\[ \int \frac {-1+x^6}{x^{19} \sqrt {1+x^6}} \, dx \]
Optimal antiderivative \[ \frac {\sqrt {x^{6}+1}\, \left (33 x^{12}-22 x^{6}+8\right )}{144 x^{18}}-\frac {11 \arctanh \left (\sqrt {x^{6}+1}\right )}{48} \]
command
integrate((x**6-1)/x**19/(x**6+1)**(1/2),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \frac {11 \log {\left (-1 + \frac {1}{\sqrt {x^{6} + 1}} \right )}}{96} - \frac {11 \log {\left (1 + \frac {1}{\sqrt {x^{6} + 1}} \right )}}{96} - \frac {7}{32 \cdot \left (1 + \frac {1}{\sqrt {x^{6} + 1}}\right )} + \frac {1}{16 \left (1 + \frac {1}{\sqrt {x^{6} + 1}}\right )^{2}} - \frac {1}{144 \left (1 + \frac {1}{\sqrt {x^{6} + 1}}\right )^{3}} - \frac {7}{32 \left (-1 + \frac {1}{\sqrt {x^{6} + 1}}\right )} - \frac {1}{16 \left (-1 + \frac {1}{\sqrt {x^{6} + 1}}\right )^{2}} - \frac {1}{144 \left (-1 + \frac {1}{\sqrt {x^{6} + 1}}\right )^{3}} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________