\[ \int \frac {1}{1-\cosh ^8(x)} \, dx \]
Optimal antiderivative \[ \frac {\coth \left (x \right )}{4}+\frac {\arctanh \left (\frac {\tanh \left (x \right )}{\sqrt {1-i}}\right )}{4 \sqrt {1-i}}+\frac {\arctanh \left (\frac {\tanh \left (x \right )}{\sqrt {1+i}}\right )}{4 \sqrt {1+i}}+\frac {\arctanh \left (\frac {\sqrt {2}\, \tanh \left (x \right )}{2}\right ) \sqrt {2}}{8} \]
command
integrate(1/(1-cosh(x)^8),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {1}{16} \, \sqrt {2} \log \left (-\frac {2 \, \sqrt {2} - e^{\left (2 \, x\right )} - 3}{2 \, \sqrt {2} + e^{\left (2 \, x\right )} + 3}\right ) + \frac {1}{2 \, {\left (e^{\left (2 \, x\right )} - 1\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________