*x))*sec(c+d*x)+1//3*a^-3*b^3*d^-1*(a^2+-1*b^2)^-1*sec(c+d*x)^3*(b+-1*a*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^5*sin(c+d*x)^8, x) == :(-1//2*b^-1*d^-1*sin(c+d*x)^2+a*b^-2*d^-1*sin(c+d*x)+-1*d^-1*(-4*b^2+4*a^2)^-1*sec(c+d*x)^4*(b+-1*a*sin(c+d*x))+-1//16*d^-1*(a+b)^-3*(24*b^2+35*a^2+57*a*b)*log(1+-1*sin(c+d*x))+1//8*d^-1*(a^2+-1*b^2)^-2*sec(c+d*x)^2*(4*b*(-3*b^2+4*a^2)+-1*a*(-9*b^2+13*a^2)*sin(c+d*x))+1//16*d^-1*(a+-1b)^-3*(24*b^2+35*a^2+-57*a*b)*log(1+sin(c+d*x))+-1*a^8*b^-3*d^-1*(a^2+-1*b^2)^-3*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^5*sin(c+d*x)^7, x) == :(-1*b^-1*d^-1*sin(c+d*x)+d^-1*(-4*b^2+4*a^2)^-1*sec(c+d*x)^4*(a+-1*b*sin(c+d*x))+-1//8*d^-1*(a^2+-1*b^2)^-2*sec(c+d*x)^2*(4*a*(-2*b^2+3*a^2)+-1*b*(-9*b^2+13*a^2)*sin(c+d*x))+-1//16*d^-1*(a+b)^-3*(15*b^2+24*a^2+37*a*b)*log(1+-1*sin(c+d*x))+-1//16*d^-1*(a+-1b)^-3*(15*b^2+24*a^2+-37*a*b)*log(1+sin(c+d*x))+a^7*b^-2*d^-1*(a^2+-1*b^2)^-3*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^5*sin(c+d*x)^6, x) == :(-1*d^-1*(-4*b^2+4*a^2)^-1*sec(c+d*x)^4*(b+-1*a*sin(c+d*x))+-1//16*d^-1*(a+b)^-3*(8*b^2+15*a^2+21*a*b)*log(1+-1*sin(c+d*x))+1//8*d^-1*(a^2+-1*b^2)^-2*sec(c+d*x)^2*(4*b*(-2*b^2+3*a^2)+-1*a*(-5*b^2+9*a^2)*sin(c+d*x))+1//16*d^-1*(a+-1b)^-3*(8*b^2+15*a^2+-21*a*b)*log(1+sin(c+d*x))+-1*a^6*b^-1*d^-1*(a^2+-1*b^2)^-3*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^5*sin(c+d*x)^5, x) == :(a^5*d^-1*(a^2+-1*b^2)^-3*log(a+b*sin(c+d*x))+d^-1*(-4*b^2+4*a^2)^-1*sec(c+d*x)^4*(a+-1*b*sin(c+d*x))+-1//8*d^-1*(a^2+-1*b^2)^-2*sec(c+d*x)^2*(4*a*(-1*b^2+2*a^2)+-1*b*(-5*b^2+9*a^2)*sin(c+d*x))+-1//16*d^-1*(a+b)^-3*(3*b^2+8*a^2+9*a*b)*log(1+-1*sin(c+d*x))+-1//16*d^-1*(a+-1b)^-3*(3*b^2+8*a^2+-9*a*b)*log(1+sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^5*sin(c+d*x)^4, x) == :(-1*d^-1*(-4*b^2+4*a^2)^-1*sec(c+d*x)^4*(b+-1*a*sin(c+d*x))+1//8*d^-1*(a^2+-1*b^2)^-2*sec(c+d*x)^2*(4*b*(-1*b^2+2*a^2)+-1*a*(-1*b^2+5*a^2)*sin(c+d*x))+-1*b*a^4*d^-1*(a^2+-1*b^2)^-3*log(a+b*sin(c+d*x))+-1//16*a*d^-1*(a+b)^-3*(b+3a)*log(1+-1*sin(c+d*x))+1//16*a*d^-1*(a+-1b)^-3*(-1b+3a)*log(1+sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^5*sin(c+d*x)^3, x) == :(d^-1*(-4*b^2+4*a^2)^-1*sec(c+d*x)^4*(a+-1*b*sin(c+d*x))+-1//8*d^-1*(a^2+-1*b^2)^-2*sec(c+d*x)^2*(4*a^3+-1*b*(-1*b^2+5*a^2)*sin(c+d*x))+a^3*b^2*d^-1*(a^2+-1*b^2)^-3*log(a+b*sin(c+d*x))+-1//16*b*d^-1*(a+-1b)^-3*(-1b+3a)*log(1+sin(c+d*x))+1//16*b*d^-1*(a+b)^-3*(b+3a)*log(1+-1*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^5*sin(c+d*x)^2, x) == :(-1*d^-1*(-4*b^2+4*a^2)^-1*sec(c+d*x)^4*(b+-1*a*sin(c+d*x))+-1*a^2*b^3*d^-1*(a^2+-1*b^2)^-3*log(a+b*sin(c+d*x))+-1//16*a*d^-1*(a+-1b)^-3*(a+-3b)*log(1+sin(c+d*x))+1//8*a*d^-1*(a^2+-1*b^2)^-2*sec(c+d*x)^2*(-1*(a^2+3*b^2)*sin(c+d*x)+4*a*b)+1//16*a*d^-1*(a+b)^-3*(a+3b)*log(1+-1*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^5*sin(c+d*x), x) == :(d^-1*(-4*b^2+4*a^2)^-1*sec(c+d*x)^4*(a+-1*b*sin(c+d*x))+-1//8*d^-1*(a^2+-1*b^2)^-2*sec(c+d*x)^2*(4*a*b^2+-1*b*(a^2+3*b^2)*sin(c+d*x))+a*b^4*d^-1*(a^2+-1*b^2)^-3*log(a+b*sin(c+d*x))+-1//16*b*d^-1*(a+b)^-3*(a+3b)*log(1+-1*sin(c+d*x))+1//16*b*d^-1*(a+-1b)^-3*(a+-3b)*log(1+sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^5*csc(c+d*x), x) == :(a^-1*d^-1*log(sin(c+d*x))+d^-1*(1+-1*sin(c+d*x))^-2*(16a+16b)^-1+d^-1*(1+sin(c+d*x))^-2*(-16b+16a)^-1+-1//16*d^-1*(a+b)^-3*(8*a^2+15*b^2+21*a*b)*log(1+-1*sin(c+d*x))+-1//16*d^-1*(a+-1b)^-3*(8*a^2+15*b^2+-21*a*b)*log(1+sin(c+d*x))+1//16*d^-1*(1+-1*sin(c+d*x))^-1*(a+b)^-2*(5a+7b)+1//16*d^-1*(1+sin(c+d*x))^-1*(a+-1b)^-2*(-7b+5a)+a^-1*b^6*d^-1*(a^2+-1*b^2)^-3*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*csc(c+d*x)^2*sec(c+d*x)^5, x) == :(d^-1*(1+-1*sin(c+d*x))^-2*(16a+16b)^-1+-1*a^-1*d^-1*csc(c+d*x)+-1*d^-1*(1+sin(c+d*x))^-2*(-16b+16a)^-1+-1*b*a^-2*d^-1*log(sin(c+d*x))+-1//16*d^-1*(1+sin(c+d*x))^-1*(a+-1b)^-2*(-9b+7a)+-1//16*d^-1*(a+b)^-3*(15*a^2+24*b^2+37*a*b)*log(1+-1*sin(c+d*x))+1//16*d^-1*(1+-1*sin(c+d*x))^-1*(a+b)^-2*(7a+9b)+1//16*d^-1*(a+-1b)^-3*(15*a^2+24*b^2+-37*a*b)*log(1+sin(c+d*x))+-1*a^-2*b^7*d^-1*(a^2+-1*b^2)^-3*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*csc(c+d*x)^3*sec(c+d*x)^5, x) == :(d^-1*(1+-1*sin(c+d*x))^-2*(16a+16b)^-1+d^-1*(1+sin(c+d*x))^-2*(-16b+16a)^-1+-1//2*a^-1*d^-1*csc(c+d*x)^2+b*a^-2*d^-1*csc(c+d*x)+a^-3*d^-1*(b^2+3*a^2)*log(sin(c+d*x))+-1//16*d^-1*(a+b)^-3*(24*a^2+35*b^2+57*a*b)*log(1+-1*sin(c+d*x))+-1//16*d^-1*(a+-1b)^-3*(24*a^2+35*b^2+-57*a*b)*log(1+sin(c+d*x))+1//16*d^-1*(1+-1*sin(c+d*x))^-1*(a+b)^-2*(9a+11b)+1//16*d^-1*(1+sin(c+d*x))^-1*(a+-1b)^-2*(-11b+9a)+a^-3*b^8*d^-1*(a^2+-1*b^2)^-3*log(a+b*sin(c+d*x)))
@test integrate(sec(c+d*x)^2*sin(c+d*x)^4*(a+b*sin(c+d*x)), x) == :(-3//2*a*x+b*d^-1*sec(c+d*x)+2*b*d^-1*cos(c+d*x)+-1//3*b*d^-1*cos(c+d*x)^3+3//2*a*d^-1*tan(c+d*x)+-1//2*a*d^-1*sin(c+d*x)^2*tan(c+d*x))
@test integrate(sec(c+d*x)^2*sin(c+d*x)^3*(a+b*sin(c+d*x)), x) == :(-3//2*b*x+a*d^-1*cos(c+d*x)+a*d^-1*sec(c+d*x)+3//2*b*d^-1*tan(c+d*x)+-1//2*b*d^-1*sin(c+d*x)^2*tan(c+d*x))
@test integrate(sec(c+d*x)^2*sin(c+d*x)^2*(a+b*sin(c+d*x)), x) == :(-1*a*x+a*d^-1*tan(c+d*x)+b*d^-1*cos(c+d*x)+b*d^-1*sec(c+d*x))
@test integrate(sec(c+d*x)^2*(a+b*sin(c+d*x))*sin(c+d*x), x) == :(-1*b*x+a*d^-1*sec(c+d*x)+b*d^-1*tan(c+d*x))
@test integrate(sec(c+d*x)^2*(a+b*sin(c+d*x))*csc(c+d*x), x) == :(a*d^-1*sec(c+d*x)+b*d^-1*tan(c+d*x)+-1*a*d^-1*arctanh(cos(c+d*x)))
@test integrate(csc(c+d*x)^2*sec(c+d*x)^2*(a+b*sin(c+d*x)), x) == :(a*d^-1*tan(c+d*x)+b*d^-1*sec(c+d*x)+-1*a*d^-1*cot(c+d*x)+-1*b*d^-1*arctanh(cos(c+d*x)))
@test integrate(csc(c+d*x)^3*sec(c+d*x)^2*(a+b*sin(c+d*x)), x) == :(b*d^-1*tan(c+d*x)+-1*b*d^-1*cot(c+d*x)+-3//2*a*d^-1*arctanh(cos(c+d*x))+3//2*a*d^-1*sec(c+d*x)+-1//2*a*d^-1*csc(c+d*x)^2*sec(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*sec(c+d*x)^2*sin(c+d*x)^3, x) == :(d^-1*(a^2+b^2)*sec(c+d*x)+d^-1*(a^2+2*b^2)*cos(c+d*x)+-3*a*b*x+-1//3*b^2*d^-1*cos(c+d*x)^3+3*a*b*d^-1*tan(c+d*x)+-1*a*b*d^-1*sin(c+d*x)^2*tan(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*sec(c+d*x)^2*sin(c+d*x)^2, x) == :(-1*x*a^2+-3//2*x*b^2+a^2*d^-1*tan(c+d*x)+3//2*b^2*d^-1*tan(c+d*x)+2*a*b*d^-1*cos(c+d*x)+2*a*b*d^-1*sec(c+d*x)+-1//2*b^2*d^-1*sin(c+d*x)^2*tan(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*sec(c+d*x)^2*sin(c+d*x), x) == :(d^-1*(a+b*sin(c+d*x))^2*sec(c+d*x)+-2*a*b*x+2*b^2*d^-1*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*csc(c+d*x)^2*sec(c+d*x)^2, x) == :(d^-1*(a^2+b^2)*tan(c+d*x)+-1*a^2*d^-1*cot(c+d*x)+-2*a*b*d^-1*arctanh(cos(c+d*x))+2*a*b*d^-1*sec(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*csc(c+d*x)^4*sec(c+d*x)^2, x) == :(d^-1*(a^2+b^2)*tan(c+d*x)+-1*d^-1*(b^2+2*a^2)*cot(c+d*x)+-1//3*a^2*d^-1*cot(c+d*x)^3+-3*a*b*d^-1*arctanh(cos(c+d*x))+3*a*b*d^-1*sec(c+d*x)+-1*a*b*d^-1*csc(c+d*x)^2*sec(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*sec(c+d*x)^2*sin(c+d*x)^3, x) == :(-15//8*x*b^3+a^3*d^-1*cos(c+d*x)+a^3*d^-1*sec(c+d*x)+-9//2*b*x*a^2+15//8*b^3*d^-1*tan(c+d*x)+-1*a*b^2*d^-1*cos(c+d*x)^3+3*a*b^2*d^-1*sec(c+d*x)+6*a*b^2*d^-1*cos(c+d*x)+-5//8*b^3*d^-1*sin(c+d*x)^2*tan(c+d*x)+-1//4*b^3*d^-1*sin(c+d*x)^4*tan(c+d*x)+9//2*b*a^2*d^-1*tan(c+d*x)+-3//2*b*a^2*d^-1*sin(c+d*x)^2*tan(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*sec(c+d*x)^2*sin(c+d*x)^2, x) == :(-1*x*a^3+a^3*d^-1*tan(c+d*x)+b^3*d^-1*sec(c+d*x)+2*b^3*d^-1*cos(c+d*x)+-9//2*a*x*b^2+-1//3*b^3*d^-1*cos(c+d*x)^3+3*b*a^2*d^-1*cos(c+d*x)+3*b*a^2*d^-1*sec(c+d*x)+9//2*a*b^2*d^-1*tan(c+d*x)+-3//2*a*b^2*d^-1*sin(c+d*x)^2*tan(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*sec(c+d*x)^2*sin(c+d*x), x) == :(d^-1*(a+b*sin(c+d*x))^3*sec(c+d*x)+-3//2*b*x*(b^2+2*a^2)+6*a*b^2*d^-1*cos(c+d*x)+3//2*b^3*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*sec(c+d*x)^2*csc(c+d*x), x) == :(-1*x*b^3+a^3*d^-1*sec(c+d*x)+b^3*d^-1*tan(c+d*x)+-1*a^3*d^-1*arctanh(cos(c+d*x))+3*a*b^2*d^-1*sec(c+d*x)+3*b*a^2*d^-1*tan(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*csc(c+d*x)^2*sec(c+d*x)^2, x) == :(a^3*d^-1*tan(c+d*x)+b^3*d^-1*sec(c+d*x)+-1*a^3*d^-1*cot(c+d*x)+-3*b*a^2*d^-1*arctanh(cos(c+d*x))+3*a*b^2*d^-1*tan(c+d*x)+3*b*a^2*d^-1*sec(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*csc(c+d*x)^3*sec(c+d*x)^2, x) == :(b^3*d^-1*tan(c+d*x)+-3//2*a^3*d^-1*arctanh(cos(c+d*x))+3//2*a^3*d^-1*sec(c+d*x)+-3*a*b^2*d^-1*arctanh(cos(c+d*x))+-3*b*a^2*d^-1*cot(c+d*x)+3*a*b^2*d^-1*sec(c+d*x)+3*b*a^2*d^-1*tan(c+d*x)+-1//2*a^3*d^-1*csc(c+d*x)^2*sec(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*csc(c+d*x)^4*sec(c+d*x)^2, x) == :(a^3*d^-1*tan(c+d*x)+b^3*d^-1*sec(c+d*x)+-1*b^3*d^-1*arctanh(cos(c+d*x))+-2*a^3*d^-1*cot(c+d*x)+-1//3*a^3*d^-1*cot(c+d*x)^3+-3*a*b^2*d^-1*cot(c+d*x)+3*a*b^2*d^-1*tan(c+d*x)+-9//2*b*a^2*d^-1*arctanh(cos(c+d*x))+9//2*b*a^2*d^-1*sec(c+d*x)+-3//2*b*a^2*d^-1*csc(c+d*x)^2*sec(c+d*x))
@test integrate((a+b*sin(c+d*x))^-2*sec(c+d*x)^2*sin(c+d*x)^4, x) == :(-1*x*b^-2+(1/2)*d^-1*(1+-1*sin(c+d*x))^-1*(a+b)^-2*cos(c+d*x)+-1//2*d^-1*(1+sin(c+d*x))^-1*(a+-1b)^-2*cos(c+d*x)+-2*a^5*b^-2*d^-1*(a^2+-1*b^2)^-5//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1*a^4*b^-1*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-2*cos(c+d*x)+4*a^3*b^-2*d^-1*(a^2+-1*b^2)^-5//2*(a^2+-2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-2*sec(c+d*x)^2*sin(c+d*x)^3, x) == :((1/2)*d^-1*(1+-1*sin(c+d*x))^-1*(a+b)^-2*cos(c+d*x)+(1/2)*d^-1*(1+sin(c+d*x))^-1*(a+-1b)^-2*cos(c+d*x)+a^3*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-2*cos(c+d*x)+2*a^4*b^-1*d^-1*(a^2+-1*b^2)^-5//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-2*a^2*b^-1*d^-1*(a^2+-1*b^2)^-5//2*(a^2+-3*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-2*sec(c+d*x)^2*sin(c+d*x)^2, x) == :((1/2)*d^-1*(1+-1*sin(c+d*x))^-1*(a+b)^-2*cos(c+d*x)+-2*a^3*d^-1*(a^2+-1*b^2)^-5//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1//2*d^-1*(1+sin(c+d*x))^-1*(a+-1b)^-2*cos(c+d*x)+-4*a*b^2*d^-1*(a^2+-1*b^2)^-5//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1*b*a^2*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-2*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-2*sec(c+d*x)^2*sin(c+d*x), x) == :(d^-1*(a^2+-1*b^2)^-2*(b^2+2*a^2+-3*a*b*sin(c+d*x))*sec(c+d*x)+-1*a*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-1*sec(c+d*x)+2*b*d^-1*(a^2+-1*b^2)^-5//2*(b^2+2*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-2*sec(c+d*x)^2*csc(c+d*x), x) == :(-1*a^-2*d^-1*arctanh(cos(c+d*x))+(1/2)*d^-1*(1+-1*sin(c+d*x))^-1*(a+b)^-2*cos(c+d*x)+(1/2)*d^-1*(1+sin(c+d*x))^-1*(a+-1b)^-2*cos(c+d*x)+2*b^3*d^-1*(a^2+-1*b^2)^-5//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+a^-1*b^4*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-2*cos(c+d*x)+2*a^-2*b^3*d^-1*(a^2+-1*b^2)^-5//2*(-1*b^2+3*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-2*csc(c+d*x)^2*sec(c+d*x)^2, x) == :(-1*a^-2*d^-1*cot(c+d*x)+(1/2)*d^-1*(1+-1*sin(c+d*x))^-1*(a+b)^-2*cos(c+d*x)+2*b*a^-3*d^-1*arctanh(cos(c+d*x))+-1//2*d^-1*(1+sin(c+d*x))^-1*(a+-1b)^-2*cos(c+d*x)+-2*a^-1*b^4*d^-1*(a^2+-1*b^2)^-5//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1*a^-2*b^5*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-2*cos(c+d*x)+-4*a^-3*b^4*d^-1*(a^2+-1*b^2)^-5//2*(-1*b^2+2*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-2*csc(c+d*x)^3*sec(c+d*x)^2, x) == :(-1//2*a^-2*d^-1*arctanh(cos(c+d*x))+(1/2)*d^-1*(1+-1*sin(c+d*x))^-1*(a+b)^-2*cos(c+d*x)+(1/2)*d^-1*(1+sin(c+d*x))^-1*(a+-1b)^-2*cos(c+d*x)+-1*a^-4*d^-1*(a^2+3*b^2)*arctanh(cos(c+d*x))+2*b*a^-3*d^-1*cot(c+d*x)+-1//2*a^-2*d^-1*cot(c+d*x)*csc(c+d*x)+2*a^-2*b^5*d^-1*(a^2+-1*b^2)^-5//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+a^-3*b^6*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-2*cos(c+d*x)+2*a^-4*b^5*d^-1*(a^2+-1*b^2)^-5//2*(-3*b^2+5*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-3*sec(c+d*x)^2*sin(c+d*x)^4, x) == :((1/2)*d^-1*(1+-1*sin(c+d*x))^-1*(a+b)^-3*cos(c+d*x)+-1//2*d^-1*(1+sin(c+d*x))^-1*(a+-1b)^-3*cos(c+d*x)+-1*a^4*b^-2*d^-1*(a^2+-1*b^2)^-7//2*(b^2+2*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-2*a^2*b^-2*d^-1*(a^2+-1*b^2)^-7//2*(a^4+6*b^4+-3*a^2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+4*a^4*b^-2*d^-1*(a^2+-1*b^2)^-7//2*(a^2+-2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-3//2*a^5*b^-1*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-3*cos(c+d*x)+-1//2*a^4*b^-1*d^-1*(a+b*sin(c+d*x))^-2*(a^2+-1*b^2)^-2*cos(c+d*x)+2*a^3*b^-1*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-3*(a^2+-2*b^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-3*sec(c+d*x)^2*sin(c+d*x)^3, x) == :((1/2)*d^-1*(1+-1*sin(c+d*x))^-1*(a+b)^-3*cos(c+d*x)+(1/2)*d^-1*(1+sin(c+d*x))^-1*(a+-1b)^-3*cos(c+d*x)+(1/2)*a^3*d^-1*(a+b*sin(c+d*x))^-2*(a^2+-1*b^2)^-2*cos(c+d*x)+3//2*a^4*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-3*cos(c+d*x)+a^3*b^-1*d^-1*(a^2+-1*b^2)^-7//2*(b^2+2*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-1*a^2*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-3*(a^2+-3*b^2)*cos(c+d*x)+-2*a^3*b^-1*d^-1*(a^2+-1*b^2)^-7//2*(a^2+-3*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+2*a*b*d^-1*(a^2+-1*b^2)^-7//2*(a^2+3*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-3*sec(c+d*x)^2*sin(c+d*x)^2, x) == :((1/2)*d^-1*(1+-1*sin(c+d*x))^-1*(a+b)^-3*cos(c+d*x)+-1//2*d^-1*(1+sin(c+d*x))^-1*(a+-1b)^-3*cos(c+d*x)+-1*a^2*d^-1*(a^2+-1*b^2)^-7//2*(b^2+2*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-4*a^2*b^2*d^-1*(a^2+-1*b^2)^-7//2*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-2*b^2*d^-1*(a^2+-1*b^2)^-7//2*(b^2+3*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-2*a*b^3*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-3*cos(c+d*x)+-3//2*b*a^3*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-3*cos(c+d*x)+-1//2*b*a^2*d^-1*(a+b*sin(c+d*x))^-2*(a^2+-1*b^2)^-2*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-3*sec(c+d*x)^2*sin(c+d*x), x) == :((1/2)*d^-1*(a^2+-1*b^2)^-3*(3*a*(2*a^2+3*b^2)+-1*b*(4*b^2+11*a^2)*sin(c+d*x))*sec(c+d*x)+-1*a*d^-1*(a+b*sin(c+d*x))^-2*(-2*b^2+2*a^2)^-1*sec(c+d*x)+-1//2*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-2*(2*b^2+3*a^2)*sec(c+d*x)+3*a*b*d^-1*(a^2+-1*b^2)^-7//2*(2*a^2+3*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x))))
@test integrate((a+b*sin(c+d*x))^-3*sec(c+d*x)^2*csc(c+d*x), x) == :(-1*a^-3*d^-1*arctanh(cos(c+d*x))+(1/2)*d^-1*(1+-1*sin(c+d*x))^-1*(a+b)^-3*cos(c+d*x)+(1/2)*d^-1*(1+sin(c+d*x))^-1*(a+-1b)^-3*cos(c+d*x)+3//2*b^4*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-3*cos(c+d*x)+a^-1*b^3*d^-1*(a^2+-1*b^2)^-7//2*(b^2+2*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+(1/2)*a^-1*b^4*d^-1*(a+b*sin(c+d*x))^-2*(a^2+-1*b^2)^-2*cos(c+d*x)+2*a^-1*b^3*d^-1*(a^2+-1*b^2)^-7//2*(-1*b^2+3*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+2*a^-3*b^3*d^-1*(a^2+-1*b^2)^-7//2*(b^4+6*a^4+-3*a^2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+a^-2*b^4*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-3*(-1*b^2+3*a^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-3*csc(c+d*x)^2*sec(c+d*x)^2, x) == :(-1*a^-3*d^-1*cot(c+d*x)+(1/2)*d^-1*(1+-1*sin(c+d*x))^-1*(a+b)^-3*cos(c+d*x)+3*b*a^-4*d^-1*arctanh(cos(c+d*x))+-1//2*d^-1*(1+sin(c+d*x))^-1*(a+-1b)^-3*cos(c+d*x)+-1*a^-2*b^4*d^-1*(a^2+-1*b^2)^-7//2*(b^2+2*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-4*a^-2*b^4*d^-1*(a^2+-1*b^2)^-7//2*(-1*b^2+2*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-2*a^-4*b^4*d^-1*(a^2+-1*b^2)^-7//2*(3*b^4+10*a^4+-9*a^2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+-3//2*a^-1*b^5*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-3*cos(c+d*x)+-1//2*a^-2*b^5*d^-1*(a+b*sin(c+d*x))^-2*(a^2+-1*b^2)^-2*cos(c+d*x)+-2*a^-3*b^5*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-3*(-1*b^2+2*a^2)*cos(c+d*x))
@test integrate((a+b*sin(c+d*x))^-3*csc(c+d*x)^3*sec(c+d*x)^2, x) == :(-1//2*a^-3*d^-1*arctanh(cos(c+d*x))+(1/2)*d^-1*(1+-1*sin(c+d*x))^-1*(a+b)^-3*cos(c+d*x)+(1/2)*d^-1*(1+sin(c+d*x))^-1*(a+-1b)^-3*cos(c+d*x)+-1*a^-5*d^-1*(a^2+6*b^2)*arctanh(cos(c+d*x))+3*b*a^-4*d^-1*cot(c+d*x)+-1//2*a^-3*d^-1*cot(c+d*x)*csc(c+d*x)+a^-3*b^5*d^-1*(a^2+-1*b^2)^-7//2*(b^2+2*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+(1/2)*a^-3*b^6*d^-1*(a+b*sin(c+d*x))^-2*(a^2+-1*b^2)^-2*cos(c+d*x)+2*a^-5*b^5*d^-1*(a^2+-1*b^2)^-7//2*(6*b^4+15*a^4+-17*a^2*b^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+2*a^-3*b^5*d^-1*(a^2+-1*b^2)^-7//2*(-3*b^2+5*a^2)*arctan((a^2+-1*b^2)^-1//2*(b+a*tan((1/2)*c+(1/2)*d*x)))+3//2*a^-2*b^6*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-3*cos(c+d*x)+a^-4*b^6*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-3*(-3*b^2+5*a^2)*cos(c+d*x))
@test integrate((d*sin(e+f*x))^-1//2*(a+b*sin(e+f*x))^(1/2)*sec(e+f*x)^2, x) == :(d^-1*f^-1*(d*sin(e+f*x))^(1/2)*(a+b*sin(e+f*x))^(1/2)*sec(e+f*x)+-1*d^-1//2*f^-1*(a*(a+b)^-1*(1+-1*csc(e+f*x)))^(1/2)*(a*(a+-1b)^-1*(1+csc(e+f*x)))^(1/2)*(a+b)^(1/2)*Elliptic.F(arcsin(d^(1/2)*(d*sin(e+f*x))^-1//2*(a+b)^-1//2*(a+b*sin(e+f*x))^(1/2)),-1*(a+-1b)^-1*(a+b))*tan(e+f*x))
@test integrate((d*sin(e+f*x))^-1//2*(a+b*sin(e+f*x))^3//2*sec(e+f*x)^2, x) == :(f^-1*(d*sin(e+f*x))^-1//2*(a+b*sin(e+f*x))^(1/2)*(b+a*sin(e+f*x))*sec(e+f*x)+-1*d^-1//2*f^-1*(a*(a+-1b)^-1*(1+csc(e+f*x)))^(1/2)*(-1*a*(a+b)^-1*(-1+csc(e+f*x)))^(1/2)*(a+b)^3//2*Elliptic.F(arcsin(d^(1/2)*(d*sin(e+f*x))^-1//2*(a+b)^-1//2*(a+b*sin(e+f*x))^(1/2)),-1*(a+-1b)^-1*(a+b))*tan(e+f*x)+-1*b*f^-1*(d*sin(e+f*x))^-1//2*((b+-1a)^-1*(b+a*csc(e+f*x)))^(1/2)*(a*(a+-1b)^-1*(1+csc(e+f*x)))^-1//2*(-1*a*(a+b)^-1*(-1+csc(e+f*x)))^(1/2)*(a+b*sin(e+f*x))^-1//2*(1+sin(e+f*x))*(a+b)*Elliptic.E(arcsin((-1*(a+-1b)^-1*(b+a*csc(e+f*x)))^(1/2)),(a+b)^-1*(b+-1a))*tan(e+f*x))
@test integrate((d*sin(e+f*x))^-1//2*(a+b*sin(e+f*x))^5//2*sec(e+f*x)^4, x) == :(1//3*d^-1*f^-1*(d*sin(e+f*x))^(1/2)*(a+b*sin(e+f*x))^5//2*sec(e+f*x)^3+5//6*a*f^-1*(d*sin(e+f*x))^-1//2*(a+b*sin(e+f*x))^(1/2)*(b+a*sin(e+f*x))*sec(e+f*x)+-5//6*a*d^-1//2*f^-1*(a*(a+-1b)^-1*(1+csc(e+f*x)))^(1/2)*(-1*a*(a+b)^-1*(-1+csc(e+f*x)))^(1/2)*(a+b)^3//2*Elliptic.F(arcsin(d^(1/2)*(d*sin(e+f*x))^-1//2*(a+b)^-1//2*(a+b*sin(e+f*x))^(1/2)),-1*(a+-1b)^-1*(a+b))*tan(e+f*x)+-5//6*a*b*f^-1*(d*sin(e+f*x))^-1//2*((b+-1a)^-1*(b+a*csc(e+f*x)))^(1/2)*(a*(a+-1b)^-1*(1+csc(e+f*x)))^-1//2*(-1*a*(a+b)^-1*(-1+csc(e+f*x)))^(1/2)*(a+b*sin(e+f*x))^-1//2*(1+sin(e+f*x))*(a+b)*Elliptic.E(arcsin((-1*(a+-1b)^-1*(b+a*csc(e+f*x)))^(1/2)),(a+b)^-1*(b+-1a))*tan(e+f*x))
@test integrate(sec(c+d*x)^5*sin(c+d*x)^7*(a+b*sin(c+d*x)), x) == :((1/2)*a*d^-1*cos(c+d*x)^2+-3*a*d^-1*log(cos(c+d*x))+-35//8*b*d^-1*sin(c+d*x)+-35//24*b*d^-1*sin(c+d*x)^3+-3//2*a*d^-1*sec(c+d*x)^2+1//4*a*d^-1*sec(c+d*x)^4+35//8*b*d^-1*arctanh(sin(c+d*x))+-7//8*b*d^-1*sin(c+d*x)^3*tan(c+d*x)^2+1//4*b*d^-1*sin(c+d*x)^3*tan(c+d*x)^4)
@test integrate(sec(c+d*x)^5*sin(c+d*x)^6*(a+b*sin(c+d*x)), x) == :((1/2)*b*d^-1*cos(c+d*x)^2+-3*b*d^-1*log(cos(c+d*x))+-15//8*a*d^-1*sin(c+d*x)+-3//2*b*d^-1*sec(c+d*x)^2+1//4*b*d^-1*sec(c+d*x)^4+15//8*a*d^-1*arctanh(sin(c+d*x))+-5//8*a*d^-1*tan(c+d*x)^2*sin(c+d*x)+1//4*a*d^-1*tan(c+d*x)^4*sin(c+d*x))
@test integrate(sec(c+d*x)^5*sin(c+d*x)^5*(a+b*sin(c+d*x)), x) == :(-15//8*b*d^-1*sin(c+d*x)+-1//8*d^-1*tan(c+d*x)^2*(4a+5*b*sin(c+d*x))+-1//16*d^-1*(-15b+8a)*log(1+sin(c+d*x))+-1//16*d^-1*(8a+15b)*log(1+-1*sin(c+d*x))+1//4*d^-1*tan(c+d*x)^4*(a+b*sin(c+d*x)))
@test integrate(sec(c+d*x)^5*sin(c+d*x)^4*(a+b*sin(c+d*x)), x) == :(-1*b*d^-1*log(cos(c+d*x))+-1//2*b*d^-1*tan(c+d*x)^2+1//4*b*d^-1*tan(c+d*x)^4+3//8*a*d^-1*arctanh(sin(c+d*x))+-3//8*a*d^-1*sec(c+d*x)*tan(c+d*x)+1//4*a*d^-1*tan(c+d*x)^3*sec(c+d*x))
@test integrate(sec(c+d*x)^5*sin(c+d*x)^3*(a+b*sin(c+d*x)), x) == :(1//4*a*d^-1*tan(c+d*x)^4+3//8*b*d^-1*arctanh(sin(c+d*x))+-3//8*b*d^-1*sec(c+d*x)*tan(c+d*x)+1//4*b*d^-1*tan(c+d*x)^3*sec(c+d*x))
@test integrate(sec(c+d*x)^5*sin(c+d*x)^2*(a+b*sin(c+d*x)), x) == :(-1//8*a*d^-1*arctanh(sin(c+d*x))+1//4*b*d^-1*tan(c+d*x)^4+-1//8*a*d^-1*sec(c+d*x)*tan(c+d*x)+1//4*a*d^-1*sec(c+d*x)^3*tan(c+d*x))
@test integrate(sec(c+d*x)^5*(a+b*sin(c+d*x))*sin(c+d*x), x) == :(-1//8*b*d^-1*arctanh(sin(c+d*x))+1//4*a*d^-1*sec(c+d*x)^4+-1//8*b*d^-1*sec(c+d*x)*tan(c+d*x)+1//4*b*d^-1*sec(c+d*x)^3*tan(c+d*x))
@test integrate(sec(c+d*x)^5*(a+b*sin(c+d*x))*csc(c+d*x), x) == :(a*d^-1*tan(c+d*x)^2+a*d^-1*log(tan(c+d*x))+1//4*a*d^-1*tan(c+d*x)^4+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(csc(c+d*x)^2*sec(c+d*x)^5*(a+b*sin(c+d*x)), x) == :(b*d^-1*tan(c+d*x)^2+b*d^-1*log(tan(c+d*x))+-15//8*a*d^-1*csc(c+d*x)+1//4*b*d^-1*tan(c+d*x)^4+15//8*a*d^-1*arctanh(sin(c+d*x))+1//4*a*d^-1*sec(c+d*x)^4*csc(c+d*x)+5//8*a*d^-1*sec(c+d*x)^2*csc(c+d*x))
@test integrate(csc(c+d*x)^3*sec(c+d*x)^5*(a+b*sin(c+d*x)), x) == :(3*a*d^-1*log(tan(c+d*x))+-15//8*b*d^-1*csc(c+d*x)+-1//2*a*d^-1*cot(c+d*x)^2+1//4*a*d^-1*tan(c+d*x)^4+3//2*a*d^-1*tan(c+d*x)^2+15//8*b*d^-1*arctanh(sin(c+d*x))+1//4*b*d^-1*sec(c+d*x)^4*csc(c+d*x)+5//8*b*d^-1*sec(c+d*x)^2*csc(c+d*x))
@test integrate(csc(c+d*x)^4*sec(c+d*x)^5*(a+b*sin(c+d*x)), x) == :(3*b*d^-1*log(tan(c+d*x))+-35//8*a*d^-1*csc(c+d*x)+-35//24*a*d^-1*csc(c+d*x)^3+-1//2*b*d^-1*cot(c+d*x)^2+1//4*b*d^-1*tan(c+d*x)^4+3//2*b*d^-1*tan(c+d*x)^2+35//8*a*d^-1*arctanh(sin(c+d*x))+1//4*a*d^-1*csc(c+d*x)^3*sec(c+d*x)^4+7//8*a*d^-1*csc(c+d*x)^3*sec(c+d*x)^2)
@test integrate((a+b*sin(c+d*x))^2*sec(c+d*x)^5*sin(c+d*x)^6, x) == :(-1*d^-1*(a^2+3*b^2)*sin(c+d*x)+-1//3*b^2*d^-1*sin(c+d*x)^3+-1//16*d^-1*(15*a^2+35*b^2+48*a*b)*log(1+-1*sin(c+d*x))+1//16*d^-1*(15*a^2+35*b^2+-48*a*b)*log(1+sin(c+d*x))+-1*a*b*d^-1*sin(c+d*x)^2+-1//8*d^-1*sec(c+d*x)^2*(a+b*sin(c+d*x))*(11b+9*a*sin(c+d*x))+1//4*d^-1*(a+b*sin(c+d*x))^2*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*sec(c+d*x)^5*sin(c+d*x)^5, x) == :(-1//2*b^2*d^-1*sin(c+d*x)^2+-1//8*d^-1*(4*a^2+12*b^2+15*a*b)*log(1+-1*sin(c+d*x))+1//4*d^-1*(a+b*sin(c+d*x))^2*sec(c+d*x)^4+1//8*d^-1*(-12*b^2+-4*a^2+15*a*b)*log(1+sin(c+d*x))+-2*a*b*d^-1*sin(c+d*x)+-1//4*d^-1*sec(c+d*x)^2*(a+b*sin(c+d*x))*(4a+5*b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^2*sec(c+d*x)^5*sin(c+d*x)^4, x) == :(-1*b^2*d^-1*sin(c+d*x)+-1//16*d^-1*(3*a^2+15*b^2+16*a*b)*log(1+-1*sin(c+d*x))+1//16*d^-1*(3*a^2+15*b^2+-16*a*b)*log(1+sin(c+d*x))+-1//8*d^-1*sec(c+d*x)^2*(a+b*sin(c+d*x))*(7b+5*a*sin(c+d*x))+1//4*d^-1*(a+b*sin(c+d*x))^2*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*sec(c+d*x)^5*sin(c+d*x)^3, x) == :(1//4*d^-1*(a+b*sin(c+d*x))^2*sec(c+d*x)^4+-1//4*d^-1*sec(c+d*x)^2*(a+b*sin(c+d*x))*(2a+3*b*sin(c+d*x))+-1//8*b*d^-1*(3a+4b)*log(1+-1*sin(c+d*x))+1//8*b*d^-1*(-4b+3a)*log(1+sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^2*sec(c+d*x)^5*sin(c+d*x)^2, x) == :(-1//8*d^-1*sec(c+d*x)^2*((a^2+3*b^2)*sin(c+d*x)+4*a*b)+-1//8*d^-1*(a^2+-3*b^2)*arctanh(sin(c+d*x))+1//4*d^-1*(a+b*sin(c+d*x))^2*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*sec(c+d*x)^5*sin(c+d*x), x) == :(-1//4*d^-1*sec(c+d*x)^2*(b^2+a*b*sin(c+d*x))+1//4*d^-1*(a+b*sin(c+d*x))^2*sec(c+d*x)^4+-1//4*a*b*d^-1*arctanh(sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^2*sec(c+d*x)^5*csc(c+d*x), x) == :(a^2*d^-1*log(sin(c+d*x))+1//4*d^-1*sec(c+d*x)^4*(a^2+b^2+2*a*b*sin(c+d*x))+-1//8*a*d^-1*(-3b+4a)*log(1+sin(c+d*x))+-1//8*a*d^-1*(3b+4a)*log(1+-1*sin(c+d*x))+1//4*a*d^-1*sec(c+d*x)^2*(2a+3*b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^2*csc(c+d*x)^2*sec(c+d*x)^5, x) == :(-1*a^2*d^-1*csc(c+d*x)+-1//16*d^-1*(3*b^2+15*a^2+16*a*b)*log(1+-1*sin(c+d*x))+1//16*d^-1*(3*b^2+15*a^2+-16*a*b)*log(1+sin(c+d*x))+2*a*b*d^-1*log(sin(c+d*x))+1//4*b*d^-1*sec(c+d*x)^4*(2a+b^-1*(a^2+b^2)*sin(c+d*x))+1//8*b*d^-1*sec(c+d*x)^2*(8a+b*(3+7*a^2*b^-2)*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^2*csc(c+d*x)^3*sec(c+d*x)^5, x) == :(d^-1*(b^2+3*a^2)*log(sin(c+d*x))+-1//2*a^2*d^-1*csc(c+d*x)^2+-1//8*d^-1*(4*b^2+12*a^2+-15*a*b)*log(1+sin(c+d*x))+-1//8*d^-1*(4*b^2+12*a^2+15*a*b)*log(1+-1*sin(c+d*x))+1//4*d^-1*sec(c+d*x)^2*(2*b^2+4*a^2+7*a*b*sin(c+d*x))+1//4*d^-1*sec(c+d*x)^4*(a^2+b^2+2*a*b*sin(c+d*x))+-2*a*b*d^-1*csc(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*sec(c+d*x)^5*sin(c+d*x)^5, x) == :(-1//3*b^3*d^-1*sin(c+d*x)^3+1//4*d^-1*(a+b*sin(c+d*x))^3*sec(c+d*x)^4+-3//2*a*b^2*d^-1*sin(c+d*x)^2+-1//8*b*d^-1*(24*a^2+35*b^2)*sin(c+d*x)+-1//8*d^-1*(a+b*sin(c+d*x))^2*sec(c+d*x)^2*(8a+11*b*sin(c+d*x))+-1//16*d^-1*(a+b)*(8*a^2+35*b^2+37*a*b)*log(1+-1*sin(c+d*x))+-1//16*d^-1*(a+-1b)*(8*a^2+35*b^2+-37*a*b)*log(1+sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^3*sec(c+d*x)^5*sin(c+d*x)^4, x) == :(-1//2*b^3*d^-1*sin(c+d*x)^2+-29//8*a*b^2*d^-1*sin(c+d*x)+-1//8*d^-1*(a+b*sin(c+d*x))^2*sec(c+d*x)^2*(8b+5*a*sin(c+d*x))+-1//16*d^-1*(3a+3b)*(a^2+8*b^2+7*a*b)*log(1+-1*sin(c+d*x))+1//4*d^-1*(a+b*sin(c+d*x))^3*sec(c+d*x)^3*tan(c+d*x)+1//16*d^-1*(-3b+3a)*(a^2+8*b^2+-7*a*b)*log(1+sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^3*sec(c+d*x)^5*sin(c+d*x)^3, x) == :(-15//8*b^3*d^-1*sin(c+d*x)+1//4*d^-1*(a+b*sin(c+d*x))^3*sec(c+d*x)^4+-1//8*d^-1*(a+b*sin(c+d*x))^2*sec(c+d*x)^2*(4a+7*b*sin(c+d*x))+-3//16*b*d^-1*(a+b)*(3a+5b)*log(1+-1*sin(c+d*x))+1//16*b*d^-1*(a+-1b)*(-15b+9a)*log(1+sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^3*sec(c+d*x)^5*sin(c+d*x)^2, x) == :(-1//16*d^-1*(a^3+8*b^3+-9*a*b^2)*log(1+sin(c+d*x))+1//16*d^-1*(a^3+-8*b^3+-9*a*b^2)*log(1+-1*sin(c+d*x))+-1//8*d^-1*sec(c+d*x)^2*(a+b*sin(c+d*x))*((a^2+4*b^2)*sin(c+d*x)+5*a*b)+1//4*d^-1*(a+b*sin(c+d*x))^3*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+b*sin(c+d*x))^3*sec(c+d*x)^5*sin(c+d*x), x) == :(1//4*d^-1*(a+b*sin(c+d*x))^3*sec(c+d*x)^4+-3//8*b*d^-1*(a^2+-1*b^2)*arctanh(sin(c+d*x))+-3//8*d^-1*sec(c+d*x)^2*(a+b*sin(c+d*x))*(b^2+a*b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^3*sec(c+d*x)^5*csc(c+d*x), x) == :(a^3*d^-1*log(sin(c+d*x))+-1//16*d^-1*(b^3+8*a^3+-9*b*a^2)*log(1+sin(c+d*x))+-1//16*d^-1*(-1*b^3+8*a^3+9*b*a^2)*log(1+-1*sin(c+d*x))+1//4*d^-1*sec(c+d*x)^4*(a*(a^2+3*b^2)+b*(b^2+3*a^2)*sin(c+d*x))+1//8*d^-1*sec(c+d*x)^2*(4*a^3+b*(-1*b^2+9*a^2)*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^3*csc(c+d*x)^2*sec(c+d*x)^5, x) == :(-1*a^3*d^-1*csc(c+d*x)+3*b*a^2*d^-1*log(sin(c+d*x))+1//4*b*d^-1*sec(c+d*x)^4*(b^2+3*a^2+a*b*(3+a^2*b^-2)*sin(c+d*x))+-3//16*a*d^-1*(a+b)*(3b+5a)*log(1+-1*sin(c+d*x))+1//8*a*b*d^-1*sec(c+d*x)^2*(12a+b*(9+7*a^2*b^-2)*sin(c+d*x))+3//16*a*d^-1*(a+-1b)*(-3b+5a)*log(1+sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^3*csc(c+d*x)^3*sec(c+d*x)^5, x) == :(-1//2*a^3*d^-1*csc(c+d*x)^2+-3*b*a^2*d^-1*csc(c+d*x)+3*a*d^-1*(a^2+b^2)*log(sin(c+d*x))+-1//16*d^-1*(-3b+3a)*(b^2+8*a^2+-7*a*b)*log(1+sin(c+d*x))+-1//16*d^-1*(3a+3b)*(b^2+8*a^2+7*a*b)*log(1+-1*sin(c+d*x))+1//4*b^2*d^-1*sec(c+d*x)^4*(a*(3+a^2*b^-2)+b*(1+3*a^2*b^-2)*sin(c+d*x))+1//8*b^2*d^-1*sec(c+d*x)^2*(4*a*(3+2*a^2*b^-2)+b*(3+21*a^2*b^-2)*sin(c+d*x)))
@test integrate((d*sin(e+f*x))^-1//2*(a+b*sin(e+f*x))^9//2*sec(e+f*x)^6, x) == :(1//5*d^-1*f^-1*(d*sin(e+f*x))^(1/2)*(a+b*sin(e+f*x))^9//2*sec(e+f*x)^5+-3//5*a*b*f^-1*(d*sin(e+f*x))^-1//2*(a+b*sin(e+f*x))^(1/2)*(b^2+-2*a^2)*cos(e+f*x)+-3//20*a*d^-1*f^-1*(d*sin(e+f*x))^(1/2)*(a+b*sin(e+f*x))^(1/2)*sec(e+f*x)^3*(sin(e+f*x)^3*(-4*b^3+8*b*a^2)+-1*a*(b^2+7*a^2)+2*b*(b^2+-7*a^2)*sin(e+f*x)+5*a*sin(e+f*x)^2*(a^2+-1*b^2))+-3//20*a*d^-1//2*f^-1*(a*(a+-1b)^-1*(1+csc(e+f*x)))^(1/2)*(-1*a*(a+b)^-1*(-1+csc(e+f*x)))^(1/2)*(a+b)^3//2*(-4*b^2+5*a^2+3*a*b)*Elliptic.F(arcsin(d^(1/2)*(d*sin(e+f*x))^-1//2*(a+b)^-1//2*(a+b*sin(e+f*x))^(1/2)),-1*(a+-1b)^-1*(a+b))*tan(e+f*x)+-3//5*b*d^-1*f^-1*(d*sin(e+f*x))^(1/2)*(-1*a*(a+b)^-1*(-1+csc(e+f*x)))^(1/2)*(-1*a*(a+-1b)^-2*csc(e+f*x)^2*(1+sin(e+f*x))*(a+b*sin(e+f*x)))^(1/2)*(a+b*sin(e+f*x))^-1//2*(b^4+2*a^4+-3*a^2*b^2)*Elliptic.E(arcsin((-1*(a+-1b)^-1*(b+a*csc(e+f*x)))^(1/2)),1+-2*a*(a+b)^-1)*tan(e+f*x))
@test integrate(cos(c+d*x)^7*(A+B*sin(c+d*x))*(a+b*sin(c+d*x)), x) == :((1/2)*d^-1*sin(c+d*x)^2*(A*b+B*a)+(1/2)*d^-1*sin(c+d*x)^6*(A*b+B*a)+-1//3*d^-1*sin(c+d*x)^3*(-1*B*b+3*A*a)+-1//4*d^-1*sin(c+d*x)^4*(3*A*b+3*B*a)+-1//7*d^-1*sin(c+d*x)^7*(A*a+-3*B*b)+-1//8*d^-1*sin(c+d*x)^8*(A*b+B*a)+1//5*d^-1*sin(c+d*x)^5*(-3*B*b+3*A*a)+A*a*d^-1*sin(c+d*x)+-1//9*B*b*d^-1*sin(c+d*x)^9)
@test integrate(cos(c+d*x)^5*(A+B*sin(c+d*x))*(a+b*sin(c+d*x)), x) == :((1/2)*d^-1*sin(c+d*x)^2*(A*b+B*a)+-1//2*d^-1*sin(c+d*x)^4*(A*b+B*a)+-1//3*d^-1*sin(c+d*x)^3*(-1*B*b+2*A*a)+1//5*d^-1*sin(c+d*x)^5*(A*a+-2*B*b)+1//6*d^-1*sin(c+d*x)^6*(A*b+B*a)+A*a*d^-1*sin(c+d*x)+1//7*B*b*d^-1*sin(c+d*x)^7)
@test integrate(cos(c+d*x)^3*(A+B*sin(c+d*x))*(a+b*sin(c+d*x)), x) == :((1/2)*d^-1*sin(c+d*x)^2*(A*b+B*a)+-1//3*d^-1*sin(c+d*x)^3*(A*a+-1*B*b)+-1//4*d^-1*sin(c+d*x)^4*(A*b+B*a)+A*a*d^-1*sin(c+d*x)+-1//5*B*b*d^-1*sin(c+d*x)^5)
@test integrate((A+B*sin(c+d*x))*(a+b*sin(c+d*x))*cos(c+d*x), x) == :((1/2)*d^-1*sin(c+d*x)^2*(A*b+B*a)+A*a*d^-1*sin(c+d*x)+1//3*B*b*d^-1*sin(c+d*x)^3)
@test integrate((A+B*sin(c+d*x))*(a+b*sin(c+d*x))*sec(c+d*x), x) == :((1/2)*d^-1*(A+-1B)*(a+-1b)*log(1+sin(c+d*x))+-1*B*b*d^-1*sin(c+d*x)+-1//2*d^-1*(A+B)*(a+b)*log(1+-1*sin(c+d*x)))
@test integrate(sec(c+d*x)^3*(A+B*sin(c+d*x))*(a+b*sin(c+d*x)), x) == :((1/2)*d^-1*sec(c+d*x)^2*(A*b+B*a+(A*a+B*b)*sin(c+d*x))+(1/2)*d^-1*(A*a+-1*B*b)*arctanh(sin(c+d*x)))
@test integrate(sec(c+d*x)^5*(A+B*sin(c+d*x))*(a+b*sin(c+d*x)), x) == :(1//4*d^-1*sec(c+d*x)^4*(A*b+B*a+(A*a+B*b)*sin(c+d*x))+1//8*d^-1*(-1*B*b+3*A*a)*arctanh(sin(c+d*x))+1//8*d^-1*(-1*B*b+3*A*a)*sec(c+d*x)*tan(c+d*x))
@test integrate(sec(c+d*x)^7*(A+B*sin(c+d*x))*(a+b*sin(c+d*x)), x) == :(1//6*d^-1*sec(c+d*x)^6*(A*b+B*a+(A*a+B*b)*sin(c+d*x))+1//16*d^-1*(-1*B*b+5*A*a)*arctanh(sin(c+d*x))+1//16*d^-1*(-1*B*b+5*A*a)*sec(c+d*x)*tan(c+d*x)+1//24*d^-1*sec(c+d*x)^3*(-1*B*b+5*A*a)*tan(c+d*x))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^7*(A+B*sin(c+d*x)), x) == :(-1//7*b^-8*d^-1*(a+b*sin(c+d*x))^7*(-35*B*a^3+-3*A*b^3+15*A*b*a^2+15*B*a*b^2)+-1//9*b^-8*d^-1*(a+b*sin(c+d*x))^9*(A*b+-7*B*a)+-1//10*B*b^-8*d^-1*(a+b*sin(c+d*x))^10+1//6*b^-8*d^-1*(a+b*sin(c+d*x))^6*(-35*B*a^4+-3*B*b^4+-12*A*a*b^3+20*A*b*a^3+30*B*a^2*b^2)+1//8*b^-8*d^-1*(a+b*sin(c+d*x))^8*(-21*B*a^2+3*B*b^2+6*A*a*b)+-1//3*b^-8*d^-1*(a+b*sin(c+d*x))^3*(a^2+-1*b^2)^3*(A*b+-1*B*a)+-1//5*b^-8*d^-1*(a+b*sin(c+d*x))^5*(-3*b^2+3*a^2)*(-1*A*b^3+-7*B*a^3+3*B*a*b^2+5*A*b*a^2)+1//4*b^-8*d^-1*(a+b*sin(c+d*x))^4*(a^2+-1*b^2)^2*(B*b^2+-7*B*a^2+6*A*a*b))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^5*(A+B*sin(c+d*x)), x) == :(-1//3*b^-6*d^-1*(a+b*sin(c+d*x))^6*(B*b^2+-5*B*a^2+2*A*a*b)+1//5*b^-6*d^-1*(a+b*sin(c+d*x))^5*(-10*B*a^3+-2*A*b^3+6*A*b*a^2+6*B*a*b^2)+1//7*b^-6*d^-1*(a+b*sin(c+d*x))^7*(A*b+-5*B*a)+1//8*B*b^-6*d^-1*(a+b*sin(c+d*x))^8+-1//4*b^-6*d^-1*(a+b*sin(c+d*x))^4*(a^2+-1*b^2)*(B*b^2+-5*B*a^2+4*A*a*b)+1//3*b^-6*d^-1*(a+b*sin(c+d*x))^3*(a^2+-1*b^2)^2*(A*b+-1*B*a))
@test integrate((a+b*sin(c+d*x))^2*cos(c+d*x)^3*(A+B*sin(c+d*x)), x) == :(-1//5*b^-4*d^-1*(a+b*sin(c+d*x))^5*(A*b+-3*B*a)+-1//6*B*b^-4*d^-1*(a+b*sin(c+d*x))^6+1//4*b^-4*d^-1*(a+b*sin(c+d*x))^4*(B*b^2+-3*B*a^2+2*A*a*b)+-1//3*b^-4*d^-1*(a+b*sin(c+d*x))^3*(a^2+-1*b^2)*(A*b+-1*B*a))
@test integrate((a+b*sin(c+d*x))^2*(A+B*sin(c+d*x))*cos(c+d*x), x) == :(1//3*b^-2*d^-1*(a+b*sin(c+d*x))^3*(A*b+-1*B*a)+1//4*B*b^-2*d^-1*(a+b*sin(c+d*x))^4)
@test integrate((a+b*sin(c+d*x))^2*(A+B*sin(c+d*x))*sec(c+d*x), x) == :((1/2)*d^-1*(a+-1b)^2*(A+-1B)*log(1+sin(c+d*x))+-1*b*d^-1*(A*b+2*B*a)*sin(c+d*x)+-1//2*B*b^2*d^-1*sin(c+d*x)^2+-1//2*d^-1*(a+b)^2*(A+B)*log(1+-1*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^2*sec(c+d*x)^3*(A+B*sin(c+d*x)), x) == :((1/2)*d^-1*sec(c+d*x)^2*(a+b*sin(c+d*x))*(A*b+B*a+(A*a+B*b)*sin(c+d*x))+-1//4*d^-1*(a+b)*(A*a+-1*b*(A+2B))*log(1+-1*sin(c+d*x))+1//4*d^-1*(a+-1b)*(A*a+b*(A+-2B))*log(1+sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^2*sec(c+d*x)^5*(A+B*sin(c+d*x)), x) == :(1//8*d^-1*sec(c+d*x)^2*((A*b^2+3*A*a^2+-2*B*a*b)*sin(c+d*x)+2*b*(-1*B*b+2*A*a))+1//8*d^-1*(-1*A*b^2+3*A*a^2+-2*B*a*b)*arctanh(sin(c+d*x))+1//4*d^-1*(a+b*sin(c+d*x))^2*sec(c+d*x)^4*(B+A*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^2*sec(c+d*x)^7*(A+B*sin(c+d*x)), x) == :(1//16*d^-1*(-1*A*b^2+5*A*a^2+-2*B*a*b)*arctanh(sin(c+d*x))+1//24*d^-1*sec(c+d*x)^4*((3*A*b^2+5*A*a^2+-2*B*a*b)*sin(c+d*x)+2*b*(-1*B*b+4*A*a))+1//6*d^-1*(a+b*sin(c+d*x))^2*sec(c+d*x)^6*(B+A*sin(c+d*x))+1//16*d^-1*(-1*A*b^2+5*A*a^2+-2*B*a*b)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^7*(A+B*sin(c+d*x)), x) == :(b^-7*d^-1*(B*b^6+-1*B*a^6+A*b*a^5+-3*A*a^3*b^3+-3*B*a^2*b^4+3*A*a*b^5+3*B*a^4*b^2)*sin(c+d*x)+-1//6*b^-2*d^-1*sin(c+d*x)^6*(A*b+-1*B*a)+-1//7*B*b^-1*d^-1*sin(c+d*x)^7+1//3*b^-5*d^-1*sin(c+d*x)^3*(-1*B*a^4+-3*B*b^4+A*b*a^3+-3*A*a*b^3+3*B*a^2*b^2)+1//5*b^-3*d^-1*sin(c+d*x)^5*(-1*B*a^2+3*B*b^2+A*a*b)+-1*b^-8*d^-1*(a^2+-1*b^2)^3*(A*b+-1*B*a)*log(a+b*sin(c+d*x))+-1//2*b^-6*d^-1*sin(c+d*x)^2*(A*b+-1*B*a)*(a^4+3*b^4+-3*a^2*b^2)+-1//4*b^-4*d^-1*sin(c+d*x)^4*(a^2+-3*b^2)*(A*b+-1*B*a))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^5*(A+B*sin(c+d*x)), x) == :(-1*b^-5*d^-1*(-1*B*a^4+-1*B*b^4+A*b*a^3+-2*A*a*b^3+2*B*a^2*b^2)*sin(c+d*x)+-1//3*b^-3*d^-1*sin(c+d*x)^3*(-1*B*a^2+2*B*b^2+A*a*b)+1//4*b^-2*d^-1*sin(c+d*x)^4*(A*b+-1*B*a)+1//5*B*b^-1*d^-1*sin(c+d*x)^5+b^-6*d^-1*(a^2+-1*b^2)^2*(A*b+-1*B*a)*log(a+b*sin(c+d*x))+(1/2)*b^-4*d^-1*sin(c+d*x)^2*(a^2+-2*b^2)*(A*b+-1*B*a))
@test integrate((a+b*sin(c+d*x))^-1*cos(c+d*x)^3*(A+B*sin(c+d*x)), x) == :(b^-3*d^-1*(B*b^2+-1*B*a^2+A*a*b)*sin(c+d*x)+-1//2*b^-2*d^-1*sin(c+d*x)^2*(A*b+-1*B*a)+-1//3*B*b^-1*d^-1*sin(c+d*x)^3+-1*b^-4*d^-1*(a^2+-1*b^2)*(A*b+-1*B*a)*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*(A+B*sin(c+d*x))*cos(c+d*x), x) == :(B*b^-1*d^-1*sin(c+d*x)+b^-2*d^-1*(A*b+-1*B*a)*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*(A+B*sin(c+d*x))*sec(c+d*x), x) == :(d^-1*(-2b+2a)^-1*(A+-1B)*log(1+sin(c+d*x))+-1*d^-1*(a^2+-1*b^2)^-1*(A*b+-1*B*a)*log(a+b*sin(c+d*x))+-1*d^-1*(2a+2b)^-1*(A+B)*log(1+-1*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^3*(A+B*sin(c+d*x)), x) == :(-1*d^-1*(-2*b^2+2*a^2)^-1*sec(c+d*x)^2*(A*b+-1*B*a+-1*(A*a+-1*B*b)*sin(c+d*x))+-1//4*d^-1*(a+b)^-2*(A*a+b*(B+2A))*log(1+-1*sin(c+d*x))+1//4*d^-1*(a+-1b)^-2*(A*a+-1*b*(-1B+2A))*log(1+sin(c+d*x))+b^2*d^-1*(a^2+-1*b^2)^-2*(A*b+-1*B*a)*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^5*(A+B*sin(c+d*x)), x) == :(-1*d^-1*(-4*b^2+4*a^2)^-1*sec(c+d*x)^4*(A*b+-1*B*a+-1*(A*a+-1*B*b)*sin(c+d*x))+-1//16*d^-1*(a+b)^-3*(b^2*(3B+8A)+3*A*a^2+a*b*(B+9A))*log(1+-1*sin(c+d*x))+1//8*d^-1*(a^2+-1*b^2)^-2*sec(c+d*x)^2*((3*A*a^3+3*B*b^3+B*b*a^2+-7*A*a*b^2)*sin(c+d*x)+4*b^2*(A*b+-1*B*a))+1//16*d^-1*(a+-1b)^-3*(b^2*(-3B+8A)+3*A*a^2+-1*a*b*(-1B+9A))*log(1+sin(c+d*x))+-1*b^4*d^-1*(a^2+-1*b^2)^-3*(A*b+-1*B*a)*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-1*sec(c+d*x)^7*(A+B*sin(c+d*x)), x) == :(-1*d^-1*(-6*b^2+6*a^2)^-1*sec(c+d*x)^6*(A*b+-1*B*a+-1*(A*a+-1*B*b)*sin(c+d*x))+-1//16*d^-1*(a^2+-1*b^2)^-3*sec(c+d*x)^2*(-1*(-5*B*b^5+5*A*a^5+B*b*a^4+-16*A*a^3*b^2+-4*B*a^2*b^3+19*A*a*b^4)*sin(c+d*x)+8*b^4*(A*b+-1*B*a))+-1//32*d^-1*(a+b)^-4*(b^3*(5B+16A)+5*A*a^3+a*b^2*(4B+29A)+b*a^2*(B+20A))*log(1+-1*sin(c+d*x))+1//24*d^-1*(a^2+-1*b^2)^-2*sec(c+d*x)^4*((5*A*a^3+5*B*b^3+B*b*a^2+-11*A*a*b^2)*sin(c+d*x)+6*b^2*(A*b+-1*B*a))+1//32*d^-1*(a+-1b)^-4*(-1*b^3*(-5B+16A)+5*A*a^3+a*b^2*(-4B+29A)+-1*b*a^2*(-1B+20A))*log(1+sin(c+d*x))+b^6*d^-1*(a^2+-1*b^2)^-4*(A*b+-1*B*a)*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^7*(A+B*sin(c+d*x)), x) == :((1/2)*b^-6*d^-1*sin(c+d*x)^2*(-5*B*a^4+-3*B*b^4+-6*A*a*b^3+4*A*b*a^3+9*B*a^2*b^2)+-1*b^-7*d^-1*(-6*B*a^5+3*A*b^5+-9*A*a^2*b^3+-6*B*a*b^4+5*A*b*a^4+12*B*a^3*b^2)*sin(c+d*x)+-1//3*b^-5*d^-1*sin(c+d*x)^3*(-4*B*a^3+-3*A*b^3+3*A*b*a^2+6*B*a*b^2)+-1//5*b^-3*d^-1*sin(c+d*x)^5*(A*b+-2*B*a)+-1//6*B*b^-2*d^-1*sin(c+d*x)^6+1//4*b^-4*d^-1*sin(c+d*x)^4*(-3*B*a^2+3*B*b^2+2*A*a*b)+b^-8*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^3*(A*b+-1*B*a)+b^-8*d^-1*(a^2+-1*b^2)^2*(B*b^2+-7*B*a^2+6*A*a*b)*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^5*(A+B*sin(c+d*x)), x) == :(b^-5*d^-1*(-4*B*a^3+-2*A*b^3+3*A*b*a^2+4*B*a*b^2)*sin(c+d*x)+-1//2*b^-4*d^-1*sin(c+d*x)^2*(-3*B*a^2+2*B*b^2+2*A*a*b)+1//3*b^-3*d^-1*sin(c+d*x)^3*(A*b+-2*B*a)+1//4*B*b^-2*d^-1*sin(c+d*x)^4+-1*b^-6*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^2*(A*b+-1*B*a)+-1*b^-6*d^-1*(a^2+-1*b^2)*(B*b^2+-5*B*a^2+4*A*a*b)*log(a+b*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-2*cos(c+d*x)^3*(A+B*sin(c+d*x)), x) == :(b^-4*d^-1*(B*b^2+-3*B*a^2+2*A*a*b)*log(a+b*sin(c+d*x))+-1*b^-3*d^-1*(A*b+-2*B*a)*sin(c+d*x)+-1//2*B*b^-2*d^-1*sin(c+d*x)^2+b^-4*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)*(A*b+-1*B*a))
@test integrate((a+b*sin(c+d*x))^-2*(A+B*sin(c+d*x))*cos(c+d*x), x) == :(B*b^-2*d^-1*log(a+b*sin(c+d*x))+-1*b^-2*d^-1*(a+b*sin(c+d*x))^-1*(A*b+-1*B*a))
@test integrate((a+b*sin(c+d*x))^-2*(A+B*sin(c+d*x))*sec(c+d*x), x) == :(d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-1*(A*b+-1*B*a)+(1/2)*d^-1*(a+-1b)^-2*(A+-1B)*log(1+sin(c+d*x))+-1*d^-1*(a^2+-1*b^2)^-2*(-1*B*a^2+-1*B*b^2+2*A*a*b)*log(a+b*sin(c+d*x))+-1//2*d^-1*(a+b)^-2*(A+B)*log(1+-1*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-2*sec(c+d*x)^3*(A+B*sin(c+d*x)), x) == :(-1//4*d^-1*(a+b)^-3*(A*a+2*B*b+3*A*b)*log(1+-1*sin(c+d*x))+1//4*d^-1*(a+-1b)^-3*(A*a+-3*A*b+2*B*b)*log(1+sin(c+d*x))+b^2*d^-1*(a^2+-1*b^2)^-3*(-1*B*b^2+-3*B*a^2+4*A*a*b)*log(a+b*sin(c+d*x))+-1*d^-1*(a+b*sin(c+d*x))^-1*(-2*b^2+2*a^2)^-1*sec(c+d*x)^2*(A*b+-1*B*a+-1*(A*a+-1*B*b)*sin(c+d*x))+-1//2*b*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-2*(A*a^2+3*A*b^2+-4*B*a*b))
@test integrate((a+b*sin(c+d*x))^-2*sec(c+d*x)^5*(A+B*sin(c+d*x)), x) == :(-1//16*d^-1*(a+b)^-4*(b^2*(8B+15A)+3*A*a^2+2*a*b*(B+6A))*log(1+-1*sin(c+d*x))+1//16*d^-1*(a+-1b)^-4*(b^2*(-8B+15A)+3*A*a^2+-2*a*b*(-1B+6A))*log(1+sin(c+d*x))+-1*b^4*d^-1*(a^2+-1*b^2)^-4*(-1*B*b^2+-5*B*a^2+6*A*a*b)*log(a+b*sin(c+d*x))+-1*d^-1*(a+b*sin(c+d*x))^-1*(-4*b^2+4*a^2)^-1*sec(c+d*x)^4*(A*b+-1*B*a+-1*(A*a+-1*B*b)*sin(c+d*x))+-1//8*b*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-3*(-15*A*b^4+3*A*a^4+-12*A*a^2*b^2+2*B*b*a^3+22*B*a*b^3)+1//8*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-2*sec(c+d*x)^2*(b*(A*a^2+5*A*b^2+-6*B*a*b)+(3*A*a^3+4*B*b^3+-9*A*a*b^2+2*B*b*a^2)*sin(c+d*x)))
@test integrate((a+b*sin(c+d*x))^-2*sec(c+d*x)^7*(A+B*sin(c+d*x)), x) == :(-1//32*d^-1*(a+b)^-5*(b^3*(16B+35A)+5*A*a^3+a*b^2*(10B+47A)+b*a^2*(2B+25A))*log(1+-1*sin(c+d*x))+1//32*d^-1*(a+-1b)^-5*(-1*a^2*(-2*B*b+25*A*b)+-1*b^3*(-16B+35A)+5*A*a^3+a*b^2*(-10B+47A))*log(1+sin(c+d*x))+b^6*d^-1*(a^2+-1*b^2)^-5*(-1*B*b^2+-7*B*a^2+8*A*a*b)*log(a+b*sin(c+d*x))+-1*d^-1*(a+b*sin(c+d*x))^-1*(-6*b^2+6*a^2)^-1*sec(c+d*x)^6*(A*b+-1*B*a+-1*(A*a+-1*B*b)*sin(c+d*x))+-1//16*b*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-4*(5*A*a^6+35*A*b^6+-54*B*a*b^5+-23*A*a^4*b^2+-12*B*a^3*b^3+2*B*b*a^5+47*A*a^2*b^4)+1//24*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-2*sec(c+d*x)^4*(b*(A*a^2+7*A*b^2+-8*B*a*b)+(5*A*a^3+6*B*b^3+-13*A*a*b^2+2*B*b*a^2)*sin(c+d*x))+1//48*d^-1*(a+b*sin(c+d*x))^-1*(a^2+-1*b^2)^-3*sec(c+d*x)^2*(b*(-35*A*b^4+5*A*a^4+-18*A*a^2*b^2+2*B*b*a^3+46*B*a*b^3)+(-24*B*b^5+15*A*a^5+-54*A*a^3*b^2+-30*B*a^2*b^3+6*B*b*a^4+87*A*a*b^4)*sin(c+d*x)))

max_stars_repo_path: test/4 Trig functions/4.1 Sine/4.1.2.2 (g cos)^p (a+b sin)^m (c+d sin)^n.jl