\[ \int (a+a \sin (e+f x))^m (c-c \sin (e+f x))^n (B (m-n)-B (1+m+n) \sin (e+f x)) \, dx \]
Optimal antiderivative \[ \frac {B \cos \left (f x +e \right ) \left (a +a \sin \left (f x +e \right )\right )^{m} \left (c -c \sin \left (f x +e \right )\right )^{n}}{f} \]
command
integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n*(B*(m-n)-B*(1+m+n)*sin(f*x+e)),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 \[ \text {Timed out} \]_______________________________________________________