# Maple integration test file: "4 Trig functions\4.2 Cosine\4.2.2.2 (g sin)^p (a+b cos)^m (c+d cos)^n.txt"

lst:=[

# Integrands of the form (g Sin[e+f x])^p (a+a Cos[e+f x])^m (c-c Cos[e+f x])^n

# Integrands of the form (g Sin[e+f x])^p (a+a Cos[e+f x])^m (c+d Cos[e+f x])^n

# Integrands of the form (g Sin[e+f x])^p (a+b Cos[e+f x])^m (c+d Cos[e+f x])^n

# Integrands of the form (g Sin[e+f x])^m (a+b Cos[e+f x])^n / (c+d Cos[e+f x])

# Integrands of the form (g Sin[e+f x])^(m/2) (d Cos[e+f x])^(n/2) / (a+b Cos[e+f x])
[sqrt(d*cos(e+f*x))*sqrt(g*sin(e+f*x))/(a+b*cos(e+f*x)),x,16,-arctan(1-sqrt(2)*sqrt(d)*sqrt(g*sin(e+f*x))/(sqrt(g)*sqrt(d*cos(e+f*x))))*sqrt(d)*sqrt(g)/(b*f*sqrt(2))+arctan(1+sqrt(2)*sqrt(d)*sqrt(g*sin(e+f*x))/(sqrt(g)*sqrt(d*cos(e+f*x))))*sqrt(d)*sqrt(g)/(b*f*sqrt(2))+1/2*log(sqrt(g)-sqrt(2)*sqrt(d)*sqrt(g*sin(e+f*x))/sqrt(d*cos(e+f*x))+sqrt(g)*tan(e+f*x))*sqrt(d)*sqrt(g)/(b*f*sqrt(2))-1/2*log(sqrt(g)+sqrt(2)*sqrt(d)*sqrt(g*sin(e+f*x))/sqrt(d*cos(e+f*x))+sqrt(g)*tan(e+f*x))*sqrt(d)*sqrt(g)/(b*f*sqrt(2))+2*a*d*EllipticPi(sqrt(g*sin(e+f*x))/(sqrt(g)*sqrt(1+cos(e+f*x))),-sqrt(-a+b)/sqrt(a+b),I)*sqrt(2)*sqrt(g)*sqrt(cos(e+f*x))/(b*f*sqrt(-a+b)*sqrt(a+b)*sqrt(d*cos(e+f*x)))-2*a*d*EllipticPi(sqrt(g*sin(e+f*x))/(sqrt(g)*sqrt(1+cos(e+f*x))),sqrt(-a+b)/sqrt(a+b),I)*sqrt(2)*sqrt(g)*sqrt(cos(e+f*x))/(b*f*sqrt(-a+b)*sqrt(a+b)*sqrt(d*cos(e+f*x)))],
[sqrt(d*cos(e+f*x))/((a+b*cos(e+f*x))*sqrt(g*sin(e+f*x))),x,4,2*EllipticPi(sqrt(d*cos(e+f*x))/(sqrt(d)*sqrt(1+sin(e+f*x))),-a/(b-sqrt(-a^2+b^2)),I)*sqrt(2)*sqrt(d)*sqrt(sin(e+f*x))/(f*sqrt(-a^2+b^2)*sqrt(g*sin(e+f*x)))-2*EllipticPi(sqrt(d*cos(e+f*x))/(sqrt(d)*sqrt(1+sin(e+f*x))),-a/(b+sqrt(-a^2+b^2)),I)*sqrt(2)*sqrt(d)*sqrt(sin(e+f*x))/(f*sqrt(-a^2+b^2)*sqrt(g*sin(e+f*x)))],
[sqrt(g*sin(e+f*x))/((a+b*cos(e+f*x))*sqrt(d*cos(e+f*x))),x,5,-2*EllipticPi(sqrt(g*sin(e+f*x))/(sqrt(g)*sqrt(1+cos(e+f*x))),-sqrt(-a+b)/sqrt(a+b),I)*sqrt(2)*sqrt(g)*sqrt(cos(e+f*x))/(f*sqrt(-a+b)*sqrt(a+b)*sqrt(d*cos(e+f*x)))+2*EllipticPi(sqrt(g*sin(e+f*x))/(sqrt(g)*sqrt(1+cos(e+f*x))),sqrt(-a+b)/sqrt(a+b),I)*sqrt(2)*sqrt(g)*sqrt(cos(e+f*x))/(f*sqrt(-a+b)*sqrt(a+b)*sqrt(d*cos(e+f*x)))],
[1/((a+b*cos(e+f*x))*sqrt(d*cos(e+f*x))*sqrt(g*sin(e+f*x))),x,7,-2*b*EllipticPi(sqrt(d*cos(e+f*x))/(sqrt(d)*sqrt(1+sin(e+f*x))),-a/(b-sqrt(-a^2+b^2)),I)*sqrt(2)*sqrt(sin(e+f*x))/(a*f*sqrt(-a^2+b^2)*sqrt(d)*sqrt(g*sin(e+f*x)))+2*b*EllipticPi(sqrt(d*cos(e+f*x))/(sqrt(d)*sqrt(1+sin(e+f*x))),-a/(b+sqrt(-a^2+b^2)),I)*sqrt(2)*sqrt(sin(e+f*x))/(a*f*sqrt(-a^2+b^2)*sqrt(d)*sqrt(g*sin(e+f*x)))+sqrt(cos(e-1/4*Pi+f*x)^2)/cos(e-1/4*Pi+f*x)*EllipticF(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(sin(2*e+2*f*x))/(a*f*sqrt(d*cos(e+f*x))*sqrt(g*sin(e+f*x)))]]:
