\[ \int \frac {1}{1-x^8} \, dx \]
Optimal antiderivative \[ \frac {\arctan \left (x \right )}{4}+\frac {\arctanh \left (x \right )}{4}+\frac {\arctan \left (-1+x \sqrt {2}\right ) \sqrt {2}}{8}+\frac {\arctan \left (1+x \sqrt {2}\right ) \sqrt {2}}{8}-\frac {\ln \left (1+x^{2}-x \sqrt {2}\right ) \sqrt {2}}{16}+\frac {\ln \left (1+x^{2}+x \sqrt {2}\right ) \sqrt {2}}{16} \]
command
integrate(1/(-x**8+1),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ - \frac {\log {\left (x - 1 \right )}}{8} + \frac {\log {\left (x + 1 \right )}}{8} - \frac {i \log {\left (x - i \right )}}{8} + \frac {i \log {\left (x + i \right )}}{8} - \operatorname {RootSum} {\left (4096 t^{4} + 1, \left ( t \mapsto t \log {\left (- 8 t + x \right )} \right )\right )} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________