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

@test integrate((b*sec(c+d*x))^5//2*(A+B*sec(c+d*x)), x) == :(2//5*B*d^-1*(b*sec(c+d*x))^5//2*sin(c+d*x)+2//3*A*b*d^-1*(b*sec(c+d*x))^3//2*sin(c+d*x)+6//5*B*b^2*d^-1*(b*sec(c+d*x))^(1/2)*sin(c+d*x)+-6//5*B*b^3*d^-1*(b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*A*b^2*d^-1*(b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*sec(c+d*x))^3//2*(A+B*sec(c+d*x)), x) == :(2//3*B*d^-1*(b*sec(c+d*x))^3//2*sin(c+d*x)+2*A*b*d^-1*(b*sec(c+d*x))^(1/2)*sin(c+d*x)+-2*A*b^2*d^-1*(b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*B*b*d^-1*(b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*sec(c+d*x))^(1/2)*(A+B*sec(c+d*x)), x) == :(2*B*d^-1*(b*sec(c+d*x))^(1/2)*sin(c+d*x)+2*A*d^-1*(b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-2*B*b*d^-1*(b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((b*sec(c+d*x))^-1//2*(A+B*sec(c+d*x)), x) == :(2*A*d^-1*(b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*B*b^-1*d^-1*(b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*sec(c+d*x))^-3//2*(A+B*sec(c+d*x)), x) == :(2//3*A*b^-1*d^-1*(b*sec(c+d*x))^-1//2*sin(c+d*x)+2*B*b^-1*d^-1*(b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*A*b^-2*d^-1*(b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((b*sec(c+d*x))^-5//2*(A+B*sec(c+d*x)), x) == :(2//3*B*b^-2*d^-1*(b*sec(c+d*x))^-1//2*sin(c+d*x)+2//5*A*b^-1*d^-1*(b*sec(c+d*x))^-3//2*sin(c+d*x)+2//3*B*b^-3*d^-1*(b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+6//5*A*b^-2*d^-1*(b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^4*(A+B*sec(c+d*x))*(a+a*sec(c+d*x)), x) == :(1//5*a*d^-1*(4B+5A)*tan(c+d*x)+1//15*a*d^-1*tan(c+d*x)^3*(4B+5A)+3//8*a*d^-1*(A+B)*arctanh(sin(c+d*x))+1//4*a*d^-1*sec(c+d*x)^3*(A+B)*tan(c+d*x)+1//5*B*a*d^-1*sec(c+d*x)^4*tan(c+d*x)+3//8*a*d^-1*(A+B)*sec(c+d*x)*tan(c+d*x))
@test integrate(sec(c+d*x)^3*(A+B*sec(c+d*x))*(a+a*sec(c+d*x)), x) == :(a*d^-1*(A+B)*tan(c+d*x)+1//3*a*d^-1*tan(c+d*x)^3*(A+B)+1//8*a*d^-1*(3B+4A)*arctanh(sin(c+d*x))+1//4*B*a*d^-1*sec(c+d*x)^3*tan(c+d*x)+1//8*a*d^-1*(3B+4A)*sec(c+d*x)*tan(c+d*x))
@test integrate(sec(c+d*x)^2*(A+B*sec(c+d*x))*(a+a*sec(c+d*x)), x) == :((1/2)*a*d^-1*(A+B)*arctanh(sin(c+d*x))+1//3*a*d^-1*(2B+3A)*tan(c+d*x)+(1/2)*a*d^-1*(A+B)*sec(c+d*x)*tan(c+d*x)+1//3*B*a*d^-1*sec(c+d*x)^2*tan(c+d*x))
@test integrate((A+B*sec(c+d*x))*(a+a*sec(c+d*x))*sec(c+d*x), x) == :(a*d^-1*(A+B)*tan(c+d*x)+(1/2)*a*d^-1*(B+2A)*arctanh(sin(c+d*x))+(1/2)*B*a*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((A+B*sec(c+d*x))*(a+a*sec(c+d*x)), x) == :(A*a*x+B*a*d^-1*tan(c+d*x)+a*d^-1*(A+B)*arctanh(sin(c+d*x)))
@test integrate((A+B*sec(c+d*x))*(a+a*sec(c+d*x))*cos(c+d*x), x) == :(a*x*(A+B)+A*a*d^-1*sin(c+d*x)+B*a*d^-1*arctanh(sin(c+d*x)))
@test integrate(cos(c+d*x)^2*(A+B*sec(c+d*x))*(a+a*sec(c+d*x)), x) == :((1/2)*a*x*(A+2B)+a*d^-1*(A+B)*sin(c+d*x)+(1/2)*A*a*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^3*(A+B*sec(c+d*x))*(a+a*sec(c+d*x)), x) == :((1/2)*a*x*(A+B)+1//3*a*d^-1*(2A+3B)*sin(c+d*x)+(1/2)*a*d^-1*(A+B)*cos(c+d*x)*sin(c+d*x)+1//3*A*a*d^-1*cos(c+d*x)^2*sin(c+d*x))
@test integrate(cos(c+d*x)^4*(A+B*sec(c+d*x))*(a+a*sec(c+d*x)), x) == :(1//8*a*x*(3A+4B)+a*d^-1*(A+B)*sin(c+d*x)+-1//3*a*d^-1*sin(c+d*x)^3*(A+B)+1//4*A*a*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//8*a*d^-1*(3A+4B)*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^5*(A+B*sec(c+d*x))*(a+a*sec(c+d*x)), x) == :(3//8*a*x*(A+B)+-1//15*a*d^-1*sin(c+d*x)^3*(4A+5B)+1//5*a*d^-1*(4A+5B)*sin(c+d*x)+1//4*a*d^-1*cos(c+d*x)^3*(A+B)*sin(c+d*x)+1//5*A*a*d^-1*cos(c+d*x)^4*sin(c+d*x)+3//8*a*d^-1*(A+B)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(1//5*a^2*d^-1*(9B+10A)*tan(c+d*x)+1//8*a^2*d^-1*(6B+7A)*arctanh(sin(c+d*x))+1//15*a^2*d^-1*tan(c+d*x)^3*(9B+10A)+1//5*B*d^-1*sec(c+d*x)^3*(a^2+a^2*sec(c+d*x))*tan(c+d*x)+1//8*a^2*d^-1*(6B+7A)*sec(c+d*x)*tan(c+d*x)+1//20*a^2*d^-1*sec(c+d*x)^3*(5A+6B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(1//6*a^2*d^-1*(7B+8A)*tan(c+d*x)+1//8*a^2*d^-1*(7B+8A)*arctanh(sin(c+d*x))+1//12*d^-1*(a+a*sec(c+d*x))^2*(-1B+4A)*tan(c+d*x)+1//4*B*a^-1*d^-1*(a+a*sec(c+d*x))^3*tan(c+d*x)+1//24*a^2*d^-1*(7B+8A)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*(A+B*sec(c+d*x))*sec(c+d*x), x) == :((1/2)*a^2*d^-1*(2B+3A)*arctanh(sin(c+d*x))+1//3*B*d^-1*(a+a*sec(c+d*x))^2*tan(c+d*x)+2//3*a^2*d^-1*(2B+3A)*tan(c+d*x)+1//6*a^2*d^-1*(2B+3A)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*(A+B*sec(c+d*x)), x) == :(A*x*a^2+(1/2)*B*d^-1*(a^2+a^2*sec(c+d*x))*tan(c+d*x)+(1/2)*a^2*d^-1*(2A+3B)*tan(c+d*x)+(1/2)*a^2*d^-1*(3B+4A)*arctanh(sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^2*(A+B*sec(c+d*x))*cos(c+d*x), x) == :(x*a^2*(B+2A)+B*d^-1*(a^2+a^2*sec(c+d*x))*sin(c+d*x)+a^2*d^-1*(A+-1B)*sin(c+d*x)+a^2*d^-1*(A+2B)*arctanh(sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^2*(A+B*sec(c+d*x)), x) == :((1/2)*x*a^2*(3A+4B)+B*a^2*d^-1*arctanh(sin(c+d*x))+(1/2)*a^2*d^-1*(2B+3A)*sin(c+d*x)+(1/2)*A*d^-1*(a^2+a^2*sec(c+d*x))*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^3*(A+B*sec(c+d*x)), x) == :((1/2)*x*a^2*(2A+3B)+2//3*a^2*d^-1*(2A+3B)*sin(c+d*x)+1//3*A*d^-1*(a+a*sec(c+d*x))^2*cos(c+d*x)^2*sin(c+d*x)+1//6*a^2*d^-1*(2A+3B)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^4*(A+B*sec(c+d*x)), x) == :(1//8*x*a^2*(7A+8B)+1//3*a^2*d^-1*(4A+5B)*sin(c+d*x)+1//4*A*d^-1*cos(c+d*x)^3*(a^2+a^2*sec(c+d*x))*sin(c+d*x)+1//8*a^2*d^-1*(7A+8B)*cos(c+d*x)*sin(c+d*x)+1//12*a^2*d^-1*cos(c+d*x)^2*(4B+5A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^5*(A+B*sec(c+d*x)), x) == :(1//8*x*a^2*(6A+7B)+-1//15*a^2*d^-1*sin(c+d*x)^3*(9A+10B)+1//5*a^2*d^-1*(9A+10B)*sin(c+d*x)+1//5*A*d^-1*cos(c+d*x)^4*(a^2+a^2*sec(c+d*x))*sin(c+d*x)+1//8*a^2*d^-1*(6A+7B)*cos(c+d*x)*sin(c+d*x)+1//20*a^2*d^-1*cos(c+d*x)^3*(5B+6A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(1//5*a^3*d^-1*(17B+19A)*tan(c+d*x)+1//15*a^3*d^-1*tan(c+d*x)^3*(17B+19A)+1//16*a^3*d^-1*(23B+26A)*arctanh(sin(c+d*x))+1//15*d^-1*sec(c+d*x)^3*(a^3+a^3*sec(c+d*x))*(3A+4B)*tan(c+d*x)+1//16*a^3*d^-1*(23B+26A)*sec(c+d*x)*tan(c+d*x)+1//40*a^3*d^-1*sec(c+d*x)^3*(21B+22A)*tan(c+d*x)+1//6*B*a*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(1//5*a^3*d^-1*(13B+15A)*tan(c+d*x)+1//8*a^3*d^-1*(13B+15A)*arctanh(sin(c+d*x))+1//20*d^-1*(a+a*sec(c+d*x))^3*(-1B+5A)*tan(c+d*x)+1//60*a^3*d^-1*tan(c+d*x)^3*(13B+15A)+1//5*B*a^-1*d^-1*(a+a*sec(c+d*x))^4*tan(c+d*x)+3//40*a^3*d^-1*(13B+15A)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*(A+B*sec(c+d*x))*sec(c+d*x), x) == :(a^3*d^-1*(3B+4A)*tan(c+d*x)+1//4*B*d^-1*(a+a*sec(c+d*x))^3*tan(c+d*x)+1//12*a^3*d^-1*tan(c+d*x)^3*(3B+4A)+5//8*a^3*d^-1*(3B+4A)*arctanh(sin(c+d*x))+3//8*a^3*d^-1*(3B+4A)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*(A+B*sec(c+d*x)), x) == :(A*x*a^3+(1/2)*a^3*d^-1*(5B+7A)*arctanh(sin(c+d*x))+1//6*d^-1*(a^3+a^3*sec(c+d*x))*(3A+5B)*tan(c+d*x)+5//2*a^3*d^-1*(A+B)*tan(c+d*x)+1//3*B*a*d^-1*(a+a*sec(c+d*x))^2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*(A+B*sec(c+d*x))*cos(c+d*x), x) == :(x*a^3*(B+3A)+d^-1*(A+2B)*(a^3+a^3*sec(c+d*x))*sin(c+d*x)+(1/2)*a^3*d^-1*(6A+7B)*arctanh(sin(c+d*x))+-5//2*B*a^3*d^-1*sin(c+d*x)+(1/2)*B*a*d^-1*(a+a*sec(c+d*x))^2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^2*(A+B*sec(c+d*x)), x) == :((1/2)*x*a^3*(6B+7A)+a^3*d^-1*(A+3B)*arctanh(sin(c+d*x))+-1//2*d^-1*(A+-2B)*(a^3+a^3*sec(c+d*x))*sin(c+d*x)+5//2*A*a^3*d^-1*sin(c+d*x)+(1/2)*A*a*d^-1*(a+a*sec(c+d*x))^2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^3*(A+B*sec(c+d*x)), x) == :((1/2)*x*a^3*(5A+7B)+B*a^3*d^-1*arctanh(sin(c+d*x))+5//2*a^3*d^-1*(A+B)*sin(c+d*x)+1//6*d^-1*(a^3+a^3*sec(c+d*x))*(3B+5A)*cos(c+d*x)*sin(c+d*x)+1//3*A*a*d^-1*(a+a*sec(c+d*x))^2*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^4*(A+B*sec(c+d*x)), x) == :(5//8*x*a^3*(3A+4B)+a^3*d^-1*(3A+4B)*sin(c+d*x)+-1//12*a^3*d^-1*sin(c+d*x)^3*(3A+4B)+1//4*A*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)^3*sin(c+d*x)+3//8*a^3*d^-1*(3A+4B)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^5*(A+B*sec(c+d*x)), x) == :(1//8*x*a^3*(13A+15B)+1//15*a^3*d^-1*(38A+45B)*sin(c+d*x)+1//8*a^3*d^-1*(13A+15B)*cos(c+d*x)*sin(c+d*x)+1//20*d^-1*cos(c+d*x)^3*(a^3+a^3*sec(c+d*x))*(5B+7A)*sin(c+d*x)+1//60*a^3*d^-1*cos(c+d*x)^2*(43A+45B)*sin(c+d*x)+1//5*A*a*d^-1*(a+a*sec(c+d*x))^2*cos(c+d*x)^4*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3*cos(c+d*x)^6*(A+B*sec(c+d*x)), x) == :(1//16*x*a^3*(23A+26B)+-1//15*a^3*d^-1*sin(c+d*x)^3*(17A+19B)+1//5*a^3*d^-1*(17A+19B)*sin(c+d*x)+1//15*d^-1*cos(c+d*x)^4*(a^3+a^3*sec(c+d*x))*(3B+4A)*sin(c+d*x)+1//16*a^3*d^-1*(23A+26B)*cos(c+d*x)*sin(c+d*x)+1//40*a^3*d^-1*cos(c+d*x)^3*(21A+22B)*sin(c+d*x)+1//6*A*a*d^-1*(a+a*sec(c+d*x))^2*cos(c+d*x)^5*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(1//30*d^-1*(a+a*sec(c+d*x))^4*(-1B+6A)*tan(c+d*x)+2//15*a^4*d^-1*tan(c+d*x)^3*(7B+8A)+4//5*a^4*d^-1*(7B+8A)*tan(c+d*x)+7//16*a^4*d^-1*(7B+8A)*arctanh(sin(c+d*x))+1//6*B*a^-1*d^-1*(a+a*sec(c+d*x))^5*tan(c+d*x)+1//40*a^4*d^-1*sec(c+d*x)^3*(7B+8A)*tan(c+d*x)+27//80*a^4*d^-1*(7B+8A)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*(A+B*sec(c+d*x))*sec(c+d*x), x) == :(1//5*B*d^-1*(a+a*sec(c+d*x))^4*tan(c+d*x)+4//15*a^4*d^-1*tan(c+d*x)^3*(4B+5A)+7//8*a^4*d^-1*(4B+5A)*arctanh(sin(c+d*x))+8//5*a^4*d^-1*(4B+5A)*tan(c+d*x)+1//20*a^4*d^-1*sec(c+d*x)^3*(4B+5A)*tan(c+d*x)+27//40*a^4*d^-1*(4B+5A)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*(A+B*sec(c+d*x)), x) == :(A*x*a^4+1//8*a^4*d^-1*(35B+48A)*arctanh(sin(c+d*x))+1//12*d^-1*(a^2+a^2*sec(c+d*x))^2*(4A+7B)*tan(c+d*x)+1//24*d^-1*(a^4+a^4*sec(c+d*x))*(32A+35B)*tan(c+d*x)+5//8*a^4*d^-1*(7B+8A)*tan(c+d*x)+1//4*B*a*d^-1*(a+a*sec(c+d*x))^3*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*(A+B*sec(c+d*x))*cos(c+d*x), x) == :(x*a^4*(B+4A)+(1/2)*a^4*d^-1*(12B+13A)*arctanh(sin(c+d*x))+(1/2)*d^-1*(a^2+a^2*sec(c+d*x))^2*(A+2B)*sin(c+d*x)+-5//2*a^4*d^-1*(A+2B)*sin(c+d*x)+1//3*d^-1*(a^4+a^4*sec(c+d*x))*(9A+11B)*sin(c+d*x)+1//3*B*a*d^-1*(a+a*sec(c+d*x))^3*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^2*(A+B*sec(c+d*x)), x) == :((1/2)*x*a^4*(8B+13A)+(1/2)*a^4*d^-1*(8A+13B)*arctanh(sin(c+d*x))+(1/2)*d^-1*(A+6B)*(a^4+a^4*sec(c+d*x))*sin(c+d*x)+-1//2*d^-1*(a^2+a^2*sec(c+d*x))^2*(A+-1B)*sin(c+d*x)+5//2*a^4*d^-1*(A+-1B)*sin(c+d*x)+(1/2)*A*a*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^3*(A+B*sec(c+d*x)), x) == :((1/2)*x*a^4*(12A+13B)+a^4*d^-1*(A+4B)*arctanh(sin(c+d*x))+-1//6*d^-1*(a^4+a^4*sec(c+d*x))*(-3B+8A)*sin(c+d*x)+5//2*a^4*d^-1*(B+2A)*sin(c+d*x)+(1/2)*d^-1*(a^2+a^2*sec(c+d*x))^2*(B+2A)*cos(c+d*x)*sin(c+d*x)+1//3*A*a*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^4*(A+B*sec(c+d*x)), x) == :(1//8*x*a^4*(35A+48B)+B*a^4*d^-1*arctanh(sin(c+d*x))+5//8*a^4*d^-1*(7A+8B)*sin(c+d*x)+1//12*d^-1*(a^2+a^2*sec(c+d*x))^2*cos(c+d*x)^2*(4B+7A)*sin(c+d*x)+1//24*d^-1*(a^4+a^4*sec(c+d*x))*(32B+35A)*cos(c+d*x)*sin(c+d*x)+1//4*A*a*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^5*(A+B*sec(c+d*x)), x) == :(7//8*x*a^4*(4A+5B)+-4//15*a^4*d^-1*sin(c+d*x)^3*(4A+5B)+8//5*a^4*d^-1*(4A+5B)*sin(c+d*x)+1//5*A*d^-1*(a+a*sec(c+d*x))^4*cos(c+d*x)^4*sin(c+d*x)+1//20*a^4*d^-1*cos(c+d*x)^3*(4A+5B)*sin(c+d*x)+27//40*a^4*d^-1*(4A+5B)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^6*(A+B*sec(c+d*x)), x) == :(7//16*x*a^4*(7A+8B)+1//15*a^4*d^-1*(72A+83B)*sin(c+d*x)+1//10*d^-1*(a^2+a^2*sec(c+d*x))^2*cos(c+d*x)^4*(2B+3A)*sin(c+d*x)+1//120*a^4*d^-1*cos(c+d*x)^2*(159A+176B)*sin(c+d*x)+1//120*d^-1*cos(c+d*x)^3*(a^4+a^4*sec(c+d*x))*(72B+73A)*sin(c+d*x)+7//16*a^4*d^-1*(7A+8B)*cos(c+d*x)*sin(c+d*x)+1//6*A*a*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)^5*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^4*cos(c+d*x)^7*(A+B*sec(c+d*x)), x) == :(1//16*x*a^4*(44A+49B)+-1//105*a^4*d^-1*sin(c+d*x)^3*(227A+252B)+1//35*a^4*d^-1*(227A+252B)*sin(c+d*x)+1//15*d^-1*cos(c+d*x)^4*(a^4+a^4*sec(c+d*x))*(7A+7B)*sin(c+d*x)+1//16*a^4*d^-1*(44A+49B)*cos(c+d*x)*sin(c+d*x)+1//42*d^-1*(a^2+a^2*sec(c+d*x))^2*cos(c+d*x)^5*(7B+10A)*sin(c+d*x)+1//280*a^4*d^-1*cos(c+d*x)^3*(276A+301B)*sin(c+d*x)+1//7*A*a*d^-1*(a+a*sec(c+d*x))^3*cos(c+d*x)^6*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^4*(A+B*sec(c+d*x)), x) == :((1/2)*a^-1*d^-1*(-3B+3A)*arctanh(sin(c+d*x))+-1*a^-1*d^-1*(-4B+3A)*tan(c+d*x)+-1//3*a^-1*d^-1*tan(c+d*x)^3*(-4B+3A)+d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^3*(A+-1B)*tan(c+d*x)+(1/2)*a^-1*d^-1*(-3B+3A)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(a^-1*d^-1*(-2B+2A)*tan(c+d*x)+-1//2*a^-1*d^-1*(-3B+2A)*arctanh(sin(c+d*x))+d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^2*(A+-1B)*tan(c+d*x)+-1//2*a^-1*d^-1*(-3B+2A)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(B*a^-1*d^-1*tan(c+d*x)+a^-1*d^-1*(A+-1B)*arctanh(sin(c+d*x))+-1*d^-1*(a+a*sec(c+d*x))^-1*(A+-1B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*(A+B*sec(c+d*x))*sec(c+d*x), x) == :(B*a^-1*d^-1*arctanh(sin(c+d*x))+d^-1*(a+a*sec(c+d*x))^-1*(A+-1B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*(A+B*sec(c+d*x)), x) == :(A*x*a^-1+-1*d^-1*(a+a*sec(c+d*x))^-1*(A+-1B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*(A+B*sec(c+d*x))*cos(c+d*x), x) == :(-1*x*a^-1*(A+-1B)+a^-1*d^-1*(-1B+2A)*sin(c+d*x)+-1*d^-1*(a+a*sec(c+d*x))^-1*(A+-1B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^2*(A+B*sec(c+d*x)), x) == :((1/2)*x*a^-1*(-2B+3A)+-1*a^-1*d^-1*(-2B+2A)*sin(c+d*x)+(1/2)*a^-1*d^-1*(-2B+3A)*cos(c+d*x)*sin(c+d*x)+-1*d^-1*(a+a*sec(c+d*x))^-1*(A+-1B)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(-1//2*x*a^-1*(-3B+3A)+a^-1*d^-1*(-3B+4A)*sin(c+d*x)+-1//3*a^-1*d^-1*sin(c+d*x)^3*(-3B+4A)+-1*d^-1*(a+a*sec(c+d*x))^-1*cos(c+d*x)^2*(A+-1B)*sin(c+d*x)+-1//2*a^-1*d^-1*(-3B+3A)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^5*(A+B*sec(c+d*x)), x) == :((1/2)*a^-2*d^-1*(-10B+7A)*arctanh(sin(c+d*x))+-1*a^-2*d^-1*(-12B+8A)*tan(c+d*x)+-1//3*a^-2*d^-1*tan(c+d*x)^3*(-12B+8A)+(1/2)*a^-2*d^-1*(-10B+7A)*sec(c+d*x)*tan(c+d*x)+1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^4*(A+-1B)*tan(c+d*x)+1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^3*(-10B+7A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^4*(A+B*sec(c+d*x)), x) == :(-1//2*a^-2*d^-1*(-7B+4A)*arctanh(sin(c+d*x))+1//3*a^-2*d^-1*(-16B+10A)*tan(c+d*x)+-1//2*a^-2*d^-1*(-7B+4A)*sec(c+d*x)*tan(c+d*x)+1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^3*(A+-1B)*tan(c+d*x)+1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^2*(-8B+5A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(a^-2*d^-1*(A+-2B)*arctanh(sin(c+d*x))+-1//3*a^-2*d^-1*(A+-4B)*tan(c+d*x)+-1*a^-2*d^-1*(1+sec(c+d*x))^-1*(A+-2B)*tan(c+d*x)+1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^2*(A+-1B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(B*a^-2*d^-1*arctanh(sin(c+d*x))+-1//3*d^-1*(a+a*sec(c+d*x))^-2*(A+-1B)*tan(c+d*x)+1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*(-5B+2A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*(A+B*sec(c+d*x))*sec(c+d*x), x) == :(1//3*d^-1*(a+a*sec(c+d*x))^-2*(A+-1B)*tan(c+d*x)+1//3*d^-1*(a^2+a^2*sec(c+d*x))^-1*(A+2B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*(A+B*sec(c+d*x)), x) == :(A*x*a^-2+-1//3*d^-1*(a+a*sec(c+d*x))^-2*(A+-1B)*tan(c+d*x)+-1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*(-1B+4A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*(A+B*sec(c+d*x))*cos(c+d*x), x) == :(-1*x*a^-2*(-1B+2A)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*(A+-1B)*sin(c+d*x)+1//3*a^-2*d^-1*(-4B+10A)*sin(c+d*x)+-1*a^-2*d^-1*(1+sec(c+d*x))^-1*(-1B+2A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^2*(A+B*sec(c+d*x)), x) == :((1/2)*x*a^-2*(-4B+7A)+-1//3*a^-2*d^-1*(-10B+16A)*sin(c+d*x)+(1/2)*a^-2*d^-1*(-4B+7A)*cos(c+d*x)*sin(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*(A+-1B)*cos(c+d*x)*sin(c+d*x)+-1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*(-5B+8A)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(-1//2*x*a^-2*(-7B+10A)+a^-2*d^-1*(-8B+12A)*sin(c+d*x)+-1//3*a^-2*d^-1*sin(c+d*x)^3*(-8B+12A)+-1//2*a^-2*d^-1*(-7B+10A)*cos(c+d*x)*sin(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)^2*(A+-1B)*sin(c+d*x)+-1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*cos(c+d*x)^2*(-7B+10A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^5*(A+B*sec(c+d*x)), x) == :(-1//2*a^-3*d^-1*(-13B+6A)*arctanh(sin(c+d*x))+1//15*a^-3*d^-1*(-152B+72A)*tan(c+d*x)+-1//2*a^-3*d^-1*(-13B+6A)*sec(c+d*x)*tan(c+d*x)+1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^4*(A+-1B)*tan(c+d*x)+1//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^2*(-76B+36A)*tan(c+d*x)+1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^3*(-11B+6A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^4*(A+B*sec(c+d*x)), x) == :(a^-3*d^-1*(A+-3B)*arctanh(sin(c+d*x))+-1*d^-1*(a^3+a^3*sec(c+d*x))^-1*(A+-3B)*tan(c+d*x)+-1//15*a^-3*d^-1*(-27B+7A)*tan(c+d*x)+1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^3*(A+-1B)*tan(c+d*x)+1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^2*(-9B+4A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(B*a^-3*d^-1*arctanh(sin(c+d*x))+1//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*(-29B+4A)*tan(c+d*x)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*(-7B+2A)*tan(c+d*x)+1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^2*(A+-1B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(-1//5*d^-1*(a+a*sec(c+d*x))^-3*(A+-1B)*tan(c+d*x)+1//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*(3A+7B)*tan(c+d*x)+1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*(-8B+3A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*(A+B*sec(c+d*x))*sec(c+d*x), x) == :(1//5*d^-1*(a+a*sec(c+d*x))^-3*(A+-1B)*tan(c+d*x)+1//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*(2A+3B)*tan(c+d*x)+1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*(2A+3B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*(A+B*sec(c+d*x)), x) == :(A*x*a^-3+-1//5*d^-1*(a+a*sec(c+d*x))^-3*(A+-1B)*tan(c+d*x)+-1//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*(-2B+22A)*tan(c+d*x)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*(-2B+7A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*(A+B*sec(c+d*x))*cos(c+d*x), x) == :(-1*x*a^-3*(-1B+3A)+-1*d^-1*(a^3+a^3*sec(c+d*x))^-1*(-1B+3A)*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*(A+-1B)*sin(c+d*x)+1//15*a^-3*d^-1*(-22B+72A)*sin(c+d*x)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*(-4B+9A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^2*(A+B*sec(c+d*x)), x) == :((1/2)*x*a^-3*(-6B+13A)+-1//15*a^-3*d^-1*(-72B+152A)*sin(c+d*x)+(1/2)*a^-3*d^-1*(-6B+13A)*cos(c+d*x)*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*(A+-1B)*cos(c+d*x)*sin(c+d*x)+-1//15*d^-1*(a^3+a^3*sec(c+d*x))^-1*(-36B+76A)*cos(c+d*x)*sin(c+d*x)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*(-6B+11A)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(-1//2*x*a^-3*(-13B+23A)+-1//15*a^-3*d^-1*sin(c+d*x)^3*(-76B+136A)+1//5*a^-3*d^-1*(-76B+136A)*sin(c+d*x)+-1//2*a^-3*d^-1*(-13B+23A)*cos(c+d*x)*sin(c+d*x)+-1//3*d^-1*(a^3+a^3*sec(c+d*x))^-1*cos(c+d*x)^2*(-13B+23A)*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*cos(c+d*x)^2*(A+-1B)*sin(c+d*x)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*cos(c+d*x)^2*(-8B+13A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*sec(c+d*x)^6*(A+B*sec(c+d*x)), x) == :(-1//2*a^-4*d^-1*(-21B+8A)*arctanh(sin(c+d*x))+1//105*a^-4*d^-1*(-1728B+664A)*tan(c+d*x)+-1//2*a^-4*d^-1*(-21B+8A)*sec(c+d*x)*tan(c+d*x)+1//7*d^-1*(a+a*sec(c+d*x))^-4*sec(c+d*x)^5*(A+-1B)*tan(c+d*x)+1//5*a^-1*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^4*(A+-2B)*tan(c+d*x)+1//105*a^-4*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^2*(-864B+332A)*tan(c+d*x)+1//105*a^-4*d^-1*(1+sec(c+d*x))^-2*sec(c+d*x)^3*(-129B+52A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*sec(c+d*x)^5*(A+B*sec(c+d*x)), x) == :(a^-4*d^-1*(A+-4B)*arctanh(sin(c+d*x))+-1//105*a^-4*d^-1*(-244B+55A)*tan(c+d*x)+-1*a^-4*d^-1*(1+sec(c+d*x))^-1*(A+-4B)*tan(c+d*x)+1//7*d^-1*(a+a*sec(c+d*x))^-4*sec(c+d*x)^4*(A+-1B)*tan(c+d*x)+1//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^3*(-12B+5A)*tan(c+d*x)+1//105*a^-4*d^-1*(1+sec(c+d*x))^-2*sec(c+d*x)^2*(-88B+25A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*sec(c+d*x)^4*(A+B*sec(c+d*x)), x) == :(B*a^-4*d^-1*arctanh(sin(c+d*x))+-1//105*a^-4*d^-1*(1+sec(c+d*x))^-2*(-55B+6A)*tan(c+d*x)+1//7*d^-1*(a+a*sec(c+d*x))^-4*sec(c+d*x)^3*(A+-1B)*tan(c+d*x)+1//105*a^-4*d^-1*(1+sec(c+d*x))^-1*(-215B+12A)*tan(c+d*x)+1//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^2*(-10B+3A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*sec(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(-1//105*d^-1*(a^2+a^2*sec(c+d*x))^-2*(24B+32A)*tan(c+d*x)+1//15*d^-1*(a^4+a^4*sec(c+d*x))^-1*(3B+4A)*tan(c+d*x)+-1//7*d^-1*(a+a*sec(c+d*x))^-4*sec(c+d*x)^3*(A+-1B)*tan(c+d*x)+1//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*(3B+4A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(-1//7*d^-1*(a+a*sec(c+d*x))^-4*(A+-1B)*tan(c+d*x)+1//105*d^-1*(a^2+a^2*sec(c+d*x))^-2*(8A+13B)*tan(c+d*x)+1//105*d^-1*(a^4+a^4*sec(c+d*x))^-1*(8A+13B)*tan(c+d*x)+1//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*(-11B+4A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*(A+B*sec(c+d*x))*sec(c+d*x), x) == :(1//7*d^-1*(a+a*sec(c+d*x))^-4*(A+-1B)*tan(c+d*x)+1//105*d^-1*(a^2+a^2*sec(c+d*x))^-2*(6A+8B)*tan(c+d*x)+1//105*d^-1*(a^4+a^4*sec(c+d*x))^-1*(6A+8B)*tan(c+d*x)+1//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*(3A+4B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*(A+B*sec(c+d*x)), x) == :(A*x*a^-4+-1//7*d^-1*(a+a*sec(c+d*x))^-4*(A+-1B)*tan(c+d*x)+-1//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*(-3B+10A)*tan(c+d*x)+-1//105*a^-4*d^-1*(1+sec(c+d*x))^-1*(-6B+160A)*tan(c+d*x)+-1//105*a^-4*d^-1*(1+sec(c+d*x))^-2*(-6B+55A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*(A+B*sec(c+d*x))*cos(c+d*x), x) == :(-1*x*a^-4*(-1B+4A)+-1//7*d^-1*(a+a*sec(c+d*x))^-4*(A+-1B)*sin(c+d*x)+1//105*a^-4*d^-1*(-160B+664A)*sin(c+d*x)+-1*a^-4*d^-1*(1+sec(c+d*x))^-1*(-1B+4A)*sin(c+d*x)+-1//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*(-5B+12A)*sin(c+d*x)+-1//105*a^-4*d^-1*(1+sec(c+d*x))^-2*(-25B+88A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*cos(c+d*x)^2*(A+B*sec(c+d*x)), x) == :((1/2)*x*a^-4*(-8B+21A)+-1//105*a^-4*d^-1*(-664B+1728A)*sin(c+d*x)+(1/2)*a^-4*d^-1*(-8B+21A)*cos(c+d*x)*sin(c+d*x)+-1//7*d^-1*(a+a*sec(c+d*x))^-4*(A+-1B)*cos(c+d*x)*sin(c+d*x)+-1//5*a^-1*d^-1*(a+a*sec(c+d*x))^-3*(-1B+2A)*cos(c+d*x)*sin(c+d*x)+-1//105*a^-4*d^-1*(1+sec(c+d*x))^-1*(-332B+864A)*cos(c+d*x)*sin(c+d*x)+-1//105*a^-4*d^-1*(1+sec(c+d*x))^-2*(-52B+129A)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-4*cos(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(-1//2*x*a^-4*(-21B+44A)+-1//105*a^-4*d^-1*sin(c+d*x)^3*(-864B+1816A)+1//35*a^-4*d^-1*(-864B+1816A)*sin(c+d*x)+-1//2*a^-4*d^-1*(-21B+44A)*cos(c+d*x)*sin(c+d*x)+-1//7*d^-1*(a+a*sec(c+d*x))^-4*cos(c+d*x)^2*(A+-1B)*sin(c+d*x)+-1//3*a^-4*d^-1*(1+sec(c+d*x))^-1*cos(c+d*x)^2*(-21B+44A)*sin(c+d*x)+-1//35*a^-1*d^-1*(a+a*sec(c+d*x))^-3*cos(c+d*x)^2*(-9B+16A)*sin(c+d*x)+-1//105*a^-4*d^-1*(1+sec(c+d*x))^-2*cos(c+d*x)^2*(-87B+178A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^4*(A+B*sec(c+d*x)), x) == :(-1//315*d^-1*(a+a*sec(c+d*x))^(1/2)*(64B+72A)*tan(c+d*x)+1//105*a^-1*d^-1*(a+a*sec(c+d*x))^3//2*(32B+36A)*tan(c+d*x)+4//45*a*d^-1*(a+a*sec(c+d*x))^-1//2*(8B+9A)*tan(c+d*x)+2//9*B*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^4*tan(c+d*x)+2//63*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*(8B+9A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(-1//105*d^-1*(a+a*sec(c+d*x))^(1/2)*(24B+28A)*tan(c+d*x)+1//35*a^-1*d^-1*(a+a*sec(c+d*x))^3//2*(12B+14A)*tan(c+d*x)+2//15*a*d^-1*(a+a*sec(c+d*x))^-1//2*(6B+7A)*tan(c+d*x)+2//7*B*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(1//15*d^-1*(a+a*sec(c+d*x))^(1/2)*(-4B+10A)*tan(c+d*x)+2//5*B*a^-1*d^-1*(a+a*sec(c+d*x))^3//2*tan(c+d*x)+2//15*a*d^-1*(a+a*sec(c+d*x))^-1//2*(5A+7B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*(A+B*sec(c+d*x))*sec(c+d*x), x) == :(2//3*B*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x)+2//3*a*d^-1*(a+a*sec(c+d*x))^-1//2*(B+3A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*(A+B*sec(c+d*x)), x) == :(2*A*a^(1/2)*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2*B*a*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*(A+B*sec(c+d*x))*cos(c+d*x), x) == :(a^(1/2)*d^-1*(A+2B)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+A*a*d^-1*(a+a*sec(c+d*x))^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(1//4*a^(1/2)*d^-1*(3A+4B)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//4*a*d^-1*(a+a*sec(c+d*x))^-1//2*(3A+4B)*sin(c+d*x)+(1/2)*A*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(1//8*a^(1/2)*d^-1*(5A+6B)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//8*a*d^-1*(a+a*sec(c+d*x))^-1//2*(5A+6B)*sin(c+d*x)+1//3*A*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*sin(c+d*x)+1//12*a*d^-1*(a+a*sec(c+d*x))^-1//2*(5A+6B)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^4*(A+B*sec(c+d*x)), x) == :(5//64*a^(1/2)*d^-1*(7A+8B)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+5//64*a*d^-1*(a+a*sec(c+d*x))^-1//2*(7A+8B)*sin(c+d*x)+1//4*A*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3*sin(c+d*x)+1//24*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*(7A+8B)*sin(c+d*x)+5//96*a*d^-1*(a+a*sec(c+d*x))^-1//2*(7A+8B)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(1//105*d^-1*(a+a*sec(c+d*x))^3//2*(68B+78A)*tan(c+d*x)+-4//315*a*d^-1*(a+a*sec(c+d*x))^(1/2)*(34B+39A)*tan(c+d*x)+2//45*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(34B+39A)*tan(c+d*x)+2//9*B*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3*tan(c+d*x)+2//63*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*(9A+10B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(1//35*d^-1*(a+a*sec(c+d*x))^3//2*(-4B+14A)*tan(c+d*x)+2//7*B*a^-1*d^-1*(a+a*sec(c+d*x))^5//2*tan(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^(1/2)*(19B+21A)*tan(c+d*x)+8//105*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(19B+21A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*(A+B*sec(c+d*x))*sec(c+d*x), x) == :(2//5*B*d^-1*(a+a*sec(c+d*x))^3//2*tan(c+d*x)+2//15*a*d^-1*(a+a*sec(c+d*x))^(1/2)*(3B+5A)*tan(c+d*x)+8//15*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(3B+5A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*(A+B*sec(c+d*x)), x) == :(2*A*a^3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//3*B*a*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x)+2//3*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(3A+4B)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*(A+B*sec(c+d*x))*cos(c+d*x), x) == :(a^3//2*d^-1*(2B+3A)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(A+-2B)*sin(c+d*x)+2*B*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(1//4*a^3//2*d^-1*(7A+12B)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//4*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(4B+5A)*sin(c+d*x)+(1/2)*A*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(1//8*a^3//2*d^-1*(11A+14B)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//8*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(11A+14B)*sin(c+d*x)+1//3*A*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^2*sin(c+d*x)+1//12*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(6B+7A)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^4*(A+B*sec(c+d*x)), x) == :(1//64*a^3//2*d^-1*(75A+88B)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//64*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(75A+88B)*sin(c+d*x)+1//4*A*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^3*sin(c+d*x)+1//24*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*(8B+9A)*sin(c+d*x)+1//96*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*(75A+88B)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(-4//3465*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(710B+803A)*tan(c+d*x)+2//495*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(710B+803A)*tan(c+d*x)+2//1155*a*d^-1*(a+a*sec(c+d*x))^3//2*(710B+803A)*tan(c+d*x)+2//11*B*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^3*tan(c+d*x)+2//99*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3*(11A+14B)*tan(c+d*x)+2//693*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*(194B+209A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(1//63*d^-1*(a+a*sec(c+d*x))^5//2*(-4B+18A)*tan(c+d*x)+2//9*B*a^-1*d^-1*(a+a*sec(c+d*x))^7//2*tan(c+d*x)+2//105*a*d^-1*(a+a*sec(c+d*x))^3//2*(13B+15A)*tan(c+d*x)+16//315*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(13B+15A)*tan(c+d*x)+64//315*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(13B+15A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*(A+B*sec(c+d*x))*sec(c+d*x), x) == :(2//7*B*d^-1*(a+a*sec(c+d*x))^5//2*tan(c+d*x)+2//35*a*d^-1*(a+a*sec(c+d*x))^3//2*(5B+7A)*tan(c+d*x)+16//105*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(5B+7A)*tan(c+d*x)+64//105*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(5B+7A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*(A+B*sec(c+d*x)), x) == :(2*A*a^5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//5*B*a*d^-1*(a+a*sec(c+d*x))^3//2*tan(c+d*x)+2//15*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(5A+8B)*tan(c+d*x)+2//15*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(32B+35A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*(A+B*sec(c+d*x))*cos(c+d*x), x) == :(a^5//2*d^-1*(2B+5A)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(A+2B)*sin(c+d*x)+-1//3*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(3A+14B)*sin(c+d*x)+2//3*B*a*d^-1*(a+a*sec(c+d*x))^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(1//4*a^5//2*d^-1*(19A+20B)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(A+-4B)*sin(c+d*x)+1//4*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(-4B+9A)*sin(c+d*x)+(1/2)*A*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(1//8*a^5//2*d^-1*(25A+38B)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//24*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(49A+54B)*sin(c+d*x)+1//3*A*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^2*sin(c+d*x)+1//4*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*(2B+3A)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^4*(A+B*sec(c+d*x)), x) == :(1//64*a^5//2*d^-1*(163A+200B)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//64*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(163A+200B)*sin(c+d*x)+1//4*A*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^3*sin(c+d*x)+1//24*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^2*(8B+11A)*sin(c+d*x)+1//96*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(95A+104B)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^5*(A+B*sec(c+d*x)), x) == :(1//128*a^5//2*d^-1*(283A+326B)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//128*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(283A+326B)*sin(c+d*x)+1//5*A*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^4*sin(c+d*x)+1//40*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^3*(10B+13A)*sin(c+d*x)+1//192*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*(283A+326B)*cos(c+d*x)*sin(c+d*x)+1//240*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*(157A+170B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^4*(A+B*sec(c+d*x)), x) == :(1//105*d^-1*(a+a*sec(c+d*x))^-1//2*(-148B+196A)*tan(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*(A+-1B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//105*a^-1*d^-1*(a+a*sec(c+d*x))^(1/2)*(-62B+14A)*tan(c+d*x)+1//35*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*(-2B+14A)*tan(c+d*x)+2//7*B*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(-1//15*d^-1*(a+a*sec(c+d*x))^-1//2*(-28B+20A)*tan(c+d*x)+2^(1/2)*a^-1//2*d^-1*(A+-1B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//15*a^-1*d^-1*(a+a*sec(c+d*x))^(1/2)*(-2B+10A)*tan(c+d*x)+2//5*B*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(1//3*d^-1*(a+a*sec(c+d*x))^-1//2*(-4B+6A)*tan(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*(A+-1B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//3*B*a^-1*d^-1*(a+a*sec(c+d*x))^(1/2)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*(A+B*sec(c+d*x))*sec(c+d*x), x) == :(2*B*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+2^(1/2)*a^-1//2*d^-1*(A+-1B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*(A+B*sec(c+d*x)), x) == :(2*A*a^-1//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1*2^(1/2)*a^-1//2*d^-1*(A+-1B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*(A+B*sec(c+d*x))*cos(c+d*x), x) == :(A*d^-1*(a+a*sec(c+d*x))^-1//2*sin(c+d*x)+-1*a^-1//2*d^-1*(A+-2B)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2^(1/2)*a^-1//2*d^-1*(A+-1B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-1//2*(A+-4B)*sin(c+d*x)+1//4*a^-1//2*d^-1*(-4B+7A)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*A*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)*sin(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*(A+-1B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(-1//8*a^-1//2*d^-1*(-14B+9A)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//8*d^-1*(a+a*sec(c+d*x))^-1//2*(-2B+7A)*sin(c+d*x)+2^(1/2)*a^-1//2*d^-1*(A+-1B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//12*d^-1*(a+a*sec(c+d*x))^-1//2*(A+-6B)*cos(c+d*x)*sin(c+d*x)+1//3*A*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^4*(A+B*sec(c+d*x)), x) == :((1/2)*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3*(A+-1B)*tan(c+d*x)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(-93B+65A)*tan(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(-15B+11A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//30*a^-2*d^-1*(a+a*sec(c+d*x))^(1/2)*(-39B+35A)*tan(c+d*x)+-1//10*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^2*(-9B+5A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3*(A+B*sec(c+d*x)), x) == :((1/2)*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^2*(A+-1B)*tan(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*(-11B+7A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//6*a^-2*d^-1*(a+a*sec(c+d*x))^(1/2)*(-7B+3A)*tan(c+d*x)+1//3*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(-13B+9A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*(A+-1B)*tan(c+d*x)+2*B*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(-7B+3A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*(A+B*sec(c+d*x))*sec(c+d*x), x) == :((1/2)*d^-1*(a+a*sec(c+d*x))^-3//2*(A+-1B)*tan(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(A+3B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*(A+B*sec(c+d*x)), x) == :(2*A*a^-3//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*(A+-1B)*tan(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*(-1B+5A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*(A+B*sec(c+d*x))*cos(c+d*x), x) == :(-1*a^-3//2*d^-1*(-2B+3A)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*(A+-1B)*sin(c+d*x)+(1/2)*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(-1B+3A)*sin(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(-5B+9A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(1//4*a^-3//2*d^-1*(-12B+19A)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*(A+-1B)*cos(c+d*x)*sin(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*(-9B+13A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(-6B+7A)*sin(c+d*x)+(1/2)*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(-1B+2A)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(-1//8*a^-3//2*d^-1*(-38B+47A)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^2*(A+-1B)*sin(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(-13B+17A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//8*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(-14B+21A)*sin(c+d*x)+-1//12*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*(-12B+13A)*cos(c+d*x)*sin(c+d*x)+1//6*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^2*(-3B+5A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^4*(A+B*sec(c+d*x)), x) == :(-1//32*2^(1/2)*a^-5//2*d^-1*(-163B+75A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//48*a^-3*d^-1*(a+a*sec(c+d*x))^(1/2)*(-95B+39A)*tan(c+d*x)+1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^3*(A+-1B)*tan(c+d*x)+1//24*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*(-197B+93A)*tan(c+d*x)+1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^2*(-17B+9A)*tan(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(-1//4*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*(A+-9B)*tan(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*(-13B+5A)*tan(c+d*x)+1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^2*(A+-1B)*tan(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(-75B+19A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*(A+-1B)*tan(c+d*x)+1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*(-13B+5A)*tan(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(5A+19B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*(A+B*sec(c+d*x))*sec(c+d*x), x) == :(1//4*d^-1*(a+a*sec(c+d*x))^-5//2*(A+-1B)*tan(c+d*x)+1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*(3A+5B)*tan(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(3A+5B)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*(A+B*sec(c+d*x)), x) == :(2*A*a^-5//2*d^-1*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*(A+-1B)*tan(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*(-3B+11A)*tan(c+d*x)+-1//32*2^(1/2)*a^-5//2*d^-1*(-3B+43A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*(A+B*sec(c+d*x))*cos(c+d*x), x) == :(-1*a^-5//2*d^-1*(-2B+5A)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*(A+-1B)*sin(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*(-7B+15A)*sin(c+d*x)+1//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*(-11B+35A)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(-43B+115A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(1//4*a^-5//2*d^-1*(-20B+39A)*arctan(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*(A+-1B)*cos(c+d*x)*sin(c+d*x)+-1//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*(-35B+63A)*sin(c+d*x)+-1//32*2^(1/2)*a^-5//2*d^-1*(-115B+219A)*arctan((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*(-11B+19A)*cos(c+d*x)*sin(c+d*x)+1//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*(-15B+31A)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+-1*a*sec(c+d*x))^-1//2*(A+A*sec(c+d*x)), x) == :(2*A*a^-1//2*d^-1*arctan(a^(1/2)*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x))+-2*A*2^(1/2)*a^-1//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+-1*a*sec(c+d*x))^-1//2*(A+A*sec(c+d*x))*cos(c+d*x), x) == :(A*d^-1*(a+-1*a*sec(c+d*x))^-1//2*sin(c+d*x)+3*A*a^-1//2*d^-1*arctan(a^(1/2)*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x))+-2*A*2^(1/2)*a^-1//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+-1*a*sec(c+d*x))^-1//2*cos(c+d*x)^2*(A+A*sec(c+d*x)), x) == :(5//4*A*d^-1*(a+-1*a*sec(c+d*x))^-1//2*sin(c+d*x)+11//4*A*a^-1//2*d^-1*arctan(a^(1/2)*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*A*d^-1*(a+-1*a*sec(c+d*x))^-1//2*cos(c+d*x)*sin(c+d*x)+-2*A*2^(1/2)*a^-1//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+-1*a*sec(c+d*x))^-1//2*cos(c+d*x)^3*(A+A*sec(c+d*x)), x) == :(9//8*A*d^-1*(a+-1*a*sec(c+d*x))^-1//2*sin(c+d*x)+23//8*A*a^-1//2*d^-1*arctan(a^(1/2)*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x))+-2*A*2^(1/2)*a^-1//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x))+1//3*A*d^-1*(a+-1*a*sec(c+d*x))^-1//2*cos(c+d*x)^2*sin(c+d*x)+7//12*A*d^-1*(a+-1*a*sec(c+d*x))^-1//2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+-1*a*sec(c+d*x))^-3//2*(A+A*sec(c+d*x))*cos(c+d*x), x) == :(-1*A*d^-1*(a+-1*a*sec(c+d*x))^-3//2*sin(c+d*x)+5*A*a^-3//2*d^-1*arctan(a^(1/2)*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x))+2*A*a^-1*d^-1*(a+-1*a*sec(c+d*x))^-1//2*sin(c+d*x)+-7//2*A*2^(1/2)*a^-3//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+-1*a*sec(c+d*x))^-3//2*cos(c+d*x)^2*(A+A*sec(c+d*x)), x) == :(31//4*A*a^-3//2*d^-1*arctan(a^(1/2)*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x))+-1*A*d^-1*(a+-1*a*sec(c+d*x))^-3//2*cos(c+d*x)*sin(c+d*x)+-11//2*A*2^(1/2)*a^-3//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x))+13//4*A*a^-1*d^-1*(a+-1*a*sec(c+d*x))^-1//2*sin(c+d*x)+3//2*A*a^-1*d^-1*(a+-1*a*sec(c+d*x))^-1//2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+-1*a*sec(c+d*x))^-3//2*cos(c+d*x)^3*(A+A*sec(c+d*x)), x) == :(85//8*A*a^-3//2*d^-1*arctan(a^(1/2)*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x))+-1*A*d^-1*(a+-1*a*sec(c+d*x))^-3//2*cos(c+d*x)^2*sin(c+d*x)+-15//2*A*2^(1/2)*a^-3//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x))+35//8*A*a^-1*d^-1*(a+-1*a*sec(c+d*x))^-1//2*sin(c+d*x)+4//3*A*a^-1*d^-1*(a+-1*a*sec(c+d*x))^-1//2*cos(c+d*x)^2*sin(c+d*x)+25//12*A*a^-1*d^-1*(a+-1*a*sec(c+d*x))^-1//2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+-1*a*sec(c+d*x))^-5//2*(A+A*sec(c+d*x))*cos(c+d*x), x) == :(7*A*a^-5//2*d^-1*arctan(a^(1/2)*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*A*d^-1*(a+-1*a*sec(c+d*x))^-5//2*sin(c+d*x)+-79//16*A*2^(1/2)*a^-5//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x))+-11//8*A*a^-1*d^-1*(a+-1*a*sec(c+d*x))^-3//2*sin(c+d*x)+23//8*A*a^-2*d^-1*(a+-1*a*sec(c+d*x))^-1//2*sin(c+d*x))
@test integrate((a+-1*a*sec(c+d*x))^-5//2*cos(c+d*x)^2*(A+A*sec(c+d*x)), x) == :(59//4*A*a^-5//2*d^-1*arctan(a^(1/2)*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x))+-167//16*A*2^(1/2)*a^-5//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*A*d^-1*(a+-1*a*sec(c+d*x))^-5//2*cos(c+d*x)*sin(c+d*x)+49//8*A*a^-2*d^-1*(a+-1*a*sec(c+d*x))^-1//2*sin(c+d*x)+-15//8*A*a^-1*d^-1*(a+-1*a*sec(c+d*x))^-3//2*cos(c+d*x)*sin(c+d*x)+23//8*A*a^-2*d^-1*(a+-1*a*sec(c+d*x))^-1//2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+-1*a*sec(c+d*x))^-5//2*cos(c+d*x)^3*(A+A*sec(c+d*x)), x) == :(203//8*A*a^-5//2*d^-1*arctan(a^(1/2)*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x))+-287//16*A*2^(1/2)*a^-5//2*d^-1*arctan((1/2)*2^(1/2)*a^(1/2)*(a+-1*a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*A*d^-1*(a+-1*a*sec(c+d*x))^-5//2*cos(c+d*x)^2*sin(c+d*x)+21//2*A*a^-2*d^-1*(a+-1*a*sec(c+d*x))^-1//2*sin(c+d*x)+-19//8*A*a^-1*d^-1*(a+-1*a*sec(c+d*x))^-3//2*cos(c+d*x)^2*sin(c+d*x)+77//24*A*a^-2*d^-1*(a+-1*a*sec(c+d*x))^-1//2*cos(c+d*x)^2*sin(c+d*x)+119//24*A*a^-2*d^-1*(a+-1*a*sec(c+d*x))^-1//2*cos(c+d*x)*sin(c+d*x))
@test integrate(sec(c+d*x)^5//2*(A+B*sec(c+d*x))*(a+a*sec(c+d*x)), x) == :(2//5*a*d^-1*sec(c+d*x)^5//2*(A+B)*sin(c+d*x)+2//7*B*a*d^-1*sec(c+d*x)^7//2*sin(c+d*x)+2//21*a*d^-1*sec(c+d*x)^3//2*(5B+7A)*sin(c+d*x)+6//5*a*d^-1*sec(c+d*x)^(1/2)*(A+B)*sin(c+d*x)+-6//5*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//21*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5B+7A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^3//2*(A+B*sec(c+d*x))*(a+a*sec(c+d*x)), x) == :(2//3*a*d^-1*sec(c+d*x)^3//2*(A+B)*sin(c+d*x)+2//5*B*a*d^-1*sec(c+d*x)^5//2*sin(c+d*x)+2//5*a*d^-1*sec(c+d*x)^(1/2)*(3B+5A)*sin(c+d*x)+-2//5*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3B+5A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+B)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^(1/2)*(A+B*sec(c+d*x))*(a+a*sec(c+d*x)), x) == :(2*a*d^-1*sec(c+d*x)^(1/2)*(A+B)*sin(c+d*x)+2//3*B*a*d^-1*sec(c+d*x)^3//2*sin(c+d*x)+-2*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(B+3A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^-1//2*(A+B*sec(c+d*x))*(a+a*sec(c+d*x)), x) == :(2*B*a*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+2*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1B)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^-3//2*(A+B*sec(c+d*x))*(a+a*sec(c+d*x)), x) == :(2//3*A*a*d^-1*sec(c+d*x)^-1//2*sin(c+d*x)+2*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+3B)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^-5//2*(A+B*sec(c+d*x))*(a+a*sec(c+d*x)), x) == :(2//3*a*d^-1*sec(c+d*x)^-1//2*(A+B)*sin(c+d*x)+2//5*A*a*d^-1*sec(c+d*x)^-3//2*sin(c+d*x)+2//3*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3A+5B)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate(sec(c+d*x)^-7//2*(A+B*sec(c+d*x))*(a+a*sec(c+d*x)), x) == :(2//5*a*d^-1*sec(c+d*x)^-3//2*(A+B)*sin(c+d*x)+2//7*A*a*d^-1*sec(c+d*x)^-5//2*sin(c+d*x)+2//21*a*d^-1*sec(c+d*x)^-1//2*(5A+7B)*sin(c+d*x)+2//21*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5A+7B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+6//5*a*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+B)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(2//7*B*d^-1*sec(c+d*x)^5//2*(a^2+a^2*sec(c+d*x))*sin(c+d*x)+2//35*a^2*d^-1*sec(c+d*x)^5//2*(7A+9B)*sin(c+d*x)+4//5*a^2*d^-1*sec(c+d*x)^(1/2)*(3B+4A)*sin(c+d*x)+4//21*a^2*d^-1*sec(c+d*x)^3//2*(6B+7A)*sin(c+d*x)+-4//5*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3B+4A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(6B+7A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(2//5*B*d^-1*sec(c+d*x)^3//2*(a^2+a^2*sec(c+d*x))*sin(c+d*x)+2//15*a^2*d^-1*sec(c+d*x)^3//2*(5A+7B)*sin(c+d*x)+4//5*a^2*d^-1*sec(c+d*x)^(1/2)*(4B+5A)*sin(c+d*x)+-4//5*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(4B+5A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//3*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(B+2A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(2//3*B*d^-1*sec(c+d*x)^(1/2)*(a^2+a^2*sec(c+d*x))*sin(c+d*x)+2//3*a^2*d^-1*sec(c+d*x)^(1/2)*(3A+5B)*sin(c+d*x)+-4*B*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//3*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2B+3A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(-2//3*a^2*d^-1*sec(c+d*x)^(1/2)*(A+-3B)*sin(c+d*x)+2//3*A*d^-1*sec(c+d*x)^-1//2*(a^2+a^2*sec(c+d*x))*sin(c+d*x)+4*A*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//3*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2A+3B)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :(2//5*A*d^-1*sec(c+d*x)^-3//2*(a^2+a^2*sec(c+d*x))*sin(c+d*x)+2//15*a^2*d^-1*sec(c+d*x)^-1//2*(5B+7A)*sin(c+d*x)+4//3*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+2B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+4//5*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(4A+5B)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^-7//2*(A+B*sec(c+d*x)), x) == :(2//7*A*d^-1*sec(c+d*x)^-5//2*(a^2+a^2*sec(c+d*x))*sin(c+d*x)+2//35*a^2*d^-1*sec(c+d*x)^-3//2*(7B+9A)*sin(c+d*x)+4//21*a^2*d^-1*sec(c+d*x)^-1//2*(6A+7B)*sin(c+d*x)+4//5*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3A+4B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(6A+7B)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^2*sec(c+d*x)^-9//2*(A+B*sec(c+d*x)), x) == :(2//9*A*d^-1*sec(c+d*x)^-7//2*(a^2+a^2*sec(c+d*x))*sin(c+d*x)+2//63*a^2*d^-1*sec(c+d*x)^-5//2*(9B+11A)*sin(c+d*x)+4//21*a^2*d^-1*sec(c+d*x)^-1//2*(5A+6B)*sin(c+d*x)+4//45*a^2*d^-1*sec(c+d*x)^-3//2*(8A+9B)*sin(c+d*x)+4//15*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(8A+9B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5A+6B)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(1//63*d^-1*sec(c+d*x)^5//2*(a^3+a^3*sec(c+d*x))*(18A+26B)*sin(c+d*x)+4//15*a^3*d^-1*sec(c+d*x)^(1/2)*(17B+21A)*sin(c+d*x)+4//21*a^3*d^-1*sec(c+d*x)^3//2*(11B+13A)*sin(c+d*x)+4//105*a^3*d^-1*sec(c+d*x)^5//2*(23B+24A)*sin(c+d*x)+-4//15*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(17B+21A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//9*B*a*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^5//2*sin(c+d*x)+4//21*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(11B+13A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(1//35*d^-1*sec(c+d*x)^3//2*(a^3+a^3*sec(c+d*x))*(14A+22B)*sin(c+d*x)+4//5*a^3*d^-1*sec(c+d*x)^(1/2)*(7B+9A)*sin(c+d*x)+4//105*a^3*d^-1*sec(c+d*x)^3//2*(41B+42A)*sin(c+d*x)+-4//5*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(7B+9A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//7*B*a*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^3//2*sin(c+d*x)+4//21*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(13B+21A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(1//15*d^-1*sec(c+d*x)^(1/2)*(a^3+a^3*sec(c+d*x))*(10A+18B)*sin(c+d*x)+4//15*a^3*d^-1*sec(c+d*x)^(1/2)*(20A+21B)*sin(c+d*x)+-4//5*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5A+9B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//5*B*a*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^(1/2)*sin(c+d*x)+4//3*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3B+5A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(-1//3*d^-1*sec(c+d*x)^(1/2)*(a^3+a^3*sec(c+d*x))*(-2B+2A)*sin(c+d*x)+4//3*a^3*d^-1*sec(c+d*x)^(1/2)*(A+4B)*sin(c+d*x)+4*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*A*a*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^-1//2*sin(c+d*x)+20//3*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+B)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :(-4//15*a^3*d^-1*sec(c+d*x)^(1/2)*(-5B+6A)*sin(c+d*x)+1//15*d^-1*sec(c+d*x)^-1//2*(a^3+a^3*sec(c+d*x))*(10B+18A)*sin(c+d*x)+2//5*A*a*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^-3//2*sin(c+d*x)+4//3*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3A+5B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+4//5*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5B+9A)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^-7//2*(A+B*sec(c+d*x)), x) == :(1//35*d^-1*sec(c+d*x)^-3//2*(a^3+a^3*sec(c+d*x))*(14B+22A)*sin(c+d*x)+4//105*a^3*d^-1*sec(c+d*x)^-1//2*(41A+42B)*sin(c+d*x)+2//7*A*a*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^-5//2*sin(c+d*x)+4//5*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(7A+9B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(13A+21B)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^-9//2*(A+B*sec(c+d*x)), x) == :(1//63*d^-1*sec(c+d*x)^-5//2*(a^3+a^3*sec(c+d*x))*(18B+26A)*sin(c+d*x)+4//21*a^3*d^-1*sec(c+d*x)^-1//2*(11A+13B)*sin(c+d*x)+4//105*a^3*d^-1*sec(c+d*x)^-3//2*(23A+24B)*sin(c+d*x)+2//9*A*a*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^-7//2*sin(c+d*x)+4//15*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(17A+21B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(11A+13B)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^3*sec(c+d*x)^-11//2*(A+B*sec(c+d*x)), x) == :(1//99*d^-1*sec(c+d*x)^-7//2*(a^3+a^3*sec(c+d*x))*(22B+30A)*sin(c+d*x)+4//45*a^3*d^-1*sec(c+d*x)^-3//2*(15A+17B)*sin(c+d*x)+4//231*a^3*d^-1*sec(c+d*x)^-1//2*(105A+121B)*sin(c+d*x)+20//693*a^3*d^-1*sec(c+d*x)^-5//2*(21A+22B)*sin(c+d*x)+2//11*A*a*d^-1*(a+a*sec(c+d*x))^2*sec(c+d*x)^-9//2*sin(c+d*x)+4//15*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(15A+17B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//231*a^3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(105A+121B)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^7//2*(A+B*sec(c+d*x)), x) == :(d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^7//2*(A+-1B)*sin(c+d*x)+-1//5*a^-1*d^-1*sec(c+d*x)^(1/2)*(-21B+15A)*sin(c+d*x)+-1//5*a^-1*d^-1*sec(c+d*x)^5//2*(-7B+5A)*sin(c+d*x)+1//3*a^-1*d^-1*sec(c+d*x)^3//2*(-5B+5A)*sin(c+d*x)+1//3*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-5B+5A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-21B+15A)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^5//2*(A+B*sec(c+d*x)), x) == :(a^-1*d^-1*sec(c+d*x)^(1/2)*(-3B+3A)*sin(c+d*x)+d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^5//2*(A+-1B)*sin(c+d*x)+-1//3*a^-1*d^-1*sec(c+d*x)^3//2*(-5B+3A)*sin(c+d*x)+a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-3A+3B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//3*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-5B+3A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^3//2*(A+-1B)*sin(c+d*x)+-1*a^-1*d^-1*sec(c+d*x)^(1/2)*(A+-3B)*sin(c+d*x)+a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-3B)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^(1/2)*(A+-1B)*sin(c+d*x)+a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1B)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^(1/2)*(A+-1B)*sin(c+d*x)+a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-1B+3A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1B)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^-1//2*(A+-1B)*sin(c+d*x)+1//3*a^-1*d^-1*sec(c+d*x)^-1//2*(-3B+5A)*sin(c+d*x)+a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-3A+3B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-3B+5A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :(-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^-3//2*(A+-1B)*sin(c+d*x)+-1//3*a^-1*d^-1*sec(c+d*x)^-1//2*(-5B+5A)*sin(c+d*x)+1//5*a^-1*d^-1*sec(c+d*x)^-3//2*(-5B+7A)*sin(c+d*x)+-1//3*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-5B+5A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-15B+21A)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-1*sec(c+d*x)^-7//2*(A+B*sec(c+d*x)), x) == :(-1*d^-1*(a+a*sec(c+d*x))^-1*sec(c+d*x)^-5//2*(A+-1B)*sin(c+d*x)+-1//5*a^-1*d^-1*sec(c+d*x)^-3//2*(-7B+7A)*sin(c+d*x)+1//7*a^-1*d^-1*sec(c+d*x)^-5//2*(-7B+9A)*sin(c+d*x)+1//21*a^-1*d^-1*sec(c+d*x)^-1//2*(-35B+45A)*sin(c+d*x)+1//5*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-21A+21B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*a^-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-35B+45A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^7//2*(A+B*sec(c+d*x)), x) == :(a^-2*d^-1*sec(c+d*x)^(1/2)*(-7B+4A)*sin(c+d*x)+-1//3*a^-2*d^-1*sec(c+d*x)^3//2*(-10B+5A)*sin(c+d*x)+1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^7//2*(A+-1B)*sin(c+d*x)+-1*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-7B+4A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-10B+5A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^5//2*(-7B+4A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^5//2*(A+B*sec(c+d*x)), x) == :(-1*a^-2*d^-1*sec(c+d*x)^(1/2)*(A+-4B)*sin(c+d*x)+1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^5//2*(A+-1B)*sin(c+d*x)+a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-4B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^3//2*(-5B+2A)*sin(c+d*x)+1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-5B+2A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^3//2*(A+-1B)*sin(c+d*x)+B*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1*B*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+2B)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^(1/2)*(A+-1B)*sin(c+d*x)+-1*A*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^(1/2)*(B+2A)*sin(c+d*x)+1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(B+2A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^(1/2)*(A+-1B)*sin(c+d*x)+a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-1B+4A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^(1/2)*(-2B+5A)*sin(c+d*x)+-1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-2B+5A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^-1//2*(A+-1B)*sin(c+d*x)+1//3*a^-2*d^-1*sec(c+d*x)^-1//2*(-5B+10A)*sin(c+d*x)+-1*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-4B+7A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//3*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^-1//2*(-4B+7A)*sin(c+d*x)+1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-5B+10A)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-2*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :(-1//3*a^-2*d^-1*sec(c+d*x)^-1//2*(-10B+15A)*sin(c+d*x)+-1//3*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^-3//2*(A+-1B)*sin(c+d*x)+1//15*a^-2*d^-1*sec(c+d*x)^-3//2*(-35B+56A)*sin(c+d*x)+-1*a^-2*d^-1*(1+sec(c+d*x))^-1*sec(c+d*x)^-3//2*(-2B+3A)*sin(c+d*x)+-1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-10B+15A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*a^-2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-35B+56A)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^9//2*(A+B*sec(c+d*x)), x) == :(-1//6*a^-3*d^-1*sec(c+d*x)^3//2*(-33B+13A)*sin(c+d*x)+1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^9//2*(A+-1B)*sin(c+d*x)+1//10*a^-3*d^-1*sec(c+d*x)^(1/2)*(-119B+49A)*sin(c+d*x)+1//30*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^5//2*(-119B+49A)*sin(c+d*x)+-1//6*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-33B+13A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//3*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^7//2*(A+-2B)*sin(c+d*x)+1//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-49A+119B)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^7//2*(A+B*sec(c+d*x)), x) == :(-1//10*a^-3*d^-1*sec(c+d*x)^(1/2)*(-49B+9A)*sin(c+d*x)+1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^7//2*(A+-1B)*sin(c+d*x)+1//6*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^3//2*(-13B+3A)*sin(c+d*x)+1//6*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-13B+3A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-49B+9A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^5//2*(-8B+3A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^5//2*(A+B*sec(c+d*x)), x) == :(-1//10*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^(1/2)*(A+9B)*sin(c+d*x)+1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^5//2*(A+-1B)*sin(c+d*x)+1//6*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+3B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+9B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^3//2*(A+-6B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^3//2*(A+-1B)*sin(c+d*x)+1//6*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^(1/2)*(A+B)*sin(c+d*x)+-1//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^(1/2)*(A+4B)*sin(c+d*x)+1//6*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+B)*Elliptic.F((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^(1/2)*(A+-1B)*sin(c+d*x)+1//6*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^(1/2)*(B+3A)*sin(c+d*x)+-1//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(B+9A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//6*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(B+3A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^(1/2)*(2B+3A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^(1/2)*(A+-1B)*sin(c+d*x)+-1//6*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^(1/2)*(-3B+13A)*sin(c+d*x)+-1//6*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-3B+13A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^(1/2)*(-3B+8A)*sin(c+d*x)+1//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-9B+49A)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^-1//2*(A+-1B)*sin(c+d*x)+-1//30*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^-1//2*(-49B+119A)*sin(c+d*x)+1//6*a^-3*d^-1*sec(c+d*x)^-1//2*(-13B+33A)*sin(c+d*x)+-1//3*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^-1//2*(-1B+2A)*sin(c+d*x)+1//6*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-13B+33A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-119A+49B)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^-3*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :(-1//2*a^-3*d^-1*sec(c+d*x)^-1//2*(-11B+21A)*sin(c+d*x)+-1//5*d^-1*(a+a*sec(c+d*x))^-3*sec(c+d*x)^-3//2*(A+-1B)*sin(c+d*x)+-1//10*d^-1*(a^3+a^3*sec(c+d*x))^-1*sec(c+d*x)^-3//2*(-33B+63A)*sin(c+d*x)+1//30*a^-3*d^-1*sec(c+d*x)^-3//2*(-119B+231A)*sin(c+d*x)+-1//2*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-11B+21A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//15*a^-1*d^-1*(a+a*sec(c+d*x))^-2*sec(c+d*x)^-3//2*(-7B+12A)*sin(c+d*x)+1//10*a^-3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-119B+231A)*Elliptic.E((1/2)*c+(1/2)*d*x,2))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^5//2*(A+B*sec(c+d*x)), x) == :(1//8*a^(1/2)*d^-1*(5B+6A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//3*B*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^7//2*sin(c+d*x)+1//8*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(5B+6A)*sin(c+d*x)+1//12*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*(5B+6A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(1//4*a^(1/2)*d^-1*(3B+4A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*B*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*sin(c+d*x)+1//4*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(3B+4A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(a^(1/2)*d^-1*(B+2A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+B*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(2*B*a^(1/2)*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2*A*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(2//3*A*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*sin(c+d*x)+2//3*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(A+3B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :(2//5*A*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*sin(c+d*x)+2//15*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(4A+5B)*sin(c+d*x)+4//15*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(4A+5B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-7//2*(A+B*sec(c+d*x)), x) == :(2//7*A*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-5//2*sin(c+d*x)+2//35*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(6A+7B)*sin(c+d*x)+8//105*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(6A+7B)*sin(c+d*x)+16//105*a*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(6A+7B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^5//2*(A+B*sec(c+d*x)), x) == :(1//64*a^3//2*d^-1*(75B+88A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//4*B*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^7//2*sin(c+d*x)+1//24*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^7//2*(8A+9B)*sin(c+d*x)+1//64*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(75B+88A)*sin(c+d*x)+1//96*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*(75B+88A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(1//8*a^3//2*d^-1*(11B+14A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//3*B*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^5//2*sin(c+d*x)+1//8*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(11B+14A)*sin(c+d*x)+1//12*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*(6A+7B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(1//4*a^3//2*d^-1*(7B+12A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*B*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3//2*sin(c+d*x)+1//4*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(4A+5B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(a^3//2*d^-1*(2A+3B)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+B*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*sin(c+d*x)+a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-1B+2A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(2*B*a^3//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//3*A*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*sin(c+d*x)+2//3*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(3B+4A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :(2//5*A*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-3//2*sin(c+d*x)+2//15*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(3A+5B)*sin(c+d*x)+8//15*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(3A+5B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^-7//2*(A+B*sec(c+d*x)), x) == :(2//7*A*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*sin(c+d*x)+2//35*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(7B+8A)*sin(c+d*x)+2//105*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(52A+63B)*sin(c+d*x)+4//105*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(52A+63B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*sec(c+d*x)^-9//2*(A+B*sec(c+d*x)), x) == :(2//9*A*a*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-7//2*sin(c+d*x)+2//63*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-5//2*(9B+10A)*sin(c+d*x)+2//105*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(34A+39B)*sin(c+d*x)+8//315*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(34A+39B)*sin(c+d*x)+16//315*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(34A+39B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^5//2*(A+B*sec(c+d*x)), x) == :(1//128*a^5//2*d^-1*(283B+326A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//5*B*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^7//2*sin(c+d*x)+1//40*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^7//2*(10A+13B)*sin(c+d*x)+1//128*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(283B+326A)*sin(c+d*x)+1//192*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*(283B+326A)*sin(c+d*x)+1//240*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^7//2*(157B+170A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(1//64*a^5//2*d^-1*(163B+200A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//4*B*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^5//2*sin(c+d*x)+1//24*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^5//2*(8A+11B)*sin(c+d*x)+1//64*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(163B+200A)*sin(c+d*x)+1//96*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*(95B+104A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(1//8*a^5//2*d^-1*(25B+38A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//3*B*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^3//2*sin(c+d*x)+1//4*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^3//2*(2A+3B)*sin(c+d*x)+1//24*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(49B+54A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(1//4*a^5//2*d^-1*(19B+20A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*B*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^(1/2)*sin(c+d*x)+1//4*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*(4A+7B)*sin(c+d*x)+1//4*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-9B+4A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(a^5//2*d^-1*(2A+5B)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//3*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^(1/2)*(-3B+2A)*sin(c+d*x)+1//3*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(3B+14A)*sin(c+d*x)+2//3*A*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :(2*B*a^5//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//5*A*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-3//2*sin(c+d*x)+2//15*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(5B+8A)*sin(c+d*x)+2//15*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(32A+35B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-7//2*(A+B*sec(c+d*x)), x) == :(2//7*A*d^-1*(a+a*sec(c+d*x))^5//2*sec(c+d*x)^-5//2*sin(c+d*x)+2//35*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-3//2*(5A+7B)*sin(c+d*x)+16//105*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(5A+7B)*sin(c+d*x)+64//105*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(5A+7B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-9//2*(A+B*sec(c+d*x)), x) == :(2//9*A*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-7//2*sin(c+d*x)+2//21*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*(3B+4A)*sin(c+d*x)+2//315*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(124A+135B)*sin(c+d*x)+2//315*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(292A+345B)*sin(c+d*x)+4//315*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(292A+345B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*sec(c+d*x)^-11//2*(A+B*sec(c+d*x)), x) == :(2//11*A*a*d^-1*(a+a*sec(c+d*x))^3//2*sec(c+d*x)^-9//2*sin(c+d*x)+2//99*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*sec(c+d*x)^-7//2*(11B+14A)*sin(c+d*x)+2//693*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-5//2*(194A+209B)*sin(c+d*x)+2//1155*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(710A+803B)*sin(c+d*x)+8//3465*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(710A+803B)*sin(c+d*x)+16//3465*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(710A+803B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*(A+B*sec(c+d*x)), x) == :(-1//4*a^-1//2*d^-1*(-7B+4A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2^(1/2)*a^-1//2*d^-1*(A+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+(1/2)*B*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*sin(c+d*x)+1//4*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(-1B+4A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(a^-1//2*d^-1*(-1B+2A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+B*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*sin(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*(A+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(2*B*a^-1//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2^(1/2)*a^-1//2*d^-1*(A+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(-1*2^(1/2)*a^-1//2*d^-1*(A+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+2*A*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(2^(1/2)*a^-1//2*d^-1*(A+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//3*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-6B+2A)*sin(c+d*x)+2//3*A*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :(-1*2^(1/2)*a^-1//2*d^-1*(A+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//15*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(-10B+2A)*sin(c+d*x)+1//15*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-10B+26A)*sin(c+d*x)+2//5*A*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-7//2*(A+B*sec(c+d*x)), x) == :(2^(1/2)*a^-1//2*d^-1*(A+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//35*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(-14B+2A)*sin(c+d*x)+-1//105*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-182B+86A)*sin(c+d*x)+1//105*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(-14B+62A)*sin(c+d*x)+2//7*A*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-5//2*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^7//2*(A+B*sec(c+d*x)), x) == :(-1//4*a^-3//2*d^-1*(-19B+12A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^7//2*(A+-1B)*sin(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(-13B+9A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//2*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^5//2*(A+-2B)*sin(c+d*x)+1//4*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(-7B+6A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^5//2*(A+B*sec(c+d*x)), x) == :(a^-3//2*d^-1*(-3B+2A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^5//2*(A+-1B)*sin(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*(-9B+5A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//2*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(A+-3B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(2*B*a^-3//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+(1/2)*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3//2*(A+-1B)*sin(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(A+-5B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3//2*(A+-1B)*sin(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(B+3A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^(1/2)*(A+-1B)*sin(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*(-3B+7A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+(1/2)*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-1B+5A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-1//2*(A+-1B)*sin(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*(-7B+11A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//6*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-15B+19A)*sin(c+d*x)+1//6*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(-3B+7A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-3//2*(A+-1B)*sin(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*(-11B+15A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//30*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(-35B+39A)*sin(c+d*x)+1//10*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(-5B+9A)*sin(c+d*x)+1//30*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-95B+147A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^7//2*(A+B*sec(c+d*x)), x) == :(a^-5//2*d^-1*(-5B+2A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//32*2^(1/2)*a^-5//2*d^-1*(-115B+43A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^7//2*(A+-1B)*sin(c+d*x)+-1//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^3//2*(-35B+11A)*sin(c+d*x)+1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^5//2*(-15B+7A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^5//2*(A+B*sec(c+d*x)), x) == :(2*B*a^-5//2*d^-1*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^5//2*(A+-1B)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(-43B+3A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3//2*(-11B+3A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^5//2*(A+-1B)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(3B+5A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^3//2*(3B+5A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^(1/2)*(A+-1B)*sin(c+d*x)+-1//32*2^(1/2)*a^-5//2*d^-1*(-19B+75A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^(1/2)*(-5B+13A)*sin(c+d*x)+1//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-9B+49A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^-1//2*(A+-1B)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*(-75B+163A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-1//2*(-9B+17A)*sin(c+d*x)+-1//48*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-147B+299A)*sin(c+d*x)+1//48*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(-39B+95A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-5//2*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*sec(c+d*x)^-3//2*(A+-1B)*sin(c+d*x)+-1//32*2^(1/2)*a^-5//2*d^-1*(-163B+283A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x))+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*sec(c+d*x)^-3//2*(-13B+21A)*sin(c+d*x)+-1//240*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(-475B+787A)*sin(c+d*x)+1//80*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(-85B+157A)*sin(c+d*x)+1//240*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-1495B+2671A)*sin(c+d*x))
@test integrate(sec(c+d*x)^3*(A+B*sec(c+d*x))*(a+b*sec(c+d*x)), x) == :(d^-1*(A*b+B*a)*tan(c+d*x)+1//3*d^-1*tan(c+d*x)^3*(A*b+B*a)+1//8*d^-1*(3*B*b+4*A*a)*arctanh(sin(c+d*x))+1//8*d^-1*(3*B*b+4*A*a)*sec(c+d*x)*tan(c+d*x)+1//4*B*b*d^-1*sec(c+d*x)^3*tan(c+d*x))
@test integrate(sec(c+d*x)^2*(A+B*sec(c+d*x))*(a+b*sec(c+d*x)), x) == :((1/2)*d^-1*(A*b+B*a)*arctanh(sin(c+d*x))+1//3*d^-1*(2*B*b+3*A*a)*tan(c+d*x)+(1/2)*d^-1*(A*b+B*a)*sec(c+d*x)*tan(c+d*x)+1//3*B*b*d^-1*sec(c+d*x)^2*tan(c+d*x))
@test integrate((A+B*sec(c+d*x))*(a+b*sec(c+d*x))*sec(c+d*x), x) == :(d^-1*(A*b+B*a)*tan(c+d*x)+(1/2)*d^-1*(B*b+2*A*a)*arctanh(sin(c+d*x))+(1/2)*B*b*d^-1*sec(c+d*x)*tan(c+d*x))
@test integrate((A+B*sec(c+d*x))*(a+b*sec(c+d*x)), x) == :(A*a*x+d^-1*(A*b+B*a)*arctanh(sin(c+d*x))+B*b*d^-1*tan(c+d*x))
@test integrate((A+B*sec(c+d*x))*(a+b*sec(c+d*x))*cos(c+d*x), x) == :(x*(A*b+B*a)+A*a*d^-1*sin(c+d*x)+B*b*d^-1*arctanh(sin(c+d*x)))
@test integrate(cos(c+d*x)^2*(A+B*sec(c+d*x))*(a+b*sec(c+d*x)), x) == :(x*(B*b+(1/2)*A*a)+d^-1*(A*b+B*a)*sin(c+d*x)+(1/2)*A*a*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate(cos(c+d*x)^3*(A+B*sec(c+d*x))*(a+b*sec(c+d*x)), x) == :(x*((1/2)*A*b+(1/2)*B*a)+1//3*d^-1*(2*A*a+3*B*b)*sin(c+d*x)+(1/2)*d^-1*(A*b+B*a)*cos(c+d*x)*sin(c+d*x)+1//3*A*a*d^-1*cos(c+d*x)^2*sin(c+d*x))
@test integrate(cos(c+d*x)^4*(A+B*sec(c+d*x))*(a+b*sec(c+d*x)), x) == :(x*((1/2)*B*b+3//8*A*a)+d^-1*(A*b+B*a)*sin(c+d*x)+-1//3*d^-1*sin(c+d*x)^3*(A*b+B*a)+1//8*d^-1*(3*A*a+4*B*b)*cos(c+d*x)*sin(c+d*x)+1//4*A*a*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(1//5*d^-1*(4*B*b^2+5*a*(B*a+2*A*b))*tan(c+d*x)+1//8*d^-1*(3*A*b^2+4*A*a^2+6*B*a*b)*arctanh(sin(c+d*x))+1//15*d^-1*tan(c+d*x)^3*(4*B*b^2+5*a*(B*a+2*A*b))+1//8*d^-1*(3*A*b^2+4*A*a^2+6*B*a*b)*sec(c+d*x)*tan(c+d*x)+1//20*b*d^-1*sec(c+d*x)^3*(5*A*b+6*B*a)*tan(c+d*x)+1//5*B*b*d^-1*sec(c+d*x)^3*(a+b*sec(c+d*x))*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(1//8*d^-1*(3*B*b^2+4*B*a^2+8*A*a*b)*arctanh(sin(c+d*x))+1//6*b^-1*d^-1*(-1*B*a^3+4*A*b^3+4*A*b*a^2+8*B*a*b^2)*tan(c+d*x)+1//24*d^-1*(-2*B*a^2+9*B*b^2+8*A*a*b)*sec(c+d*x)*tan(c+d*x)+1//4*B*b^-1*d^-1*(a+b*sec(c+d*x))^3*tan(c+d*x)+1//12*b^-1*d^-1*(a+b*sec(c+d*x))^2*(-1*B*a+4*A*b)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*(A+B*sec(c+d*x))*sec(c+d*x), x) == :((1/2)*d^-1*(A*b^2+2*A*a^2+2*B*a*b)*arctanh(sin(c+d*x))+1//3*d^-1*(2*B*a^2+2*B*b^2+6*A*a*b)*tan(c+d*x)+1//3*B*d^-1*(a+b*sec(c+d*x))^2*tan(c+d*x)+1//6*b*d^-1*(2*B*a+3*A*b)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*(A+B*sec(c+d*x)), x) == :(A*x*a^2+(1/2)*d^-1*(B*b^2+2*B*a^2+4*A*a*b)*arctanh(sin(c+d*x))+(1/2)*b*d^-1*(2*A*b+3*B*a)*tan(c+d*x)+(1/2)*B*b*d^-1*(a+b*sec(c+d*x))*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*(A+B*sec(c+d*x))*cos(c+d*x), x) == :(a*x*(B*a+2*A*b)+A*a^2*d^-1*sin(c+d*x)+B*b^2*d^-1*tan(c+d*x)+b*d^-1*(A*b+2*B*a)*arctanh(sin(c+d*x)))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(x*(A*b^2+(1/2)*A*a^2+2*B*a*b)+B*b^2*d^-1*arctanh(sin(c+d*x))+a*d^-1*(B*a+2*A*b)*sin(c+d*x)+(1/2)*A*a^2*d^-1*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(x*(B*b^2+(1/2)*B*a^2+A*a*b)+1//3*d^-1*(2*A*a^2+3*A*b^2+6*B*a*b)*sin(c+d*x)+(1/2)*a*d^-1*(B*a+2*A*b)*cos(c+d*x)*sin(c+d*x)+1//3*A*a^2*d^-1*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^4*(A+B*sec(c+d*x)), x) == :(x*((1/2)*A*b^2+3//8*A*a^2+B*a*b)+d^-1*(B*a^2+B*b^2+2*A*a*b)*sin(c+d*x)+-1//3*a*d^-1*sin(c+d*x)^3*(B*a+2*A*b)+1//8*d^-1*(3*A*a^2+4*A*b^2+8*B*a*b)*cos(c+d*x)*sin(c+d*x)+1//4*A*a^2*d^-1*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^5*(A+B*sec(c+d*x)), x) == :(x*((1/2)*B*b^2+3//8*B*a^2+3//4*A*a*b)+-1//15*d^-1*sin(c+d*x)^3*(4*A*a^2+5*A*b^2+10*B*a*b)+1//5*d^-1*(4*A*a^2+5*A*b^2+10*B*a*b)*sin(c+d*x)+1//8*d^-1*(3*B*a^2+4*B*b^2+6*A*a*b)*cos(c+d*x)*sin(c+d*x)+1//4*a*d^-1*cos(c+d*x)^3*(B*a+2*A*b)*sin(c+d*x)+1//5*A*a^2*d^-1*cos(c+d*x)^4*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(1//8*d^-1*(3*A*b^3+4*B*a^3+9*B*a*b^2+12*A*b*a^2)*arctanh(sin(c+d*x))+1//30*b^-1*d^-1*(-3*B*a^4+16*B*b^4+15*A*b*a^3+52*B*a^2*b^2+60*A*a*b^3)*tan(c+d*x)+1//120*d^-1*(-6*B*a^3+45*A*b^3+30*A*b*a^2+71*B*a*b^2)*sec(c+d*x)*tan(c+d*x)+1//5*B*b^-1*d^-1*(a+b*sec(c+d*x))^4*tan(c+d*x)+1//20*b^-1*d^-1*(a+b*sec(c+d*x))^3*(-1*B*a+5*A*b)*tan(c+d*x)+1//60*b^-1*d^-1*(a+b*sec(c+d*x))^2*(-3*B*a^2+16*B*b^2+15*A*a*b)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*(A+B*sec(c+d*x))*sec(c+d*x), x) == :(1//6*d^-1*(3*B*a^3+4*A*b^3+12*B*a*b^2+16*A*b*a^2)*tan(c+d*x)+1//8*d^-1*(3*B*b^3+8*A*a^3+12*A*a*b^2+12*B*b*a^2)*arctanh(sin(c+d*x))+1//4*B*d^-1*(a+b*sec(c+d*x))^3*tan(c+d*x)+1//12*d^-1*(a+b*sec(c+d*x))^2*(3*B*a+4*A*b)*tan(c+d*x)+1//24*b*d^-1*(6*B*a^2+9*B*b^2+20*A*a*b)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*(A+B*sec(c+d*x)), x) == :(A*x*a^3+(1/2)*d^-1*(A*b^3+2*B*a^3+3*B*a*b^2+6*A*b*a^2)*arctanh(sin(c+d*x))+1//3*b*d^-1*(2*B*b^2+8*B*a^2+9*A*a*b)*tan(c+d*x)+1//3*B*b*d^-1*(a+b*sec(c+d*x))^2*tan(c+d*x)+1//6*b^2*d^-1*(3*A*b+5*B*a)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^2*(A+B*sec(c+d*x)), x) == :((1/2)*a*x*(A*a^2+6*A*b^2+6*B*a*b)+a^2*d^-1*(B*a+2*A*b)*sin(c+d*x)+b^2*d^-1*(A*b+3*B*a)*arctanh(sin(c+d*x))+-1//2*b^2*d^-1*(A*a+-2*B*b)*tan(c+d*x)+(1/2)*A*a*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(x*(A*b^3+(1/2)*B*a^3+3*B*a*b^2+3//2*A*b*a^2)+B*b^3*d^-1*arctanh(sin(c+d*x))+1//3*a*d^-1*(2*A*a^2+8*A*b^2+9*B*a*b)*sin(c+d*x)+1//6*a^2*d^-1*(3*B*a+5*A*b)*cos(c+d*x)*sin(c+d*x)+1//3*A*a*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^4*(A+B*sec(c+d*x)), x) == :(x*(B*b^3+3//8*A*a^3+3//2*A*a*b^2+3//2*B*b*a^2)+1//3*d^-1*(2*B*a^3+3*A*b^3+6*A*b*a^2+9*B*a*b^2)*sin(c+d*x)+1//6*a^2*d^-1*cos(c+d*x)^2*(2*B*a+3*A*b)*sin(c+d*x)+1//8*a*d^-1*(3*A*a^2+10*A*b^2+12*B*a*b)*cos(c+d*x)*sin(c+d*x)+1//4*A*a*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^3*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*cos(c+d*x)^5*(A+B*sec(c+d*x)), x) == :(x*((1/2)*A*b^3+3//8*B*a^3+3//2*B*a*b^2+9//8*A*b*a^2)+1//5*d^-1*(4*A*a^3+5*B*b^3+14*A*a*b^2+15*B*b*a^2)*sin(c+d*x)+-1//15*a*d^-1*sin(c+d*x)^3*(4*A*a^2+12*A*b^2+15*B*a*b)+1//8*d^-1*(3*B*a^3+4*A*b^3+9*A*b*a^2+12*B*a*b^2)*cos(c+d*x)*sin(c+d*x)+1//20*a^2*d^-1*cos(c+d*x)^3*(5*B*a+7*A*b)*sin(c+d*x)+1//5*A*a*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^4*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(1//16*d^-1*(5*B*b^4+8*B*a^4+24*A*a*b^3+32*A*b*a^3+36*B*a^2*b^2)*arctanh(sin(c+d*x))+1//60*b^-1*d^-1*(-4*B*a^5+32*A*b^5+24*A*b*a^4+121*B*a^3*b^2+128*B*a*b^4+224*A*a^2*b^3)*tan(c+d*x)+1//240*d^-1*(-8*B*a^4+75*B*b^4+48*A*b*a^3+178*B*a^2*b^2+232*A*a*b^3)*sec(c+d*x)*tan(c+d*x)+1//6*B*b^-1*d^-1*(a+b*sec(c+d*x))^5*tan(c+d*x)+1//30*b^-1*d^-1*(a+b*sec(c+d*x))^4*(-1*B*a+6*A*b)*tan(c+d*x)+1//120*b^-1*d^-1*(a+b*sec(c+d*x))^2*(-4*B*a^3+32*A*b^3+24*A*b*a^2+53*B*a*b^2)*tan(c+d*x)+1//120*b^-1*d^-1*(a+b*sec(c+d*x))^3*(-4*B*a^2+25*B*b^2+24*A*a*b)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*(A+B*sec(c+d*x))*sec(c+d*x), x) == :(1//8*d^-1*(3*A*b^4+8*A*a^4+12*B*a*b^3+16*B*b*a^3+24*A*a^2*b^2)*arctanh(sin(c+d*x))+1//30*d^-1*(12*B*a^4+16*B*b^4+80*A*a*b^3+95*A*b*a^3+112*B*a^2*b^2)*tan(c+d*x)+1//5*B*d^-1*(a+b*sec(c+d*x))^4*tan(c+d*x)+1//20*d^-1*(a+b*sec(c+d*x))^3*(4*B*a+5*A*b)*tan(c+d*x)+1//60*d^-1*(a+b*sec(c+d*x))^2*(12*B*a^2+16*B*b^2+35*A*a*b)*tan(c+d*x)+1//120*b*d^-1*(24*B*a^3+45*A*b^3+116*B*a*b^2+130*A*b*a^2)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*(A+B*sec(c+d*x)), x) == :(A*x*a^4+1//8*d^-1*(3*B*b^4+8*B*a^4+16*A*a*b^3+24*B*a^2*b^2+32*A*b*a^3)*arctanh(sin(c+d*x))+1//6*b*d^-1*(4*A*b^3+19*B*a^3+16*B*a*b^2+34*A*b*a^2)*tan(c+d*x)+1//4*B*b*d^-1*(a+b*sec(c+d*x))^3*tan(c+d*x)+1//12*b*d^-1*(a+b*sec(c+d*x))^2*(4*A*b+7*B*a)*tan(c+d*x)+1//24*b^2*d^-1*(9*B*b^2+26*B*a^2+32*A*a*b)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*(A+B*sec(c+d*x))*cos(c+d*x), x) == :(x*a^3*(B*a+4*A*b)+(1/2)*b*d^-1*(A*b^3+8*B*a^3+4*B*a*b^2+12*A*b*a^2)*arctanh(sin(c+d*x))+-1//3*b*d^-1*(-2*B*b^3+6*A*a^3+-17*B*b*a^2+-12*A*a*b^2)*tan(c+d*x)+A*a*d^-1*(a+b*sec(c+d*x))^3*sin(c+d*x)+-1//3*b*d^-1*(a+b*sec(c+d*x))^2*(-1*B*b+3*A*a)*tan(c+d*x)+-1//6*b^2*d^-1*(-3*A*b^2+6*A*a^2+-8*B*a*b)*sec(c+d*x)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^2*(A+B*sec(c+d*x)), x) == :((1/2)*x*a^2*(A*a^2+12*A*b^2+8*B*a*b)+(1/2)*b^2*d^-1*(B*b^2+12*B*a^2+8*A*a*b)*arctanh(sin(c+d*x))+-1//2*b*d^-1*(-2*A*b^3+4*B*a^3+-8*B*a*b^2+13*A*b*a^2)*tan(c+d*x)+(1/2)*a*d^-1*(a+b*sec(c+d*x))^2*(2*B*a+5*A*b)*sin(c+d*x)+-1//2*b^2*d^-1*(-1*B*b^2+2*B*a^2+6*A*a*b)*sec(c+d*x)*tan(c+d*x)+(1/2)*A*a*d^-1*(a+b*sec(c+d*x))^3*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^3*(A+B*sec(c+d*x)), x) == :((1/2)*a*x*(B*a^3+8*A*b^3+4*A*b*a^2+12*B*a*b^2)+b^3*d^-1*(A*b+4*B*a)*arctanh(sin(c+d*x))+-1//6*b^2*d^-1*(-6*B*b^2+3*B*a^2+8*A*a*b)*tan(c+d*x)+1//3*a^2*d^-1*(2*A*a^2+9*A*b^2+9*B*a*b)*sin(c+d*x)+(1/2)*a*d^-1*(a+b*sec(c+d*x))^2*(B*a+2*A*b)*cos(c+d*x)*sin(c+d*x)+1//3*A*a*d^-1*(a+b*sec(c+d*x))^3*cos(c+d*x)^2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^4*(A+B*sec(c+d*x)), x) == :(x*(A*b^4+3//8*A*a^4+2*B*b*a^3+3*A*a^2*b^2+4*B*a*b^3)+B*b^4*d^-1*arctanh(sin(c+d*x))+1//6*a*d^-1*(4*B*a^3+19*A*b^3+16*A*b*a^2+34*B*a*b^2)*sin(c+d*x)+1//24*a^2*d^-1*(9*A*a^2+26*A*b^2+32*B*a*b)*cos(c+d*x)*sin(c+d*x)+1//4*A*a*d^-1*(a+b*sec(c+d*x))^3*cos(c+d*x)^3*sin(c+d*x)+1//12*a*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^2*(4*B*a+7*A*b)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^5*(A+B*sec(c+d*x)), x) == :(x*(B*b^4+3//8*B*a^4+2*A*a*b^3+3*B*a^2*b^2+3//2*A*b*a^3)+1//15*d^-1*(8*A*a^4+15*A*b^4+40*B*b*a^3+60*A*a^2*b^2+60*B*a*b^3)*sin(c+d*x)+1//30*a^2*d^-1*cos(c+d*x)^2*(8*A*a^2+18*A*b^2+25*B*a*b)*sin(c+d*x)+1//40*a*d^-1*(15*B*a^3+56*A*b^3+60*A*b*a^2+110*B*a*b^2)*cos(c+d*x)*sin(c+d*x)+1//5*A*a*d^-1*(a+b*sec(c+d*x))^3*cos(c+d*x)^4*sin(c+d*x)+1//20*a*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^3*(5*B*a+8*A*b)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^4*cos(c+d*x)^6*(A+B*sec(c+d*x)), x) == :(x*((1/2)*A*b^4+5//16*A*a^4+2*B*a*b^3+3//2*B*b*a^3+9//4*A*a^2*b^2)+1//15*d^-1*(12*B*a^4+15*B*b^4+48*A*b*a^3+53*A*a*b^3+87*B*a^2*b^2)*sin(c+d*x)+-1//15*a*d^-1*sin(c+d*x)^3*(4*B*a^3+13*A*b^3+16*A*b*a^2+27*B*a*b^2)+1//16*d^-1*(5*A*a^4+8*A*b^4+24*B*b*a^3+32*B*a*b^3+36*A*a^2*b^2)*cos(c+d*x)*sin(c+d*x)+1//120*a^2*d^-1*cos(c+d*x)^3*(25*A*a^2+48*A*b^2+72*B*a*b)*sin(c+d*x)+1//6*A*a*d^-1*(a+b*sec(c+d*x))^3*cos(c+d*x)^5*sin(c+d*x)+1//10*a*d^-1*(a+b*sec(c+d*x))^2*cos(c+d*x)^4*(2*B*a+3*A*b)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-1*sec(c+d*x)^4*(A+B*sec(c+d*x)), x) == :(-1//3*b^-3*d^-1*(-3*B*a^2+-2*B*b^2+3*A*a*b)*tan(c+d*x)+(1/2)*b^-4*d^-1*(b^2+2*a^2)*(A*b+-1*B*a)*arctanh(sin(c+d*x))+(1/2)*b^-2*d^-1*(A*b+-1*B*a)*sec(c+d*x)*tan(c+d*x)+1//3*B*b^-1*d^-1*sec(c+d*x)^2*tan(c+d*x)+-2*a^3*b^-4*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(A*b+-1*B*a)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*sec(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(b^-2*d^-1*(A*b+-1*B*a)*tan(c+d*x)+-1//2*b^-3*d^-1*(-1*B*b^2+-2*B*a^2+2*A*a*b)*arctanh(sin(c+d*x))+(1/2)*B*b^-1*d^-1*sec(c+d*x)*tan(c+d*x)+2*a^2*b^-3*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(A*b+-1*B*a)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(B*b^-1*d^-1*tan(c+d*x)+b^-2*d^-1*(A*b+-1*B*a)*arctanh(sin(c+d*x))+-2*a*b^-2*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(A*b+-1*B*a)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*(A+B*sec(c+d*x))*sec(c+d*x), x) == :(B*b^-1*d^-1*arctanh(sin(c+d*x))+b^-1*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(-2*B*a+2*A*b)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*(A+B*sec(c+d*x)), x) == :(A*x*a^-1+-1*a^-1*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(-2*B*a+2*A*b)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*(A+B*sec(c+d*x))*cos(c+d*x), x) == :(-1*x*a^-2*(A*b+-1*B*a)+A*a^-1*d^-1*sin(c+d*x)+2*b*a^-2*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(A*b+-1*B*a)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*cos(c+d*x)^2*(A+B*sec(c+d*x)), x) == :((1/2)*x*a^-3*(A*a^2+2*A*b^2+-2*B*a*b)+-1*a^-2*d^-1*(A*b+-1*B*a)*sin(c+d*x)+(1/2)*A*a^-1*d^-1*cos(c+d*x)*sin(c+d*x)+-2*a^-3*b^2*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(A*b+-1*B*a)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*cos(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(-1//2*x*a^-4*(a^2+2*b^2)*(A*b+-1*B*a)+1//3*a^-3*d^-1*(2*A*a^2+3*A*b^2+-3*B*a*b)*sin(c+d*x)+-1//2*a^-2*d^-1*(A*b+-1*B*a)*cos(c+d*x)*sin(c+d*x)+1//3*A*a^-1*d^-1*cos(c+d*x)^2*sin(c+d*x)+2*a^-4*b^3*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(A*b+-1*B*a)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*cos(c+d*x)^4*(A+B*sec(c+d*x)), x) == :(1//8*x*a^-5*(3*A*a^4+8*A*b^4+-8*B*a*b^3+-4*B*b*a^3+4*A*a^2*b^2)+-1//3*a^-4*d^-1*(2*a^2+3*b^2)*(A*b+-1*B*a)*sin(c+d*x)+-1//3*a^-2*d^-1*cos(c+d*x)^2*(A*b+-1*B*a)*sin(c+d*x)+1//4*A*a^-1*d^-1*cos(c+d*x)^3*sin(c+d*x)+1//8*a^-3*d^-1*(3*A*a^2+4*A*b^2+-4*B*a*b)*cos(c+d*x)*sin(c+d*x)+-2*a^-5*b^4*d^-1*(a+b)^-1//2*(a+-1b)^-1//2*(A*b+-1*B*a)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-2*sec(c+d*x)^4*(A+B*sec(c+d*x)), x) == :(-1//2*b^-4*d^-1*(-1*B*b^2+-6*B*a^2+4*A*a*b)*arctanh(sin(c+d*x))+b^-3*d^-1*(a^2+-1*b^2)^-1*(-1*A*b^3+-3*B*a^3+2*A*b*a^2+2*B*a*b^2)*tan(c+d*x)+-1//2*b^-2*d^-1*(a^2+-1*b^2)^-1*(B*b^2+-3*B*a^2+2*A*a*b)*sec(c+d*x)*tan(c+d*x)+2*a^2*b^-4*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-3*A*b^3+-3*B*a^3+2*A*b*a^2+4*B*a*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+a*b^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*sec(c+d*x)^2*(A*b+-1*B*a)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-2*sec(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(B*b^-2*d^-1*tan(c+d*x)+b^-3*d^-1*(A*b+-2*B*a)*arctanh(sin(c+d*x))+-1*a^2*b^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*(A*b+-1*B*a)*tan(c+d*x)+-2*a*b^-3*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-2*A*b^3+-2*B*a^3+A*b*a^2+3*B*a*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-2*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(B*b^-2*d^-1*arctanh(sin(c+d*x))+-1*b^-2*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(2*A*b^3+2*B*a^3+-4*B*a*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+a*b^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*(A*b+-1*B*a)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-2*(A+B*sec(c+d*x))*sec(c+d*x), x) == :(d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-2*B*b+2*A*a)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*(A*b+-1*B*a)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-2*(A+B*sec(c+d*x)), x) == :(A*x*a^-2+-1*a^-2*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-2*A*b^3+-2*B*a^3+4*A*b*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+b*a^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*(A*b+-1*B*a)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-2*(A+B*sec(c+d*x))*cos(c+d*x), x) == :(-1*x*a^-3*(-1*B*a+2*A*b)+a^-2*d^-1*(a^2+-1*b^2)^-1*(A*a^2+-2*A*b^2+B*a*b)*sin(c+d*x)+b*a^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*(A*b+-1*B*a)*sin(c+d*x)+2*b*a^-3*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-2*A*b^3+-2*B*a^3+B*a*b^2+3*A*b*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-2*cos(c+d*x)^2*(A+B*sec(c+d*x)), x) == :((1/2)*x*a^-4*(A*a^2+6*A*b^2+-4*B*a*b)+-1*a^-3*d^-1*(a^2+-1*b^2)^-1*(-1*B*a^3+-3*A*b^3+2*A*b*a^2+2*B*a*b^2)*sin(c+d*x)+(1/2)*a^-2*d^-1*(a^2+-1*b^2)^-1*(A*a^2+-3*A*b^2+2*B*a*b)*cos(c+d*x)*sin(c+d*x)+-2*a^-4*b^2*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-3*A*b^3+-3*B*a^3+2*B*a*b^2+4*A*b*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+b*a^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*(A*b+-1*B*a)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-2*cos(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(-1//2*x*a^-5*(-1*B*a^3+8*A*b^3+-6*B*a*b^2+2*A*b*a^2)+1//3*a^-4*d^-1*(a^2+-1*b^2)^-1*(-12*A*b^4+2*A*a^4+-6*B*b*a^3+7*A*a^2*b^2+9*B*a*b^3)*sin(c+d*x)+-1//2*a^-3*d^-1*(a^2+-1*b^2)^-1*(-1*B*a^3+-4*A*b^3+2*A*b*a^2+3*B*a*b^2)*cos(c+d*x)*sin(c+d*x)+1//3*a^-2*d^-1*(a^2+-1*b^2)^-1*cos(c+d*x)^2*(A*a^2+-4*A*b^2+3*B*a*b)*sin(c+d*x)+2*a^-5*b^3*d^-1*(a+b)^-3//2*(a+-1b)^-3//2*(-4*A*b^3+-4*B*a^3+3*B*a*b^2+5*A*b*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+b*a^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-1*cos(c+d*x)^2*(A*b+-1*B*a)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*sec(c+d*x)^5*(A+B*sec(c+d*x)), x) == :(-1//2*b^-5*d^-1*(-1*B*b^2+-12*B*a^2+6*A*a*b)*arctanh(sin(c+d*x))+(1/2)*b^-4*d^-1*(a^2+-1*b^2)^-2*(-12*B*a^5+2*A*b^5+-11*A*a^2*b^3+-6*B*a*b^4+6*A*b*a^4+21*B*a^3*b^2)*tan(c+d*x)+-1//2*b^-3*d^-1*(a^2+-1*b^2)^-2*(-1*B*b^4+-6*B*a^4+-6*A*a*b^3+3*A*b*a^3+10*B*a^2*b^2)*sec(c+d*x)*tan(c+d*x)+a^2*b^-5*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(-12*B*a^5+12*A*b^5+-20*B*a*b^4+-15*A*a^2*b^3+6*A*b*a^4+29*B*a^3*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+(1/2)*a*b^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*sec(c+d*x)^3*(A*b+-1*B*a)*tan(c+d*x)+(1/2)*a*b^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*sec(c+d*x)^2*(-5*A*b^3+-4*B*a^3+2*A*b*a^2+7*B*a*b^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*sec(c+d*x)^4*(A+B*sec(c+d*x)), x) == :(b^-4*d^-1*(A*b+-3*B*a)*arctanh(sin(c+d*x))+-1//2*b^-3*d^-1*(a^2+-1*b^2)^-1*(-3*B*a^2+2*B*b^2+A*a*b)*tan(c+d*x)+-1*a*b^-4*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(-6*B*a^5+6*A*b^5+-12*B*a*b^4+-5*A*a^2*b^3+2*A*b*a^4+15*B*a^3*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1//2*a^2*b^-3*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-4*A*b^3+-3*B*a^3+A*b*a^2+6*B*a*b^2)*tan(c+d*x)+(1/2)*a*b^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*sec(c+d*x)^2*(A*b+-1*B*a)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*sec(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(B*b^-3*d^-1*arctanh(sin(c+d*x))+b^-3*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(-2*B*a^5+2*A*b^5+A*a^2*b^3+-6*B*a*b^4+5*B*a^3*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+(1/2)*a*b^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-4*A*b^3+-3*B*a^3+A*b*a^2+6*B*a*b^2)*tan(c+d*x)+-1//2*a^2*b^-2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*(A*b+-1*B*a)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(-1*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(-1*B*a^2+-2*B*b^2+3*A*a*b)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+(1/2)*b^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(B*a^3+2*A*b^3+A*b*a^2+-4*B*a*b^2)*tan(c+d*x)+(1/2)*a*b^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*(A*b+-1*B*a)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*(A+B*sec(c+d*x))*sec(c+d*x), x) == :(d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(A*b^2+2*A*a^2+-3*B*a*b)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1*d^-1*(a+b*sec(c+d*x))^-2*(-2*b^2+2*a^2)^-1*(A*b+-1*B*a)*tan(c+d*x)+-1//2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-1*B*a^2+-2*B*b^2+3*A*a*b)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*(A+B*sec(c+d*x)), x) == :(A*x*a^-3+-1*a^-3*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(-2*B*a^5+2*A*b^5+-1*B*a^3*b^2+-5*A*a^2*b^3+6*A*b*a^4)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+(1/2)*b*a^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*(A*b+-1*B*a)*tan(c+d*x)+(1/2)*b*a^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-3*B*a^3+-2*A*b^3+5*A*b*a^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*(A+B*sec(c+d*x))*cos(c+d*x), x) == :(-1*x*a^-4*(-1*B*a+3*A*b)+(1/2)*a^-3*d^-1*(a^2+-1*b^2)^-2*(2*A*a^4+6*A*b^4+-11*A*a^2*b^2+-2*B*a*b^3+5*B*b*a^3)*sin(c+d*x)+b*a^-4*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(-6*B*a^5+6*A*b^5+-15*A*a^2*b^3+-2*B*a*b^4+5*B*a^3*b^2+12*A*b*a^4)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+(1/2)*b*a^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*(A*b+-1*B*a)*sin(c+d*x)+(1/2)*b*a^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-4*B*a^3+-3*A*b^3+B*a*b^2+6*A*b*a^2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3*cos(c+d*x)^2*(A+B*sec(c+d*x)), x) == :((1/2)*x*a^-5*(A*a^2+12*A*b^2+-6*B*a*b)+-1//2*a^-4*d^-1*(a^2+-1*b^2)^-2*(-2*B*a^5+12*A*b^5+-21*A*a^2*b^3+-6*B*a*b^4+6*A*b*a^4+11*B*a^3*b^2)*sin(c+d*x)+(1/2)*a^-3*d^-1*(a^2+-1*b^2)^-2*(A*a^4+6*A*b^4+-10*A*a^2*b^2+-3*B*a*b^3+6*B*b*a^3)*cos(c+d*x)*sin(c+d*x)+-1*a^-5*b^2*d^-1*(a+b)^-5//2*(a+-1b)^-5//2*(-12*B*a^5+12*A*b^5+-29*A*a^2*b^3+-6*B*a*b^4+15*B*a^3*b^2+20*A*b*a^4)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+(1/2)*b*a^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-1*(A*b+-1*B*a)*cos(c+d*x)*sin(c+d*x)+(1/2)*b*a^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-2*(-5*B*a^3+-4*A*b^3+2*B*a*b^2+7*A*b*a^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*sec(c+d*x)^5*(A+B*sec(c+d*x)), x) == :(b^-5*d^-1*(A*b+-4*B*a)*arctanh(sin(c+d*x))+-1//6*b^-4*d^-1*(a^2+-1*b^2)^-2*(-12*B*a^4+-6*B*b^4+-8*A*a*b^3+3*A*b*a^3+23*B*a^2*b^2)*tan(c+d*x)+-1*a*b^-5*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(-8*A*b^7+-8*B*a^7+-35*B*a^3*b^4+-7*A*a^4*b^3+2*A*b*a^6+8*A*a^2*b^5+20*B*a*b^6+28*B*a^5*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1//2*a^2*b^-4*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(-4*B*a^5+6*A*b^5+A*b*a^4+-12*B*a*b^4+-2*A*a^2*b^3+11*B*a^3*b^2)*tan(c+d*x)+1//3*a*b^-1*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*sec(c+d*x)^3*(A*b+-1*B*a)*tan(c+d*x)+1//6*a*b^-2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*sec(c+d*x)^2*(-6*A*b^3+-4*B*a^3+A*b*a^2+9*B*a*b^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*sec(c+d*x)^4*(A+B*sec(c+d*x)), x) == :(B*b^-4*d^-1*arctanh(sin(c+d*x))+-1*b^-4*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(2*A*b^7+2*B*a^7+-8*B*a*b^6+-7*B*a^5*b^2+3*A*a^2*b^5+8*B*a^3*b^4)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1//6*a*b^-3*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(-16*A*b^5+9*B*a^5+A*a^2*b^3+-28*B*a^3*b^2+34*B*a*b^4)*tan(c+d*x)+1//6*a^2*b^-3*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(3*B*a^3+5*A*b^3+-8*B*a*b^2)*tan(c+d*x)+1//3*a*b^-1*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*sec(c+d*x)^2*(A*b+-1*B*a)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*sec(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(A*a^3+-2*B*b^3+-3*B*b*a^2+4*A*a*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+1//6*b^-2*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(-6*A*b^5+2*B*a^5+A*b*a^4+-10*A*a^2*b^3+-5*B*a^3*b^2+18*B*a*b^4)*tan(c+d*x)+-1//3*a^2*b^-2*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*(A*b+-1*B*a)*tan(c+d*x)+1//6*a*b^-2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(-6*A*b^3+-4*B*a^3+A*b*a^2+9*B*a*b^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(-1*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(A*b^3+-1*B*a^3+-4*B*a*b^2+4*A*b*a^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+1//6*b^-1*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(B*a^4+-6*B*b^4+-10*B*a^2*b^2+2*A*b*a^3+13*A*a*b^3)*tan(c+d*x)+1//6*b^-1*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(B*a^3+3*A*b^3+-6*B*a*b^2+2*A*b*a^2)*tan(c+d*x)+1//3*a*b^-1*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*(A*b+-1*B*a)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*(A+B*sec(c+d*x))*sec(c+d*x), x) == :(d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(-1*B*b^3+2*A*a^3+-4*B*b*a^2+3*A*a*b^2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+-1*d^-1*(a+b*sec(c+d*x))^-3*(-3*b^2+3*a^2)^-1*(A*b+-1*B*a)*tan(c+d*x)+-1//6*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(-2*B*a^3+4*A*b^3+-13*B*a*b^2+11*A*b*a^2)*tan(c+d*x)+-1//6*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(-3*B*b^2+-2*B*a^2+5*A*a*b)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*(A+B*sec(c+d*x)), x) == :(A*x*a^-4+-1*a^-4*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(-2*A*b^7+-2*B*a^7+-8*A*a^4*b^3+-3*B*a^5*b^2+7*A*a^2*b^5+8*A*b*a^6)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+1//3*b*a^-1*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*(A*b+-1*B*a)*tan(c+d*x)+1//6*b*a^-3*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(-11*B*a^5+6*A*b^5+-17*A*a^2*b^3+-4*B*a^3*b^2+26*A*b*a^4)*tan(c+d*x)+1//6*b*a^-2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(-5*B*a^3+-3*A*b^3+8*A*b*a^2)*tan(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*(A+B*sec(c+d*x))*cos(c+d*x), x) == :(-1*x*a^-5*(-1*B*a+4*A*b)+1//6*a^-4*d^-1*(a^2+-1*b^2)^-3*(-24*A*b^6+6*A*a^6+-65*A*a^4*b^2+-17*B*a^3*b^3+6*B*a*b^5+26*B*b*a^5+68*A*a^2*b^4)*sin(c+d*x)+b*a^-5*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(-8*A*b^7+-8*B*a^7+-35*A*a^4*b^3+-7*B*a^3*b^4+2*B*a*b^6+8*B*a^5*b^2+20*A*b*a^6+28*A*a^2*b^5)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+(1/2)*b*a^-3*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(-6*B*a^5+4*A*b^5+-1*B*a*b^4+-11*A*a^2*b^3+2*B*a^3*b^2+12*A*b*a^4)*sin(c+d*x)+1//3*b*a^-1*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*(A*b+-1*B*a)*sin(c+d*x)+1//6*b*a^-2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(-6*B*a^3+-4*A*b^3+B*a*b^2+9*A*b*a^2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-4*cos(c+d*x)^2*(A+B*sec(c+d*x)), x) == :((1/2)*x*a^-6*(A*a^2+20*A*b^2+-8*B*a*b)+-1//6*a^-5*d^-1*(a^2+-1*b^2)^-3*(-60*A*b^7+-6*B*a^7+-146*A*a^4*b^3+-68*B*a^3*b^4+24*A*b*a^6+24*B*a*b^6+65*B*a^5*b^2+167*A*a^2*b^5)*sin(c+d*x)+(1/2)*a^-4*d^-1*(a^2+-1*b^2)^-3*(A*a^6+-10*A*b^6+-23*A*a^4*b^2+-11*B*a^3*b^3+4*B*a*b^5+12*B*b*a^5+27*A*a^2*b^4)*cos(c+d*x)*sin(c+d*x)+-1*a^-6*b^2*d^-1*(a+b)^-7//2*(a+-1b)^-7//2*(-20*A*b^7+-20*B*a^7+-84*A*a^4*b^3+-28*B*a^3*b^4+8*B*a*b^6+35*B*a^5*b^2+40*A*b*a^6+69*A*a^2*b^5)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x))+1//3*b*a^-1*d^-1*(a+b*sec(c+d*x))^-3*(a^2+-1*b^2)^-1*(A*b+-1*B*a)*cos(c+d*x)*sin(c+d*x)+1//6*b*a^-3*d^-1*(a+b*sec(c+d*x))^-1*(a^2+-1*b^2)^-3*(-27*B*a^5+20*A*b^5+-53*A*a^2*b^3+-8*B*a*b^4+20*B*a^3*b^2+48*A*b*a^4)*cos(c+d*x)*sin(c+d*x)+1//6*b*a^-2*d^-1*(a+b*sec(c+d*x))^-2*(a^2+-1*b^2)^-2*(-7*B*a^3+-5*A*b^3+2*B*a*b^2+10*A*b*a^2)*cos(c+d*x)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-1*(B*sec(c+d*x)+B*b*a^-1), x) == :(B*b*x*a^-2+2*B*a^-2*d^-1*(a+b)^(1/2)*(a+-1b)^(1/2)*arctanh((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^-1*(B*sec(c+d*x)+B*a*b^-1), x) == :(B*x*b^-1)
@test integrate((b+a*sec(c+d*x))^-2*(a+b*sec(c+d*x)), x) == :(a*x*b^-2+-1*a*b^-1*d^-1*(b+a*sec(c+d*x))^-1*tan(c+d*x)+-2*b^-2*d^-1*(a+b)^(1/2)*(a+-1b)^(1/2)*arctan((a+b)^-1//2*(a+-1b)^(1/2)*tan((1/2)*c+(1/2)*d*x)))
@test integrate((2+-1*sec(c+d*x))^-1*(3+sec(c+d*x)), x) == :(3//2*x+-5//6*3^(1/2)*d^-1*log(-1*3^(1/2)*sin((1/2)*c+(1/2)*d*x)+cos((1/2)*c+(1/2)*d*x))+5//6*3^(1/2)*d^-1*log(3^(1/2)*sin((1/2)*c+(1/2)*d*x)+cos((1/2)*c+(1/2)*d*x)))
@test integrate((a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^4*(A+B*sec(c+d*x)), x) == :(-1//315*b^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(-150*A*b^3+-16*B*a^3+-26*B*a*b^2+24*A*b*a^2)*tan(c+d*x)+2//9*B*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^3*tan(c+d*x)+1//63*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^2*(2*B*a+18*A*b)*tan(c+d*x)+1//315*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(-12*B*a^2+98*B*b^2+18*A*a*b)*sec(c+d*x)*tan(c+d*x)+-1//315*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-16*B*a^3+3*b^3*(-49B+25A)+12*b*a^2*(-1B+2A)+18*a*b^2*(A+-2B))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//315*b^-5*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(-16*B*a^4+147*B*b^4+-24*B*a^2*b^2+24*A*b*a^3+57*A*a*b^3)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(1//105*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(-8*B*a^2+50*B*b^2+14*A*a*b)*tan(c+d*x)+2//7*B*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^2*tan(c+d*x)+1//35*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*(2*B*a+14*A*b)*sec(c+d*x)*tan(c+d*x)+1//105*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-63*A*b^3+-8*B*a^3+-19*B*a*b^2+14*A*b*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//105*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(b^2*(-25B+63A)+-8*B*a^2+2*a*b*(-3B+7A))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(1//15*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*(-4*B*a+10*A*b)*tan(c+d*x)+2//5*B*b^-1*d^-1*(a+b*sec(c+d*x))^3//2*tan(c+d*x)+-1//15*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-9*B*b+-2*B*a+5*A*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//15*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(-2*B*a^2+9*B*b^2+5*A*a*b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^(1/2)*(A+B*sec(c+d*x))*sec(c+d*x), x) == :(2//3*B*d^-1*(a+b*sec(c+d*x))^(1/2)*tan(c+d*x)+1//3*b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-1B+3A)*(-2b+2a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//3*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(B*a+3*A*b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^3//2*sec(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(-1//315*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(-150*A*b^3+-16*B*a^3+-78*B*a*b^2+36*A*b*a^2)*tan(c+d*x)+-1//315*b^-2*d^-1*(a+b*sec(c+d*x))^3//2*(-98*B*b^2+-16*B*a^2+36*A*a*b)*tan(c+d*x)+1//63*b^-2*d^-1*(a+b*sec(c+d*x))^5//2*(-8*B*a+18*A*b)*tan(c+d*x)+2//9*B*b^-1*d^-1*(a+b*sec(c+d*x))^5//2*sec(c+d*x)*tan(c+d*x)+-1//315*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(3*b^3*(-49B+25A)+8*B*a^3+-6*b*a^2*(-1B+3A)+-3*a*b^2*(-13B+57A))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//315*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-147*B*b^4+-8*B*a^4+-246*A*a*b^3+-33*B*a^2*b^2+18*A*b*a^3)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^3//2*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(1//35*b^-1*d^-1*(a+b*sec(c+d*x))^3//2*(-4*B*a+14*A*b)*tan(c+d*x)+1//105*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*(-12*B*a^2+50*B*b^2+42*A*a*b)*tan(c+d*x)+2//7*B*b^-1*d^-1*(a+b*sec(c+d*x))^5//2*tan(c+d*x)+1//105*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(-6*B*a^3+63*A*b^3+21*A*b*a^2+82*B*a*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//105*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(b^2*(-25B+63A)+-1*a*(-57*B*b+21*A*b)+6*B*a^2)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^3//2*(A+B*sec(c+d*x))*sec(c+d*x), x) == :(1//15*d^-1*(a+b*sec(c+d*x))^(1/2)*(6*B*a+10*A*b)*tan(c+d*x)+2//5*B*d^-1*(a+b*sec(c+d*x))^3//2*tan(c+d*x)+1//15*b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-5*A*b+-3*B*a+9*B*b+15*A*a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//15*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(3*B*a^2+9*B*b^2+20*A*a*b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^5//2*sec(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(-1//693*b^-2*d^-1*(a+b*sec(c+d*x))^5//2*(-162*B*b^2+-16*B*a^2+44*A*a*b)*tan(c+d*x)+-1//3465*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(-1350*B*b^4+-80*B*a^4+-2508*A*a*b^3+-570*B*a^2*b^2+220*A*b*a^3)*tan(c+d*x)+-1//3465*b^-2*d^-1*(a+b*sec(c+d*x))^3//2*(-1078*A*b^3+-80*B*a^3+-670*B*a*b^2+220*A*b*a^2)*tan(c+d*x)+1//99*b^-2*d^-1*(a+b*sec(c+d*x))^7//2*(-8*B*a+22*A*b)*tan(c+d*x)+2//11*B*b^-1*d^-1*(a+b*sec(c+d*x))^7//2*sec(c+d*x)*tan(c+d*x)+-1//3465*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-1*a^3*(-30*B*b+110*A*b)+-3*b^4*(-225B+539A)+40*B*a^4+-15*a^2*b^2*(-19B+121A)+6*a*b^3*(-505B+209A))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//3465*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-1617*A*b^5+-40*B*a^5+-3705*B*a*b^4+-3069*A*a^2*b^3+-255*B*a^3*b^2+110*A*b*a^4)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^5//2*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(1//63*b^-1*d^-1*(a+b*sec(c+d*x))^5//2*(-4*B*a+18*A*b)*tan(c+d*x)+1//315*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*(-20*B*a^3+150*A*b^3+90*A*b*a^2+228*B*a*b^2)*tan(c+d*x)+1//315*b^-1*d^-1*(a+b*sec(c+d*x))^3//2*(-20*B*a^2+98*B*b^2+90*A*a*b)*tan(c+d*x)+2//9*B*b^-1*d^-1*(a+b*sec(c+d*x))^7//2*tan(c+d*x)+-1//315*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-10*B*a^3+3*b^3*(-49B+25A)+-6*a*b^2*(-19B+60A)+15*b*a^2*(-11B+3A))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//315*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(-10*B*a^4+147*B*b^4+45*A*b*a^3+279*B*a^2*b^2+435*A*a*b^3)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^5//2*(A+B*sec(c+d*x))*sec(c+d*x), x) == :(1//35*d^-1*(a+b*sec(c+d*x))^3//2*(10*B*a+14*A*b)*tan(c+d*x)+1//105*d^-1*(a+b*sec(c+d*x))^(1/2)*(30*B*a^2+50*B*b^2+112*A*a*b)*tan(c+d*x)+2//7*B*d^-1*(a+b*sec(c+d*x))^5//2*tan(c+d*x)+1//105*b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(b^2*(-25B+63A)+15*a^2*(-1B+7A)+-8*a*b*(-15B+7A))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//105*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(15*B*a^3+63*A*b^3+145*B*a*b^2+161*A*b*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-1//2*sec(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(1//15*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(-8*B*a+10*A*b)*tan(c+d*x)+2//5*B*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)*tan(c+d*x)+2//15*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(b^2*(-9B+5A)+-8*B*a^2+2*a*b*(B+5A))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//15*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2b+2a)*(-9*B*b^2+-8*B*a^2+10*A*a*b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-1//2*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(2//3*B*b^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*tan(c+d*x)+-2//3*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-1*B*(b+2a)+3*A*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//3*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*(-2*B*a+3*A*b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-1//2*(A+B*sec(c+d*x))*sec(c+d*x), x) == :(2*b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(A+-1B)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+B*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^(1/2)*(-2a+2b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3//2*sec(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(2//3*B*b^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*tan(c+d*x)+-2*a^2*b^-2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*(A*b+-1*B*a)*tan(c+d*x)+-1//3*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(-16*B*a^3+-6*A*b^3+10*B*a*b^2+12*A*b*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+-1//3*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(2b+4a)*(-1*B*(b+4a)+3*A*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3//2*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(2*a*b^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*(A*b+-1*B*a)*tan(c+d*x)+b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(-4*B*a^2+2*B*b^2+2*A*a*b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(-2*B*(b+2a)+2*A*b)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3//2*(A+B*sec(c+d*x))*sec(c+d*x), x) == :(-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*(-2*B*a+2*A*b)*tan(c+d*x)+b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(2A+2B)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(-2*A*b+2*B*a)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^4*(A+B*sec(c+d*x)), x) == :(-1//3*b^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*(-4*B*a^2+2*B*b^2+2*A*a*b)*tan(c+d*x)+-2//3*a^2*b^-3*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*(-7*A*b^3+-6*B*a^3+3*A*b*a^2+10*B*a*b^2)*tan(c+d*x)+2//3*a*b^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*sec(c+d*x)^2*(A*b+-1*B*a)*tan(c+d*x)+b^-5*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(-3b+3a)^-1*(-6*A*b^5+32*B*a^5+-56*B*a^3*b^2+-16*A*b*a^4+16*B*a*b^4+30*A*a^2*b^3)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//3*b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(a^2+-1*b^2)^-1*(-2*a^3*(-12*B*b+8*A*b)+2*b^4*(-1B+3A)+32*B*a^4+-4*a^2*b^2*(3A+8B)+18*a*b^3*(A+-1B))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^3*(A+B*sec(c+d*x)), x) == :(-2//3*a^2*b^-2*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*(A*b+-1*B*a)*tan(c+d*x)+2//3*a*b^-2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*(-6*A*b^3+-5*B*a^3+2*A*b*a^2+9*B*a*b^2)*tan(c+d*x)+b^-4*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(-3b+3a)^-1*(-16*B*a^4+-6*B*b^4+-12*A*a*b^3+4*A*b*a^3+30*B*a^2*b^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//3*b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(a^2+-1*b^2)^-1*(-16*B*a^3+-6*b^3*(A+-1B)+4*b*a^2*(A+-3B)+6*a*b^2*(A+3B))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^2*(A+B*sec(c+d*x)), x) == :(1//3*b^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*(4*B*a^3+6*A*b^3+-12*B*a*b^2+2*A*b*a^2)*tan(c+d*x)+2//3*a*b^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*(A*b+-1*B*a)*tan(c+d*x)+b^-3*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(-3b+3a)^-1*(4*B*a^3+6*A*b^3+-12*B*a*b^2+2*A*b*a^2)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+1//3*b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-1//2*(a^2+-1*b^2)^-1*(-6*b^2*(A+B)+4*B*a^2+2*a*b*(A+3B))*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*(A+B*sec(c+d*x))*sec(c+d*x), x) == :(-1*d^-1*(a+b*sec(c+d*x))^-3//2*(-3*b^2+3*a^2)^-1*(-2*B*a+2*A*b)*tan(c+d*x)+-1//3*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*(-6*B*b^2+-2*B*a^2+8*A*a*b)*tan(c+d*x)+b^-1*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(-3b+3a)^-1*(-6*B*b+-2*A*b+2*B*a+6*A*a)*Elliptic.F(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x)+b^-2*d^-1*(b*(a+b)^-1*(1+-1*sec(c+d*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(c+d*x)))^(1/2)*(a+b)^-3//2*(-3b+3a)^-1*(2*B*a^2+6*B*b^2+-8*A*a*b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(c+d*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(c+d*x))
@test integrate((a+b*sec(e+f*x))^-1//2*(A+A*sec(e+f*x))*sec(e+f*x), x) == :(-2*A*b^-2*f^-1*(b*(a+b)^-1*(1+-1*sec(e+f*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(e+f*x)))^(1/2)*(a+b)^(1/2)*(a+-1b)*Elliptic.E(arcsin((a+b)^-1//2*(a+b*sec(e+f*x))^(1/2)),(a+-1b)^-1*(a+b))*cot(e+f*x))
@test integrate((a+b*sec(e+f*x))^-1//2*(A+-1*A*sec(e+f*x))*sec(e+f*x), x) == :(2*A*b^-2*f^-1*(b*(a+b)^-1*(1+-1*sec(e+f*x)))^(1/2)*(-1*b*(a+-1b)^-1*(1+sec(e+f*x)))^(1/2)*(a+-1b)^(1/2)*(a+b)*Elliptic.E(arcsin((a+-1b)^-1//2*(a+b*sec(e+f*x))^(1/2)),(a+b)^-1*(a+-1b))*cot(e+f*x))
@test integrate(sec(c+d*x)^3//2*(A+B*sec(c+d*x))*(a+b*sec(c+d*x)), x) == :(1//3*d^-1*sec(c+d*x)^3//2*(2*A*b+2*B*a)*sin(c+d*x)+1//5*d^-1*sec(c+d*x)^(1/2)*(6*B*b+10*A*a)*sin(c+d*x)+-1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(6*B*b+10*A*a)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*A*b+2*B*a)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*B*b*d^-1*sec(c+d*x)^5//2*sin(c+d*x))
@test integrate(sec(c+d*x)^(1/2)*(A+B*sec(c+d*x))*(a+b*sec(c+d*x)), x) == :(d^-1*sec(c+d*x)^(1/2)*(2*A*b+2*B*a)*sin(c+d*x)+-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*A*b+2*B*a)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*B*b+6*A*a)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*B*b*d^-1*sec(c+d*x)^3//2*sin(c+d*x))
@test integrate(sec(c+d*x)^-1//2*(A+B*sec(c+d*x))*(a+b*sec(c+d*x)), x) == :(d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-2*B*b+2*A*a)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*A*b+2*B*a)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*B*b*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate(sec(c+d*x)^-3//2*(A+B*sec(c+d*x))*(a+b*sec(c+d*x)), x) == :(d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*A*b+2*B*a)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*A*a+6*B*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*A*a*d^-1*sec(c+d*x)^-1//2*sin(c+d*x))
@test integrate(sec(c+d*x)^-5//2*(A+B*sec(c+d*x))*(a+b*sec(c+d*x)), x) == :(1//3*d^-1*sec(c+d*x)^-1//2*(2*A*b+2*B*a)*sin(c+d*x)+1//3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*A*b+2*B*a)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(6*A*a+10*B*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//5*A*a*d^-1*sec(c+d*x)^-3//2*sin(c+d*x))
@test integrate(sec(c+d*x)^-7//2*(A+B*sec(c+d*x))*(a+b*sec(c+d*x)), x) == :(1//5*d^-1*sec(c+d*x)^-3//2*(2*A*b+2*B*a)*sin(c+d*x)+1//21*d^-1*sec(c+d*x)^-1//2*(10*A*a+14*B*b)*sin(c+d*x)+1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(6*A*b+6*B*a)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(10*A*a+14*B*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//7*A*a*d^-1*sec(c+d*x)^-5//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(1//5*d^-1*sec(c+d*x)^(1/2)*(6*A*b^2+10*A*a^2+12*B*a*b)*sin(c+d*x)+1//21*d^-1*sec(c+d*x)^3//2*(10*B*b^2+14*a*(B*a+2*A*b))*sin(c+d*x)+-1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(6*A*b^2+10*A*a^2+12*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(10*B*b^2+14*a*(B*a+2*A*b))*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//35*b*d^-1*sec(c+d*x)^5//2*(7*A*b+9*B*a)*sin(c+d*x)+2//7*B*b*d^-1*sec(c+d*x)^5//2*(a+b*sec(c+d*x))*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(1//5*d^-1*sec(c+d*x)^(1/2)*(6*B*b^2+10*a*(B*a+2*A*b))*sin(c+d*x)+-1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(6*B*b^2+10*a*(B*a+2*A*b))*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*A*b^2+6*A*a^2+4*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//15*b*d^-1*sec(c+d*x)^3//2*(5*A*b+7*B*a)*sin(c+d*x)+2//5*B*b*d^-1*sec(c+d*x)^3//2*(a+b*sec(c+d*x))*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-2*A*b^2+2*A*a^2+-4*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*B*b^2+6*B*a^2+12*A*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*b*d^-1*sec(c+d*x)^(1/2)*(3*A*b+5*B*a)*sin(c+d*x)+2//3*B*b*d^-1*sec(c+d*x)^(1/2)*(a+b*sec(c+d*x))*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(-1*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-2*a*(B*a+2*A*b)+2*B*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*B*b^2*d^-1*sec(c+d*x)^(1/2)*sin(c+d*x)+1//3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*A*a^2+6*A*b^2+12*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*A*a^2*d^-1*sec(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :(1//3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*B*a^2+6*B*b^2+4*A*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(6*A*a^2+10*A*b^2+20*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*sec(c+d*x)^-1//2*(B*a+2*A*b)*sin(c+d*x)+2//5*A*a^2*d^-1*sec(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^-7//2*(A+B*sec(c+d*x)), x) == :(1//21*d^-1*sec(c+d*x)^-1//2*(10*A*a^2+14*A*b^2+28*B*a*b)*sin(c+d*x)+1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(6*B*a^2+10*B*b^2+12*A*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(10*A*a^2+14*A*b^2+28*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*a*d^-1*sec(c+d*x)^-3//2*(B*a+2*A*b)*sin(c+d*x)+2//7*A*a^2*d^-1*sec(c+d*x)^-5//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*sec(c+d*x)^-9//2*(A+B*sec(c+d*x)), x) == :(1//21*d^-1*sec(c+d*x)^-1//2*(10*a*(B*a+2*A*b)+14*B*b^2)*sin(c+d*x)+1//45*d^-1*sec(c+d*x)^-3//2*(14*A*a^2+18*A*b^2+36*B*a*b)*sin(c+d*x)+1//15*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(14*A*a^2+18*A*b^2+36*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(10*a*(B*a+2*A*b)+14*B*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//7*a*d^-1*sec(c+d*x)^-5//2*(B*a+2*A*b)*sin(c+d*x)+2//9*A*a^2*d^-1*sec(c+d*x)^-7//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(1//15*d^-1*sec(c+d*x)^(1/2)*(14*B*b^3+30*A*a^3+54*A*a*b^2+54*B*b*a^2)*sin(c+d*x)+1//21*d^-1*sec(c+d*x)^3//2*(10*A*b^3+14*B*a^3+30*B*a*b^2+42*A*b*a^2)*sin(c+d*x)+-1//15*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(14*B*b^3+30*A*a^3+54*A*a*b^2+54*B*b*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(10*A*b^3+14*B*a^3+30*B*a*b^2+42*A*b*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//45*b*d^-1*sec(c+d*x)^5//2*(7*B*b^2+22*B*a^2+27*A*a*b)*sin(c+d*x)+2//63*b^2*d^-1*sec(c+d*x)^7//2*(9*A*b+13*B*a)*sin(c+d*x)+2//9*B*b*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^5//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(1//5*d^-1*sec(c+d*x)^(1/2)*(6*A*b^3+10*B*a^3+18*B*a*b^2+30*A*b*a^2)*sin(c+d*x)+-1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(6*A*b^3+10*B*a^3+18*B*a*b^2+30*A*b*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(10*B*b^3+42*A*a^3+42*A*a*b^2+42*B*b*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//21*b*d^-1*sec(c+d*x)^3//2*(5*B*b^2+18*B*a^2+21*A*a*b)*sin(c+d*x)+2//35*b^2*d^-1*sec(c+d*x)^5//2*(7*A*b+11*B*a)*sin(c+d*x)+2//7*B*b*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^3//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(1//3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*A*b^3+6*B*a^3+6*B*a*b^2+18*A*b*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-6*B*b^3+10*A*a^3+-30*A*a*b^2+-30*B*b*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//5*b*d^-1*sec(c+d*x)^(1/2)*(3*B*b^2+14*B*a^2+15*A*a*b)*sin(c+d*x)+2//15*b^2*d^-1*sec(c+d*x)^3//2*(5*A*b+9*B*a)*sin(c+d*x)+2//5*B*b*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-2*A*b^3+2*B*a^3+-6*B*a*b^2+6*A*b*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-2//3*b*d^-1*sec(c+d*x)^(1/2)*(-3*A*b^2+2*A*a^2+-9*B*a*b)*sin(c+d*x)+-2//3*b^2*d^-1*sec(c+d*x)^3//2*(A*a+-1*B*b)*sin(c+d*x)+1//3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*A*a^3+2*B*b^3+18*A*a*b^2+18*B*b*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*A*a*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^-1//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :(-2//5*b^2*d^-1*sec(c+d*x)^(1/2)*(A*a+-5*B*b)*sin(c+d*x)+1//3*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2*B*a^3+6*A*b^3+6*A*b*a^2+18*B*a*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-10*B*b^3+6*A*a^3+30*A*a*b^2+30*B*b*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//15*a^2*d^-1*sec(c+d*x)^-1//2*(5*B*a+9*A*b)*sin(c+d*x)+2//5*A*a*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^-7//2*(A+B*sec(c+d*x)), x) == :(1//5*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(6*B*a^3+10*A*b^3+18*A*b*a^2+30*B*a*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(10*A*a^3+42*B*b^3+42*A*a*b^2+42*B*b*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//21*a*d^-1*sec(c+d*x)^-1//2*(5*A*a^2+18*A*b^2+21*B*a*b)*sin(c+d*x)+2//35*a^2*d^-1*sec(c+d*x)^-3//2*(7*B*a+11*A*b)*sin(c+d*x)+2//7*A*a*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^-5//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^-9//2*(A+B*sec(c+d*x)), x) == :(1//21*d^-1*sec(c+d*x)^-1//2*(10*B*a^3+14*A*b^3+30*A*b*a^2+42*B*a*b^2)*sin(c+d*x)+1//15*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(14*A*a^3+30*B*b^3+54*A*a*b^2+54*B*b*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(10*B*a^3+14*A*b^3+30*A*b*a^2+42*B*a*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//45*a*d^-1*sec(c+d*x)^-3//2*(7*A*a^2+22*A*b^2+27*B*a*b)*sin(c+d*x)+2//63*a^2*d^-1*sec(c+d*x)^-5//2*(9*B*a+13*A*b)*sin(c+d*x)+2//9*A*a*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^-7//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^3*sec(c+d*x)^-11//2*(A+B*sec(c+d*x)), x) == :(1//45*d^-1*sec(c+d*x)^-3//2*(14*B*a^3+18*A*b^3+42*A*b*a^2+54*B*a*b^2)*sin(c+d*x)+1//231*d^-1*sec(c+d*x)^-1//2*(90*A*a^3+154*B*b^3+330*A*a*b^2+330*B*b*a^2)*sin(c+d*x)+1//15*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(14*B*a^3+18*A*b^3+42*A*b*a^2+54*B*a*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//231*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(90*A*a^3+154*B*b^3+330*A*a*b^2+330*B*b*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//77*a*d^-1*sec(c+d*x)^-5//2*(9*A*a^2+26*A*b^2+33*B*a*b)*sin(c+d*x)+2//99*a^2*d^-1*sec(c+d*x)^-7//2*(11*B*a+15*A*b)*sin(c+d*x)+2//11*A*a*d^-1*(a+b*sec(c+d*x))^2*sec(c+d*x)^-9//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(2//3*A*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*sin(c+d*x)+1//3*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(2*A*b+6*B*a)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2//3*A*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(a^2+-1*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :(2//5*A*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*sin(c+d*x)+1//15*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(2*A*b+10*B*a)*sin(c+d*x)+1//15*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(-4*A*b^2+18*A*a^2+10*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//15*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-2*a^2+2*b^2)*(-5*B*a+2*A*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-7//2*(A+B*sec(c+d*x)), x) == :(2//7*A*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*sin(c+d*x)+1//35*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*(2*A*b+14*B*a)*sin(c+d*x)+1//105*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(-8*A*b^2+50*A*a^2+14*B*a*b)*sin(c+d*x)+1//105*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(16*A*b^3+126*B*a^3+-28*B*a*b^2+38*A*b*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//105*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-2*b^2+2*a^2)*(8*A*b^2+25*A*a^2+-14*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^3//2*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :(1//15*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(10*B*a+12*A*b)*sin(c+d*x)+2//5*A*a*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*sin(c+d*x)+1//15*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(6*A*b^2+18*A*a^2+40*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//15*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-2*b^2+2*a^2)*(3*A*b+5*B*a)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^3//2*sec(c+d*x)^-7//2*(A+B*sec(c+d*x)), x) == :(1//35*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*(14*B*a+16*A*b)*sin(c+d*x)+1//105*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(6*A*b^2+50*A*a^2+84*B*a*b)*sin(c+d*x)+2//7*A*a*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*sin(c+d*x)+1//105*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(-12*A*b^3+126*B*a^3+42*B*a*b^2+164*A*b*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//105*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-2*b^2+2*a^2)*(-6*A*b^2+25*A*a^2+21*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^3//2*sec(c+d*x)^-9//2*(A+B*sec(c+d*x)), x) == :(1//63*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*(18*B*a+20*A*b)*sin(c+d*x)+1//315*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*(6*A*b^2+98*A*a^2+144*B*a*b)*sin(c+d*x)+1//315*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(-8*A*b^3+150*B*a^3+18*B*a*b^2+176*A*b*a^2)*sin(c+d*x)+2//9*A*a*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-7//2*sin(c+d*x)+1//315*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(16*A*b^4+294*A*a^4+-36*B*a*b^3+66*A*a^2*b^2+492*B*b*a^3)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//315*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-2*b^2+2*a^2)*(8*A*b^3+75*B*a^3+-18*B*a*b^2+39*A*b*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^5//2*sec(c+d*x)^-7//2*(A+B*sec(c+d*x)), x) == :(1//105*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(50*A*a^2+90*A*b^2+154*B*a*b)*sin(c+d*x)+2//7*A*a*d^-1*(a+b*sec(c+d*x))^3//2*sec(c+d*x)^-5//2*sin(c+d*x)+2//35*a*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*(7*B*a+10*A*b)*sin(c+d*x)+1//105*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(30*A*b^3+126*B*a^3+290*A*b*a^2+322*B*a*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//105*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-2*b^2+2*a^2)*(15*A*b^2+25*A*a^2+56*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^5//2*sec(c+d*x)^-9//2*(A+B*sec(c+d*x)), x) == :(1//315*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*(98*A*a^2+150*A*b^2+270*B*a*b)*sin(c+d*x)+1//315*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(10*A*b^3+150*B*a^3+270*B*a*b^2+326*A*b*a^2)*sin(c+d*x)+2//9*A*a*d^-1*(a+b*sec(c+d*x))^3//2*sec(c+d*x)^-7//2*sin(c+d*x)+2//21*a*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*(3*B*a+4*A*b)*sin(c+d*x)+1//315*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(-20*A*b^4+294*A*a^4+90*B*a*b^3+558*A*a^2*b^2+870*B*b*a^3)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//315*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-2*b^2+2*a^2)*(-10*A*b^3+75*B*a^3+45*B*a*b^2+114*A*b*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^5//2*sec(c+d*x)^-11//2*(A+B*sec(c+d*x)), x) == :(1//693*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-5//2*(162*A*a^2+226*A*b^2+418*B*a*b)*sin(c+d*x)+1//3465*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*(30*A*b^3+1078*B*a^3+1650*B*a*b^2+2290*A*b*a^2)*sin(c+d*x)+1//3465*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(-40*A*b^4+1350*A*a^4+110*B*a*b^3+2050*A*a^2*b^2+3586*B*b*a^3)*sin(c+d*x)+2//11*A*a*d^-1*(a+b*sec(c+d*x))^3//2*sec(c+d*x)^-9//2*sin(c+d*x)+2//99*a*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-7//2*(11*B*a+14*A*b)*sin(c+d*x)+1//3465*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(80*A*b^5+3234*B*a^5+-220*B*a*b^4+510*A*a^2*b^3+6138*B*a^3*b^2+7410*A*b*a^4)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3465*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-2*b^2+2*a^2)*(40*A*b^4+675*A*a^4+-110*B*a*b^3+285*A*a^2*b^2+1254*B*b*a^3)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-1//2*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-2*A*b+2*B*a)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2*A*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-1//2*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(2//3*A*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*sin(c+d*x)+-1//3*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(-6*B*a+4*A*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(2*A*a^2+4*A*b^2+-6*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-1//2*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :(-1//15*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(-10*B*a+8*A*b)*sin(c+d*x)+2//5*A*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-3//2*sin(c+d*x)+1//15*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-16*A*b^3+10*B*a^3+-14*A*b*a^2+20*B*a*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//15*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*sec(c+d*x)^-1//2*(16*A*b^2+18*A*a^2+-20*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-3//2*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*(-2*B*a+2*A*b)*sin(c+d*x)+2*A*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*sec(c+d*x)^-1//2*(-2*B*a+2*A*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-3//2*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-4*A*b+2*B*a)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*sec(c+d*x)^-1//2*(-4*A*b^2+2*A*a^2+2*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2*b*a^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*(A*b+-1*B*a)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3//2*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(1//3*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(2*A*a^2+16*A*b^2+-12*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*sec(c+d*x)^-1//2*(-8*A*b^2+2*A*a^2+6*B*a*b)*sin(c+d*x)+2*b*a^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^-1//2*(A*b+-1*B*a)*sin(c+d*x)+-1//3*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*sec(c+d*x)^-1//2*(-16*A*b^3+-6*B*a^3+10*A*b*a^2+12*B*a*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-3//2*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :(-1//15*a^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*sec(c+d*x)^-1//2*(-48*A*b^3+-10*B*a^3+18*A*b*a^2+40*B*a*b^2)*sin(c+d*x)+1//5*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*sec(c+d*x)^-3//2*(-12*A*b^2+2*A*a^2+10*B*a*b)*sin(c+d*x)+1//15*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*(-96*A*b^3+10*B*a^3+-24*A*b*a^2+80*B*a*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2*b*a^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^-3//2*(A*b+-1*B*a)*sin(c+d*x)+1//15*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*sec(c+d*x)^-1//2*(-96*A*b^4+18*A*a^4+-50*B*b*a^3+48*A*a^2*b^2+80*B*a*b^3)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(1//3*b^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*sec(c+d*x)^(1/2)*(2*B*a^3+4*A*b^3+-10*B*a*b^2+4*A*b*a^2)*sin(c+d*x)+-1//3*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*sec(c+d*x)^-1//2*(2*A*b^2+6*A*a^2+-8*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*(-2*A*b+2*B*a)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2//3*a*b^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*(A*b+-1*B*a)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(-1*d^-1*(a+b*sec(c+d*x))^-3//2*(-3*b^2+3*a^2)^-1*sec(c+d*x)^(1/2)*(-2*B*a+2*A*b)*sin(c+d*x)+-1//3*a^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*sec(c+d*x)^(1/2)*(-4*B*a^3+-2*A*b^3+-4*B*a*b^2+10*A*b*a^2)*sin(c+d*x)+1//3*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*(-4*A*b^2+6*A*a^2+-2*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*sec(c+d*x)^-1//2*(-6*B*a^3+-4*A*b^3+-2*B*a*b^2+12*A*b*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(1//3*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*(6*B*a^3+16*A*b^3+-18*A*b*a^2+-4*B*a*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*sec(c+d*x)^-1//2*(6*A*a^4+16*A*b^4+-30*A*a^2*b^2+-4*B*a*b^3+12*B*b*a^3)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2//3*b*a^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*(A*b+-1*B*a)*sin(c+d*x)+2//3*b*a^-2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*sec(c+d*x)^(1/2)*(-5*B*a^3+-4*A*b^3+B*a*b^2+8*A*b*a^2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(1//3*a^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*sec(c+d*x)^-1//2*(2*A*a^4+16*A*b^4+-26*A*a^2*b^2+-8*B*a*b^3+16*B*b*a^3)*sin(c+d*x)+-1//3*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*sec(c+d*x)^-1//2*(-6*B*a^5+32*A*b^5+-56*A*a^2*b^3+-16*B*a*b^4+16*A*b*a^4+30*B*a^3*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*(-32*A*b^4+2*A*a^4+-18*B*b*a^3+16*B*a*b^3+32*A*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2//3*b*a^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*sec(c+d*x)^-1//2*(A*b+-1*B*a)*sin(c+d*x)+2//3*b*a^-2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*sec(c+d*x)^-1//2*(-7*B*a^3+-6*A*b^3+3*B*a*b^2+10*A*b*a^2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*sec(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :(-1//15*a^-4*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*sec(c+d*x)^-1//2*(-10*B*a^5+128*A*b^5+-196*A*a^2*b^3+-80*B*a*b^4+28*A*b*a^4+130*B*a^3*b^2)*sin(c+d*x)+1//15*a^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*sec(c+d*x)^-3//2*(6*A*a^4+96*A*b^4+-142*A*a^2*b^2+-60*B*a*b^3+100*B*b*a^3)*sin(c+d*x)+1//15*a^-5*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*sec(c+d*x)^(1/2)*(10*B*a^5+256*A*b^5+-232*A*a^2*b^3+-160*B*a*b^4+-34*A*b*a^4+160*B*a^3*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//15*a^-5*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*sec(c+d*x)^-1//2*(18*A*a^6+256*A*b^6+-424*A*a^2*b^4+-160*B*a*b^5+-80*B*b*a^5+110*A*a^4*b^2+280*B*a^3*b^3)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2//3*b*a^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*sec(c+d*x)^-3//2*(A*b+-1*B*a)*sin(c+d*x)+2//3*b*a^-2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*sec(c+d*x)^-3//2*(-9*B*a^3+-8*A*b^3+5*B*a*b^2+12*A*b*a^2)*sin(c+d*x))
@test integrate(cos(c+d*x)^7//2*(A+B*sec(c+d*x))*(a+a*sec(c+d*x)), x) == :(2//21*a*d^-1*(5A+7B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+6//5*a*d^-1*(A+B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//5*a*d^-1*cos(c+d*x)^3//2*(A+B)*sin(c+d*x)+2//7*A*a*d^-1*cos(c+d*x)^5//2*sin(c+d*x)+2//21*a*d^-1*cos(c+d*x)^(1/2)*(5A+7B)*sin(c+d*x))
@test integrate(cos(c+d*x)^5//2*(A+B*sec(c+d*x))*(a+a*sec(c+d*x)), x) == :(2//3*a*d^-1*(A+B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*a*d^-1*(3A+5B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*cos(c+d*x)^(1/2)*(A+B)*sin(c+d*x)+2//5*A*a*d^-1*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate(cos(c+d*x)^3//2*(A+B*sec(c+d*x))*(a+a*sec(c+d*x)), x) == :(2*a*d^-1*(A+B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*(A+3B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*A*a*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate(cos(c+d*x)^(1/2)*(A+B*sec(c+d*x))*(a+a*sec(c+d*x)), x) == :(2*a*d^-1*(A+B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*a*d^-1*(A+-1B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2*B*a*d^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate(cos(c+d*x)^-1//2*(A+B*sec(c+d*x))*(a+a*sec(c+d*x)), x) == :(-2*a*d^-1*(A+B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*(B+3A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*a*d^-1*cos(c+d*x)^-1//2*(A+B)*sin(c+d*x)+2//3*B*a*d^-1*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate(cos(c+d*x)^-3//2*(A+B*sec(c+d*x))*(a+a*sec(c+d*x)), x) == :(-2//5*a*d^-1*(3B+5A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*(A+B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*a*d^-1*cos(c+d*x)^-3//2*(A+B)*sin(c+d*x)+2//5*B*a*d^-1*cos(c+d*x)^-5//2*sin(c+d*x)+2//5*a*d^-1*cos(c+d*x)^-1//2*(3B+5A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^9//2*(A+B*sec(c+d*x)), x) == :(4//15*a^2*d^-1*(8A+9B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^2*d^-1*(5A+6B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//9*A*d^-1*cos(c+d*x)^5//2*(a^2+a^2*cos(c+d*x))*sin(c+d*x)+2//63*a^2*d^-1*cos(c+d*x)^5//2*(9B+11A)*sin(c+d*x)+4//21*a^2*d^-1*cos(c+d*x)^(1/2)*(5A+6B)*sin(c+d*x)+4//45*a^2*d^-1*cos(c+d*x)^3//2*(8A+9B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^7//2*(A+B*sec(c+d*x)), x) == :(4//5*a^2*d^-1*(3A+4B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^2*d^-1*(6A+7B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//7*A*d^-1*cos(c+d*x)^3//2*(a^2+a^2*cos(c+d*x))*sin(c+d*x)+2//35*a^2*d^-1*cos(c+d*x)^3//2*(7B+9A)*sin(c+d*x)+4//21*a^2*d^-1*cos(c+d*x)^(1/2)*(6A+7B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^5//2*(A+B*sec(c+d*x)), x) == :(4//3*a^2*d^-1*(A+2B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+4//5*a^2*d^-1*(4A+5B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//5*A*d^-1*cos(c+d*x)^(1/2)*(a^2+a^2*cos(c+d*x))*sin(c+d*x)+2//15*a^2*d^-1*cos(c+d*x)^(1/2)*(5B+7A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(4*A*a^2*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//3*a^2*d^-1*(2A+3B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*B*d^-1*cos(c+d*x)^-1//2*(a^2+a^2*cos(c+d*x))*sin(c+d*x)+2//3*a^2*d^-1*cos(c+d*x)^(1/2)*(A+-3B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(-4*B*a^2*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//3*a^2*d^-1*(2B+3A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*B*d^-1*cos(c+d*x)^-3//2*(a^2+a^2*cos(c+d*x))*sin(c+d*x)+2//3*a^2*d^-1*cos(c+d*x)^-1//2*(3A+5B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(-4//5*a^2*d^-1*(4B+5A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//3*a^2*d^-1*(B+2A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//5*B*d^-1*cos(c+d*x)^-5//2*(a^2+a^2*cos(c+d*x))*sin(c+d*x)+2//15*a^2*d^-1*cos(c+d*x)^-3//2*(5A+7B)*sin(c+d*x)+4//5*a^2*d^-1*cos(c+d*x)^-1//2*(4B+5A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^2*cos(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(-4//5*a^2*d^-1*(3B+4A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+4//21*a^2*d^-1*(6B+7A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//7*B*d^-1*cos(c+d*x)^-7//2*(a^2+a^2*cos(c+d*x))*sin(c+d*x)+2//35*a^2*d^-1*cos(c+d*x)^-5//2*(7A+9B)*sin(c+d*x)+4//5*a^2*d^-1*cos(c+d*x)^-1//2*(3B+4A)*sin(c+d*x)+4//21*a^2*d^-1*cos(c+d*x)^-3//2*(6B+7A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^5//2*(A+B*sec(c+d*x)), x) == :(-1//3*a^-1*d^-1*(-5B+5A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*a^-1*d^-1*(-15B+21A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1*d^-1*(a+a*cos(c+d*x))^-1*cos(c+d*x)^5//2*(A+-1B)*sin(c+d*x)+-1//3*a^-1*d^-1*cos(c+d*x)^(1/2)*(-5B+5A)*sin(c+d*x)+1//5*a^-1*d^-1*cos(c+d*x)^3//2*(-5B+7A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(-1*a^-1*d^-1*(-3B+3A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-1*d^-1*(-3B+5A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1*d^-1*(a+a*cos(c+d*x))^-1*cos(c+d*x)^3//2*(A+-1B)*sin(c+d*x)+1//3*a^-1*d^-1*cos(c+d*x)^(1/2)*(-3B+5A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(a^-1*d^-1*(-1B+3A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1*a^-1*d^-1*(A+-1B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1*d^-1*(a+a*cos(c+d*x))^-1*cos(c+d*x)^(1/2)*(A+-1B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(a^-1*d^-1*(A+B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1*a^-1*d^-1*(A+-1B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+d^-1*(a+a*cos(c+d*x))^-1*cos(c+d*x)^(1/2)*(A+-1B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(a^-1*d^-1*(A+-1B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+a^-1*d^-1*(A+-3B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+d^-1*(a+a*cos(c+d*x))^-1*cos(c+d*x)^-1//2*(A+-1B)*sin(c+d*x)+-1*a^-1*d^-1*cos(c+d*x)^-1//2*(A+-3B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1*cos(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :(-1*a^-1*d^-1*(-3B+3A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//3*a^-1*d^-1*(-5B+3A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+a^-1*d^-1*cos(c+d*x)^-1//2*(-3B+3A)*sin(c+d*x)+d^-1*(a+a*cos(c+d*x))^-1*cos(c+d*x)^-3//2*(A+-1B)*sin(c+d*x)+-1//3*a^-1*d^-1*cos(c+d*x)^-3//2*(-5B+3A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^5//2*(A+B*sec(c+d*x)), x) == :(-1//3*a^-2*d^-1*(-10B+15A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*a^-2*d^-1*(-35B+56A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*(-10B+15A)*sin(c+d*x)+-1//3*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^7//2*(A+-1B)*sin(c+d*x)+1//15*a^-2*d^-1*cos(c+d*x)^3//2*(-35B+56A)*sin(c+d*x)+-1*a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^5//2*(-2B+3A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(-1*a^-2*d^-1*(-4B+7A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-2*d^-1*(-5B+10A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//3*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^5//2*(A+-1B)*sin(c+d*x)+1//3*a^-2*d^-1*cos(c+d*x)^(1/2)*(-5B+10A)*sin(c+d*x)+-1//3*a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^3//2*(-4B+7A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(a^-2*d^-1*(-1B+4A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//3*a^-2*d^-1*(-2B+5A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//3*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^3//2*(A+-1B)*sin(c+d*x)+-1//3*a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^(1/2)*(-2B+5A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(-1*A*a^-2*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-2*d^-1*(B+2A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//3*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^(1/2)*(A+-1B)*sin(c+d*x)+A*a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(B*a^-2*d^-1*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-2*d^-1*(A+2B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^(1/2)*(A+-1B)*sin(c+d*x)+-1*B*a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :(a^-2*d^-1*(A+-4B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*a^-2*d^-1*(-5B+2A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1*a^-2*d^-1*cos(c+d*x)^-1//2*(A+-4B)*sin(c+d*x)+1//3*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^-1//2*(A+-1B)*sin(c+d*x)+1//3*a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^-1//2*(-5B+2A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-2*cos(c+d*x)^-7//2*(A+B*sec(c+d*x)), x) == :(-1*a^-2*d^-1*(-7B+4A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//3*a^-2*d^-1*(-10B+5A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+a^-2*d^-1*cos(c+d*x)^-1//2*(-7B+4A)*sin(c+d*x)+-1//3*a^-2*d^-1*cos(c+d*x)^-3//2*(-10B+5A)*sin(c+d*x)+1//3*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^-3//2*(A+-1B)*sin(c+d*x)+1//3*a^-2*d^-1*(1+cos(c+d*x))^-1*cos(c+d*x)^-3//2*(-7B+4A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(-1//10*a^-3*d^-1*(-49B+119A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//6*a^-3*d^-1*(-13B+33A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^7//2*(A+-1B)*sin(c+d*x)+-1//30*d^-1*(a^3+a^3*cos(c+d*x))^-1*cos(c+d*x)^3//2*(-49B+119A)*sin(c+d*x)+1//6*a^-3*d^-1*cos(c+d*x)^(1/2)*(-13B+33A)*sin(c+d*x)+-1//3*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^5//2*(-1B+2A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(-1//6*a^-3*d^-1*(-3B+13A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//10*a^-3*d^-1*(-9B+49A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^5//2*(A+-1B)*sin(c+d*x)+-1//6*d^-1*(a^3+a^3*cos(c+d*x))^-1*cos(c+d*x)^(1/2)*(-3B+13A)*sin(c+d*x)+-1//15*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^3//2*(-3B+8A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(-1//10*a^-3*d^-1*(B+9A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//6*a^-3*d^-1*(B+3A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^3//2*(A+-1B)*sin(c+d*x)+1//10*d^-1*(a^3+a^3*cos(c+d*x))^-1*cos(c+d*x)^(1/2)*(B+9A)*sin(c+d*x)+-1//15*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^(1/2)*(-1B+6A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(-1//10*a^-3*d^-1*(A+-1B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//6*a^-3*d^-1*(A+B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+-1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^(1/2)*(A+-1B)*sin(c+d*x)+1//10*d^-1*(a^3+a^3*cos(c+d*x))^-1*cos(c+d*x)^(1/2)*(A+-1B)*sin(c+d*x)+1//15*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^(1/2)*(B+4A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :(1//6*a^-3*d^-1*(A+3B)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//10*a^-3*d^-1*(A+9B)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//10*d^-1*(a^3+a^3*cos(c+d*x))^-1*cos(c+d*x)^(1/2)*(A+9B)*sin(c+d*x)+1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^(1/2)*(A+-1B)*sin(c+d*x)+1//15*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^(1/2)*(A+-6B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-3*cos(c+d*x)^-7//2*(A+B*sec(c+d*x)), x) == :(1//6*a^-3*d^-1*(-13B+3A)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//10*a^-3*d^-1*(-49B+9A)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+-1//10*a^-3*d^-1*cos(c+d*x)^-1//2*(-49B+9A)*sin(c+d*x)+1//5*d^-1*(a+a*cos(c+d*x))^-3*cos(c+d*x)^-1//2*(A+-1B)*sin(c+d*x)+1//6*d^-1*(a^3+a^3*cos(c+d*x))^-1*cos(c+d*x)^-1//2*(-13B+3A)*sin(c+d*x)+1//15*a^-1*d^-1*(a+a*cos(c+d*x))^-2*cos(c+d*x)^-1//2*(-8B+3A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^9//2*(A+B*sec(c+d*x)), x) == :(2//9*A*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^7//2*sin(c+d*x)+2//63*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^5//2*(8A+9B)*sin(c+d*x)+4//105*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(8A+9B)*sin(c+d*x)+16//315*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(8A+9B)*sin(c+d*x)+32//315*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(8A+9B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^7//2*(A+B*sec(c+d*x)), x) == :(2//7*A*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^5//2*sin(c+d*x)+2//35*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(6A+7B)*sin(c+d*x)+8//105*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(6A+7B)*sin(c+d*x)+16//105*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(6A+7B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*(A+B*sec(c+d*x)), x) == :(2//5*A*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x)+2//15*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(4A+5B)*sin(c+d*x)+4//15*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(4A+5B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(2//3*A*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x)+2//3*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(A+3B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(2*A*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+2*B*a^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(B*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+a^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(B+2A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :((1/2)*B*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x)+1//4*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(3B+4A)*sin(c+d*x)+1//4*a^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3B+4A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :(1//3*B*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-7//2*sin(c+d*x)+1//8*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(5B+6A)*sin(c+d*x)+1//8*a^(1/2)*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5B+6A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//12*a*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*(5B+6A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^11//2*(A+B*sec(c+d*x)), x) == :(2//11*A*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^9//2*sin(c+d*x)+2//99*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^7//2*(11B+12A)*sin(c+d*x)+2//693*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^5//2*(168A+187B)*sin(c+d*x)+4//1155*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(168A+187B)*sin(c+d*x)+16//3465*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(168A+187B)*sin(c+d*x)+32//3465*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(168A+187B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^9//2*(A+B*sec(c+d*x)), x) == :(2//9*A*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^7//2*sin(c+d*x)+2//63*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^5//2*(9B+10A)*sin(c+d*x)+2//105*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(34A+39B)*sin(c+d*x)+8//315*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(34A+39B)*sin(c+d*x)+16//315*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(34A+39B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^7//2*(A+B*sec(c+d*x)), x) == :(2//7*A*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*sin(c+d*x)+2//35*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(7B+8A)*sin(c+d*x)+2//105*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(52A+63B)*sin(c+d*x)+4//105*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(52A+63B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^5//2*(A+B*sec(c+d*x)), x) == :(2//5*A*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^3//2*sin(c+d*x)+2//15*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(3A+5B)*sin(c+d*x)+8//15*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(3A+5B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(2*B*a^3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//3*A*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x)+2//3*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(3B+4A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(B*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-1//2*sin(c+d*x)+a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-1B+2A)*sin(c+d*x)+a^3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2A+3B)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :((1/2)*B*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-3//2*sin(c+d*x)+1//4*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(4A+5B)*sin(c+d*x)+1//4*a^3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(7B+12A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(1//3*B*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-5//2*sin(c+d*x)+1//8*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(11B+14A)*sin(c+d*x)+1//8*a^3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(11B+14A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//12*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*(6A+7B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^3//2*cos(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :(1//4*B*a*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-7//2*sin(c+d*x)+1//24*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-7//2*(8A+9B)*sin(c+d*x)+1//64*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(75B+88A)*sin(c+d*x)+1//64*a^3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(75B+88A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//96*a^2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*(75B+88A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^11//2*(A+B*sec(c+d*x)), x) == :(2//11*A*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^9//2*sin(c+d*x)+2//99*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^7//2*(11B+14A)*sin(c+d*x)+2//693*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^5//2*(194A+209B)*sin(c+d*x)+2//1155*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(710A+803B)*sin(c+d*x)+8//3465*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(710A+803B)*sin(c+d*x)+16//3465*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(710A+803B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^9//2*(A+B*sec(c+d*x)), x) == :(2//9*A*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^7//2*sin(c+d*x)+2//21*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*(3B+4A)*sin(c+d*x)+2//315*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(292A+345B)*sin(c+d*x)+2//315*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(124A+135B)*sin(c+d*x)+4//315*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(292A+345B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^7//2*(A+B*sec(c+d*x)), x) == :(2//7*A*d^-1*(a+a*sec(c+d*x))^5//2*cos(c+d*x)^5//2*sin(c+d*x)+2//35*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^3//2*(5A+7B)*sin(c+d*x)+16//105*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(5A+7B)*sin(c+d*x)+64//105*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(5A+7B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^5//2*(A+B*sec(c+d*x)), x) == :(2*B*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2//5*A*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^3//2*sin(c+d*x)+2//15*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(5B+8A)*sin(c+d*x)+2//15*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(32A+35B)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(2A+5B)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//3*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-1//2*(-3B+2A)*sin(c+d*x)+1//3*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(3B+14A)*sin(c+d*x)+2//3*A*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :((1/2)*B*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^-1//2*sin(c+d*x)+1//4*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-1//2*(4A+7B)*sin(c+d*x)+1//4*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-9B+4A)*sin(c+d*x)+1//4*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(19B+20A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x)))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(1//3*B*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^-3//2*sin(c+d*x)+1//4*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-3//2*(2A+3B)*sin(c+d*x)+1//8*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(25B+38A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//24*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(49B+54A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(1//4*B*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^-5//2*sin(c+d*x)+1//24*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-5//2*(8A+11B)*sin(c+d*x)+1//64*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(163B+200A)*sin(c+d*x)+1//64*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(163B+200A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//96*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*(95B+104A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^5//2*cos(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :(1//5*B*a*d^-1*(a+a*sec(c+d*x))^3//2*cos(c+d*x)^-7//2*sin(c+d*x)+1//40*a^2*d^-1*(a+a*sec(c+d*x))^(1/2)*cos(c+d*x)^-7//2*(10A+13B)*sin(c+d*x)+1//128*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(283B+326A)*sin(c+d*x)+1//128*a^5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(283B+326A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//192*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*(283B+326A)*sin(c+d*x)+1//240*a^3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-7//2*(157B+170A)*sin(c+d*x))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^7//2*(A+B*sec(c+d*x)), x) == :(-1//35*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(-14B+2A)*sin(c+d*x)+-1//105*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-182B+86A)*sin(c+d*x)+1//105*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(-14B+62A)*sin(c+d*x)+2//7*A*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^5//2*sin(c+d*x)+2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^5//2*(A+B*sec(c+d*x)), x) == :(-1//15*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(-10B+2A)*sin(c+d*x)+1//15*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-10B+26A)*sin(c+d*x)+2//5*A*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*sin(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(-1//3*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-6B+2A)*sin(c+d*x)+2//3*A*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*sin(c+d*x)+2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(2*A*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*sin(c+d*x)+-1*2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(2*B*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(B*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*sin(c+d*x)+a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-1B+2A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1*2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :((1/2)*B*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*sin(c+d*x)+1//4*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(-1B+4A)*sin(c+d*x)+-1//4*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-7B+4A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+2^(1/2)*a^-1//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-1B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^5//2*(A+B*sec(c+d*x)), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^3//2*(A+-1B)*sin(c+d*x)+-1//30*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(-35B+39A)*sin(c+d*x)+1//10*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(-5B+9A)*sin(c+d*x)+1//30*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-95B+147A)*sin(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-11B+15A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^(1/2)*(A+-1B)*sin(c+d*x)+-1//6*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-15B+19A)*sin(c+d*x)+1//6*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(-3B+7A)*sin(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-7B+11A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-1//2*(A+-1B)*sin(c+d*x)+(1/2)*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-1B+5A)*sin(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-3B+7A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(-1//2*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-3//2*(A+-1B)*sin(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(B+3A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :((1/2)*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-3//2*(A+-1B)*sin(c+d*x)+2*B*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(A+-5B)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :((1/2)*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-5//2*(A+-1B)*sin(c+d*x)+a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-3B+2A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//2*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(A+-3B)*sin(c+d*x)+-1//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-9B+5A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-7//2*(A+B*sec(c+d*x)), x) == :((1/2)*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-7//2*(A+-1B)*sin(c+d*x)+-1//2*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-5//2*(A+-2B)*sin(c+d*x)+-1//4*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-19B+12A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//4*a^-1*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(-7B+6A)*sin(c+d*x)+1//4*2^(1/2)*a^-3//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-13B+9A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^5//2*(A+B*sec(c+d*x)), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^3//2*(A+-1B)*sin(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^3//2*(-13B+21A)*sin(c+d*x)+-1//240*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(-475B+787A)*sin(c+d*x)+1//80*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(-85B+157A)*sin(c+d*x)+1//240*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-1495B+2671A)*sin(c+d*x)+-1//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-163B+283A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^(1/2)*(A+-1B)*sin(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^(1/2)*(-9B+17A)*sin(c+d*x)+-1//48*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-147B+299A)*sin(c+d*x)+1//48*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(-39B+95A)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-75B+163A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-1//2*(A+-1B)*sin(c+d*x)+-1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-1//2*(-5B+13A)*sin(c+d*x)+1//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-9B+49A)*sin(c+d*x)+-1//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-19B+75A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-1//2*(A+-1B)*sin(c+d*x)+-1//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-1B+9A)*sin(c+d*x)+1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-1//2*(3B+5A)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(5B+19A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(-1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-5//2*(A+-1B)*sin(c+d*x)+1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-3//2*(3B+5A)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(3B+5A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-5//2*(A+B*sec(c+d*x)), x) == :(1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-5//2*(A+-1B)*sin(c+d*x)+2*B*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-3//2*(-11B+3A)*sin(c+d*x)+1//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-43B+3A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate((a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-7//2*(A+B*sec(c+d*x)), x) == :(1//4*d^-1*(a+a*sec(c+d*x))^-5//2*cos(c+d*x)^-7//2*(A+-1B)*sin(c+d*x)+a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-5B+2A)*arcsinh(a^(1/2)*(a+a*sec(c+d*x))^-1//2*tan(c+d*x))+-1//16*a^-2*d^-1*(a+a*sec(c+d*x))^-1//2*cos(c+d*x)^-3//2*(-35B+11A)*sin(c+d*x)+1//16*a^-1*d^-1*(a+a*sec(c+d*x))^-3//2*cos(c+d*x)^-5//2*(-15B+7A)*sin(c+d*x)+-1//32*2^(1/2)*a^-5//2*d^-1*cos(c+d*x)^(1/2)*sec(c+d*x)^(1/2)*(-115B+43A)*arctanh((1/2)*2^(1/2)*a^(1/2)*(a+a*sec(c+d*x))^-1//2*sec(c+d*x)^(1/2)*sin(c+d*x)))
@test integrate(cos(c+d*x)^7//2*(A+B*sec(c+d*x))*(a+b*sec(c+d*x)), x) == :(1//5*d^-1*(6*A*b+6*B*a)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*(10*A*a+14*B*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*cos(c+d*x)^3//2*(2*A*b+2*B*a)*sin(c+d*x)+1//21*d^-1*cos(c+d*x)^(1/2)*(10*A*a+14*B*b)*sin(c+d*x)+2//7*A*a*d^-1*cos(c+d*x)^5//2*sin(c+d*x))
@test integrate(cos(c+d*x)^5//2*(A+B*sec(c+d*x))*(a+b*sec(c+d*x)), x) == :(1//3*d^-1*(2*A*b+2*B*a)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*(6*A*a+10*B*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*cos(c+d*x)^(1/2)*(2*A*b+2*B*a)*sin(c+d*x)+2//5*A*a*d^-1*cos(c+d*x)^3//2*sin(c+d*x))
@test integrate(cos(c+d*x)^3//2*(A+B*sec(c+d*x))*(a+b*sec(c+d*x)), x) == :(d^-1*(2*A*b+2*B*a)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*(2*A*a+6*B*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2//3*A*a*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate(cos(c+d*x)^(1/2)*(A+B*sec(c+d*x))*(a+b*sec(c+d*x)), x) == :(d^-1*(-2*B*b+2*A*a)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+d^-1*(2*A*b+2*B*a)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*B*b*d^-1*cos(c+d*x)^-1//2*sin(c+d*x))
@test integrate(cos(c+d*x)^-1//2*(A+B*sec(c+d*x))*(a+b*sec(c+d*x)), x) == :(d^-1*(-2*A*b+-2*B*a)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*(2*B*b+6*A*a)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+d^-1*cos(c+d*x)^-1//2*(2*A*b+2*B*a)*sin(c+d*x)+2//3*B*b*d^-1*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate(cos(c+d*x)^-3//2*(A+B*sec(c+d*x))*(a+b*sec(c+d*x)), x) == :(1//3*d^-1*(2*A*b+2*B*a)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*(-10*A*a+-6*B*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*cos(c+d*x)^-3//2*(2*A*b+2*B*a)*sin(c+d*x)+1//5*d^-1*cos(c+d*x)^-1//2*(6*B*b+10*A*a)*sin(c+d*x)+2//5*B*b*d^-1*cos(c+d*x)^-5//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^7//2*(A+B*sec(c+d*x)), x) == :(1//5*d^-1*(6*B*a^2+10*B*b^2+12*A*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*(10*A*a^2+14*b*(A*b+2*B*a))*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*cos(c+d*x)^(1/2)*(10*A*a^2+14*b*(A*b+2*B*a))*sin(c+d*x)+2//35*a*d^-1*cos(c+d*x)^3//2*(7*B*a+9*A*b)*sin(c+d*x)+2//7*A*a*d^-1*cos(c+d*x)^3//2*(b+a*cos(c+d*x))*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^5//2*(A+B*sec(c+d*x)), x) == :(1//3*d^-1*(2*B*a^2+6*B*b^2+4*A*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*(6*A*a^2+10*b*(A*b+2*B*a))*Elliptic.E((1/2)*c+(1/2)*d*x,2)+2//15*a*d^-1*cos(c+d*x)^(1/2)*(5*B*a+7*A*b)*sin(c+d*x)+2//5*A*a*d^-1*cos(c+d*x)^(1/2)*(b+a*cos(c+d*x))*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(d^-1*(-2*B*b^2+2*B*a^2+4*A*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*(2*A*a^2+6*A*b^2+12*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*B*b^2*d^-1*cos(c+d*x)^-1//2*sin(c+d*x)+2//3*A*a^2*d^-1*cos(c+d*x)^(1/2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(d^-1*(-2*A*b^2+2*A*a^2+-4*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*(2*B*b^2+6*B*a^2+12*A*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+2*b*d^-1*cos(c+d*x)^-1//2*(A*b+2*B*a)*sin(c+d*x)+2//3*B*b^2*d^-1*cos(c+d*x)^-3//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(-1//5*d^-1*(6*B*b^2+10*B*a^2+20*A*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//3*d^-1*(2*A*b^2+6*A*a^2+4*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*cos(c+d*x)^-1//2*(6*B*b^2+10*B*a^2+20*A*a*b)*sin(c+d*x)+2//3*b*d^-1*cos(c+d*x)^-3//2*(A*b+2*B*a)*sin(c+d*x)+2//5*B*b^2*d^-1*cos(c+d*x)^-5//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^2*cos(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(-1//5*d^-1*(6*A*b^2+10*A*a^2+12*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2)+1//21*d^-1*(10*B*b^2+14*B*a^2+28*A*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2)+1//5*d^-1*cos(c+d*x)^-1//2*(6*A*b^2+10*A*a^2+12*B*a*b)*sin(c+d*x)+1//21*d^-1*cos(c+d*x)^-3//2*(10*B*b^2+14*B*a^2+28*A*a*b)*sin(c+d*x)+2//5*b*d^-1*cos(c+d*x)^-5//2*(A*b+2*B*a)*sin(c+d*x)+2//7*B*b^2*d^-1*cos(c+d*x)^-7//2*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^7//2*(A+B*sec(c+d*x)), x) == :(2//7*A*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*sin(c+d*x)+1//35*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*(2*A*b+14*B*a)*sin(c+d*x)+1//105*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(-8*A*b^2+50*A*a^2+14*B*a*b)*sin(c+d*x)+1//105*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(16*A*b^3+126*B*a^3+-28*B*a*b^2+38*A*b*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//105*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-2*b^2+2*a^2)*(8*A*b^2+25*A*a^2+-14*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*(A+B*sec(c+d*x)), x) == :(2//5*A*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*sin(c+d*x)+1//15*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(2*A*b+10*B*a)*sin(c+d*x)+1//15*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(-4*A*b^2+18*A*a^2+10*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//15*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-2*a^2+2*b^2)*(-5*B*a+2*A*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(2//3*A*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x)+1//3*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(2*A*b+6*B*a)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2//3*A*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(a^2+-1*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^3//2*cos(c+d*x)^9//2*(A+B*sec(c+d*x)), x) == :(1//63*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*(18*B*a+20*A*b)*sin(c+d*x)+1//315*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*(6*A*b^2+98*A*a^2+144*B*a*b)*sin(c+d*x)+1//315*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(-8*A*b^3+150*B*a^3+18*B*a*b^2+176*A*b*a^2)*sin(c+d*x)+2//9*A*a*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^7//2*sin(c+d*x)+1//315*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(16*A*b^4+294*A*a^4+-36*B*a*b^3+66*A*a^2*b^2+492*B*b*a^3)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//315*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-2*b^2+2*a^2)*(8*A*b^3+75*B*a^3+-18*B*a*b^2+39*A*b*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^3//2*cos(c+d*x)^7//2*(A+B*sec(c+d*x)), x) == :(1//35*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*(14*B*a+16*A*b)*sin(c+d*x)+1//105*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(6*A*b^2+50*A*a^2+84*B*a*b)*sin(c+d*x)+2//7*A*a*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*sin(c+d*x)+1//105*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(-12*A*b^3+126*B*a^3+42*B*a*b^2+164*A*b*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//105*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-2*b^2+2*a^2)*(-6*A*b^2+25*A*a^2+21*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^3//2*cos(c+d*x)^5//2*(A+B*sec(c+d*x)), x) == :(1//15*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(10*B*a+12*A*b)*sin(c+d*x)+2//5*A*a*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*sin(c+d*x)+1//15*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(6*A*b^2+18*A*a^2+40*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//15*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-2*b^2+2*a^2)*(3*A*b+5*B*a)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^5//2*cos(c+d*x)^11//2*(A+B*sec(c+d*x)), x) == :(1//693*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*(162*A*a^2+226*A*b^2+418*B*a*b)*sin(c+d*x)+1//3465*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*(30*A*b^3+1078*B*a^3+1650*B*a*b^2+2290*A*b*a^2)*sin(c+d*x)+1//3465*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(-40*A*b^4+1350*A*a^4+110*B*a*b^3+2050*A*a^2*b^2+3586*B*b*a^3)*sin(c+d*x)+2//11*A*a*d^-1*(a+b*sec(c+d*x))^3//2*cos(c+d*x)^9//2*sin(c+d*x)+2//99*a*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^7//2*(11*B*a+14*A*b)*sin(c+d*x)+1//3465*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(80*A*b^5+3234*B*a^5+-220*B*a*b^4+510*A*a^2*b^3+6138*B*a^3*b^2+7410*A*b*a^4)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3465*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-2*b^2+2*a^2)*(40*A*b^4+675*A*a^4+-110*B*a*b^3+285*A*a^2*b^2+1254*B*b*a^3)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^5//2*cos(c+d*x)^9//2*(A+B*sec(c+d*x)), x) == :(1//315*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*(98*A*a^2+150*A*b^2+270*B*a*b)*sin(c+d*x)+1//315*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(10*A*b^3+150*B*a^3+270*B*a*b^2+326*A*b*a^2)*sin(c+d*x)+2//9*A*a*d^-1*(a+b*sec(c+d*x))^3//2*cos(c+d*x)^7//2*sin(c+d*x)+2//21*a*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^5//2*(3*B*a+4*A*b)*sin(c+d*x)+1//315*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(-20*A*b^4+294*A*a^4+90*B*a*b^3+558*A*a^2*b^2+870*B*b*a^3)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//315*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-2*b^2+2*a^2)*(-10*A*b^3+75*B*a^3+45*B*a*b^2+114*A*b*a^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^5//2*cos(c+d*x)^7//2*(A+B*sec(c+d*x)), x) == :(1//105*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(50*A*a^2+90*A*b^2+154*B*a*b)*sin(c+d*x)+2//7*A*a*d^-1*(a+b*sec(c+d*x))^3//2*cos(c+d*x)^5//2*sin(c+d*x)+2//35*a*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*(7*B*a+10*A*b)*sin(c+d*x)+1//105*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(30*A*b^3+126*B*a^3+290*A*b*a^2+322*B*a*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//105*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-2*b^2+2*a^2)*(15*A*b^2+25*A*a^2+56*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-1//2*cos(c+d*x)^5//2*(A+B*sec(c+d*x)), x) == :(-1//15*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(-10*B*a+8*A*b)*sin(c+d*x)+2//5*A*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^3//2*sin(c+d*x)+1//15*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-16*A*b^3+10*B*a^3+-14*A*b*a^2+20*B*a*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//15*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(16*A*b^2+18*A*a^2+-20*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-1//2*cos(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(2//3*A*a^-1*d^-1*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*sin(c+d*x)+-1//3*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*(-6*B*a+4*A*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(2*A*a^2+4*A*b^2+-6*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-1//2*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-2*A*b+2*B*a)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2*A*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*cos(c+d*x)^(1/2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-3//2*cos(c+d*x)^5//2*(A+B*sec(c+d*x)), x) == :(-1//15*a^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*cos(c+d*x)^(1/2)*(-48*A*b^3+-10*B*a^3+18*A*b*a^2+40*B*a*b^2)*sin(c+d*x)+1//5*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*cos(c+d*x)^3//2*(-12*A*b^2+2*A*a^2+10*B*a*b)*sin(c+d*x)+1//15*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-96*A*b^3+10*B*a^3+-24*A*b*a^2+80*B*a*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2*b*a^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^3//2*(A*b+-1*B*a)*sin(c+d*x)+1//15*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*cos(c+d*x)^(1/2)*(-96*A*b^4+18*A*a^4+-50*B*b*a^3+48*A*a^2*b^2+80*B*a*b^3)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-3//2*cos(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(1//3*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(2*A*a^2+16*A*b^2+-12*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3*a^-2*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*cos(c+d*x)^(1/2)*(-8*A*b^2+2*A*a^2+6*B*a*b)*sin(c+d*x)+2*b*a^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^(1/2)*(A*b+-1*B*a)*sin(c+d*x)+-1//3*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*cos(c+d*x)^(1/2)*(-16*A*b^3+-6*B*a^3+10*A*b*a^2+12*B*a*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-3//2*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*(-4*A*b+2*B*a)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*cos(c+d*x)^(1/2)*(-4*A*b^2+2*A*a^2+2*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2*b*a^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*(A*b+-1*B*a)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-3//2*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*(-2*B*a+2*A*b)*sin(c+d*x)+2*A*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*cos(c+d*x)^-1//2*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-1*cos(c+d*x)^(1/2)*(-2*B*a+2*A*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-5//2*cos(c+d*x)^5//2*(A+B*sec(c+d*x)), x) == :(-1//15*a^-4*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*cos(c+d*x)^(1/2)*(-10*B*a^5+128*A*b^5+-196*A*a^2*b^3+-80*B*a*b^4+28*A*b*a^4+130*B*a^3*b^2)*sin(c+d*x)+1//15*a^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*cos(c+d*x)^3//2*(6*A*a^4+96*A*b^4+-142*A*a^2*b^2+-60*B*a*b^3+100*B*b*a^3)*sin(c+d*x)+1//15*a^-5*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*(10*B*a^5+256*A*b^5+-232*A*a^2*b^3+-160*B*a*b^4+-34*A*b*a^4+160*B*a^3*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//15*a^-5*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*cos(c+d*x)^(1/2)*(18*A*a^6+256*A*b^6+-424*A*a^2*b^4+-160*B*a*b^5+-80*B*b*a^5+110*A*a^4*b^2+280*B*a^3*b^3)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2//3*b*a^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*cos(c+d*x)^3//2*(A*b+-1*B*a)*sin(c+d*x)+2//3*b*a^-2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*cos(c+d*x)^3//2*(-9*B*a^3+-8*A*b^3+5*B*a*b^2+12*A*b*a^2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*cos(c+d*x)^3//2*(A+B*sec(c+d*x)), x) == :(1//3*a^-3*d^-1*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*cos(c+d*x)^(1/2)*(2*A*a^4+16*A*b^4+-26*A*a^2*b^2+-8*B*a*b^3+16*B*b*a^3)*sin(c+d*x)+-1//3*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*cos(c+d*x)^(1/2)*(-6*B*a^5+32*A*b^5+-56*A*a^2*b^3+-16*B*a*b^4+16*A*b*a^4+30*B*a^3*b^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3*a^-4*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*(-32*A*b^4+2*A*a^4+-18*B*b*a^3+16*B*a*b^3+32*A*a^2*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2//3*b*a^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*cos(c+d*x)^(1/2)*(A*b+-1*B*a)*sin(c+d*x)+2//3*b*a^-2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*cos(c+d*x)^(1/2)*(-7*B*a^3+-6*A*b^3+3*B*a*b^2+10*A*b*a^2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*cos(c+d*x)^(1/2)*(A+B*sec(c+d*x)), x) == :(1//3*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*(6*B*a^3+16*A*b^3+-18*A*b*a^2+-4*B*a*b^2)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3*a^-3*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*cos(c+d*x)^(1/2)*(6*A*a^4+16*A*b^4+-30*A*a^2*b^2+-4*B*a*b^3+12*B*b*a^3)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2//3*b*a^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*(A*b+-1*B*a)*sin(c+d*x)+2//3*b*a^-2*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*cos(c+d*x)^-1//2*(-5*B*a^3+-4*A*b^3+B*a*b^2+8*A*b*a^2)*sin(c+d*x))
@test integrate((a+b*sec(c+d*x))^-5//2*cos(c+d*x)^-1//2*(A+B*sec(c+d*x)), x) == :(-1*d^-1*(a+b*sec(c+d*x))^-3//2*(-3*b^2+3*a^2)^-1*cos(c+d*x)^-1//2*(-2*B*a+2*A*b)*sin(c+d*x)+-1//3*a^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*cos(c+d*x)^-1//2*(-4*B*a^3+-2*A*b^3+-4*B*a*b^2+10*A*b*a^2)*sin(c+d*x)+1//3*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*(-4*A*b^2+6*A*a^2+-2*B*a*b)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3*a^-2*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*cos(c+d*x)^(1/2)*(-6*B*a^3+-4*A*b^3+-2*B*a*b^2+12*A*b*a^2)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1))
@test integrate((a+b*sec(c+d*x))^-5//2*cos(c+d*x)^-3//2*(A+B*sec(c+d*x)), x) == :(1//3*b^-1*d^-1*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-2*cos(c+d*x)^-1//2*(2*B*a^3+4*A*b^3+-10*B*a*b^2+4*A*b*a^2)*sin(c+d*x)+-1//3*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^-1//2*(a+b*sec(c+d*x))^(1/2)*(a^2+-1*b^2)^-2*cos(c+d*x)^(1/2)*(2*A*b^2+6*A*a^2+-8*B*a*b)*Elliptic.E((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+1//3*a^-1*d^-1*((a+b)^-1*(b+a*cos(c+d*x)))^(1/2)*(a+b*sec(c+d*x))^-1//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*(-2*A*b+2*B*a)*Elliptic.F((1/2)*c+(1/2)*d*x,2*a*(a+b)^-1)+2//3*a*b^-1*d^-1*(a+b*sec(c+d*x))^-3//2*(a^2+-1*b^2)^-1*cos(c+d*x)^-1//2*(A*b+-1*B*a)*sin(c+d*x))

max_stars_repo_path: test/4 Trig functions/4.5 Secant/4.5.3.1 (a+b sec)^m (d sec)^n (A+B sec).jl