\[ \int \tan ^6(e+f x) \left (a+b \tan ^2(e+f x)\right )^2 \, dx \]
Optimal antiderivative \[ -\left (a -b \right )^{2} x +\frac {\left (a -b \right )^{2} \tan \left (f x +e \right )}{f}-\frac {\left (a -b \right )^{2} \left (\tan ^{3}\left (f x +e \right )\right )}{3 f}+\frac {\left (a -b \right )^{2} \left (\tan ^{5}\left (f x +e \right )\right )}{5 f}+\frac {\left (2 a -b \right ) b \left (\tan ^{7}\left (f x +e \right )\right )}{7 f}+\frac {b^{2} \left (\tan ^{9}\left (f x +e \right )\right )}{9 f} \]
command
integrate(tan(f*x+e)^6*(a+b*tan(f*x+e)^2)^2,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 \[ \text {Timed out} \]_______________________________________________________