48.2 Problem number 440

\[ \int \frac {\cos ^4(e+f x) \sin (e+f x)}{(a+a \sin (e+f x))^6} \, dx \]

Optimal antiderivative \[ \frac {\cos ^{5}\left (f x +e \right )}{7 f \left (a +a \sin \left (f x +e \right )\right )^{6}}-\frac {6 \left (\cos ^{5}\left (f x +e \right )\right )}{35 a f \left (a +a \sin \left (f x +e \right )\right )^{5}} \]

command

integrate(cos(f*x+e)**4*sin(f*x+e)/(a+a*sin(f*x+e))**6,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 \[ \text {Timed out} \]_____________________________________________________