\[ \int \frac {\cot ^3(e+f x)}{\left (a+b \tan ^2(e+f x)\right )^2} \, dx \]
Optimal antiderivative \[ -\frac {\cot ^{2}\left (f x +e \right )}{2 a^{2} f}-\frac {\ln \left (\cos \left (f x +e \right )\right )}{\left (a -b \right )^{2} f}-\frac {\left (a +2 b \right ) \ln \left (\tan \left (f x +e \right )\right )}{a^{3} f}-\frac {\left (3 a -2 b \right ) b^{2} \ln \left (a +b \left (\tan ^{2}\left (f x +e \right )\right )\right )}{2 a^{3} \left (a -b \right )^{2} f}+\frac {b^{2}}{2 a^{2} \left (a -b \right ) f \left (a +b \left (\tan ^{2}\left (f x +e \right )\right )\right )} \]
command
integrate(cot(f*x+e)**3/(a+b*tan(f*x+e)**2)**2,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 \[ \text {Timed out} \]_____________________________________________________