\[ \int \frac {1}{(\cos (x)+\cos (3 x))^5} \, dx \]
Optimal antiderivative \[ -\frac {523 \arctanh \left (\sin \left (x \right )\right )}{256}+\frac {\sin \left (x \right )}{32 \left (1-2 \left (\sin ^{2}\left (x \right )\right )\right )^{4}}-\frac {17 \sin \left (x \right )}{192 \left (1-2 \left (\sin ^{2}\left (x \right )\right )\right )^{3}}+\frac {203 \sin \left (x \right )}{768 \left (1-2 \left (\sin ^{2}\left (x \right )\right )\right )^{2}}-\frac {437 \sin \left (x \right )}{512 \left (1-2 \left (\sin ^{2}\left (x \right )\right )\right )}+\frac {1483 \arctanh \left (\sin \left (x \right ) \sqrt {2}\right ) \sqrt {2}}{1024}-\frac {43 \sec \left (x \right ) \tan \left (x \right )}{256}-\frac {\left (\sec ^{3}\left (x \right )\right ) \tan \left (x \right )}{128} \]
command
integrate(1/(cos(x)+cos(3*x))^5,x, algorithm="maxima")
Maxima 5.46 SBCL 2.0.1.debian via sagemath 9.6 output
\[ \text {output too large to display} \]
Maxima 5.44 via sagemath 9.3 output \[ \text {Timed out} \]_____________________________________________________