49.8 Problem number 220

\[ \int (a+a \sin (e+f x))^m (c-c \sin (e+f x))^3 (B (-3+m)-B (4+m) \sin (e+f x)) \, dx \]

Optimal antiderivative \[ \frac {a^{3} B \,c^{3} \left (\cos ^{7}\left (f x +e \right )\right ) \left (a +a \sin \left (f x +e \right )\right )^{-3+m}}{f} \]

command

integrate((a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**3*(B*(-3+m)-B*(4+m)*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 \[ \text {Timed out} \]_____________________________________________________