\[ \int \cos ^5(e+f x) (a+a \sin (e+f x))^m (A+B \sin (e+f x)) \, dx \]
Optimal antiderivative \[ \frac {4 \left (A -B \right ) \left (a +a \sin \left (f x +e \right )\right )^{3+m}}{a^{3} f \left (3+m \right )}-\frac {4 \left (A -2 B \right ) \left (a +a \sin \left (f x +e \right )\right )^{4+m}}{a^{4} f \left (4+m \right )}+\frac {\left (A -5 B \right ) \left (a +a \sin \left (f x +e \right )\right )^{5+m}}{a^{5} f \left (5+m \right )}+\frac {B \left (a +a \sin \left (f x +e \right )\right )^{6+m}}{a^{6} f \left (6+m \right )} \]
command
integrate(cos(f*x+e)**5*(a+a*sin(f*x+e))**m*(A+B*sin(f*x+e)),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {output too large to display} \]
Sympy 1.8 under Python 3.8.8 output \[ \text {Timed out} \]_____________________________________________________