\[ \int \frac {x^{31} \sqrt {1+x^{16}}}{1-x^{16}} \, dx \]
Optimal antiderivative \[ -\frac {\left (x^{16}+1\right )^{\frac {3}{2}}}{24}+\frac {\arctanh \left (\frac {\sqrt {x^{16}+1}\, \sqrt {2}}{2}\right ) \sqrt {2}}{8}-\frac {\sqrt {x^{16}+1}}{8} \]
command
integrate(x**31*(x**16+1)**(1/2)/(-x**16+1),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ - \frac {\left (x^{16} + 1\right )^{\frac {3}{2}}}{24} - \frac {\sqrt {x^{16} + 1}}{8} - \frac {\begin {cases} - \frac {\sqrt {2} \operatorname {acoth}{\left (\frac {\sqrt {2} \sqrt {x^{16} + 1}}{2} \right )}}{2} & \text {for}\: x^{16} > 1 \\- \frac {\sqrt {2} \operatorname {atanh}{\left (\frac {\sqrt {2} \sqrt {x^{16} + 1}}{2} \right )}}{2} & \text {for}\: x^{16} < 1 \end {cases}}{4} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________