\[ \int \frac {\cos ^3(c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx \]
Optimal antiderivative \[ -\frac {d \cosineIntegral \left (\frac {2 d e}{f}+2 d x \right ) \cos \left (2 c -\frac {2 d e}{f}\right )}{a \,f^{2}}-\frac {\cos \left (d x +c \right )}{a f \left (f x +e \right )}-\frac {d \cos \left (c -\frac {d e}{f}\right ) \sinIntegral \left (\frac {d e}{f}+d x \right )}{a \,f^{2}}+\frac {d \sinIntegral \left (\frac {2 d e}{f}+2 d x \right ) \sin \left (2 c -\frac {2 d e}{f}\right )}{a \,f^{2}}-\frac {d \cosineIntegral \left (\frac {d e}{f}+d x \right ) \sin \left (c -\frac {d e}{f}\right )}{a \,f^{2}}+\frac {\sin \left (2 d x +2 c \right )}{2 a f \left (f x +e \right )} \]
command
integrate(cos(d*x+c)^3/(f*x+e)^2/(a+a*sin(d*x+c)),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {output too large to display} \]
Giac 1.7.0 via sagemath 9.3 output \[ \text {Timed out} \]_______________________________________________________