\[ \int \frac {1}{(a+a \sin (e+f x)) (c+d \sin (e+f x))} \, dx \]
Optimal antiderivative \[ -\frac {\cos \left (f x +e \right )}{\left (c -d \right ) f \left (a +a \sin \left (f x +e \right )\right )}-\frac {2 d \arctan \left (\frac {d +c \tan \left (\frac {f x}{2}+\frac {e}{2}\right )}{\sqrt {c^{2}-d^{2}}}\right )}{a \left (c -d \right ) f \sqrt {c^{2}-d^{2}}} \]
command
integrate(1/(a+a*sin(f*x+e))/(c+d*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 \[ \text {Timed out} \]_____________________________________________________