\[ \int \left (1+\cot ^2(9 x)\right )^2 \left (1+\tan ^2(9 x)\right )^3 \, dx \]
Optimal antiderivative \[ -\frac {4 \cot \left (9 x \right )}{9}-\frac {\left (\cot ^{3}\left (9 x \right )\right )}{27}+\frac {2 \tan \left (9 x \right )}{3}+\frac {4 \left (\tan ^{3}\left (9 x \right )\right )}{27}+\frac {\left (\tan ^{5}\left (9 x \right )\right )}{45} \]
command
integrate((1+cot(9*x)^2)^2*(1+tan(9*x)^2)^3,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {1}{45} \, \tan \left (9 \, x\right )^{5} + \frac {4}{27} \, \tan \left (9 \, x\right )^{3} - \frac {12 \, \tan \left (9 \, x\right )^{2} + 1}{27 \, \tan \left (9 \, x\right )^{3}} + \frac {2}{3} \, \tan \left (9 \, x\right ) \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________