13.2 Problem number 1314

\[ \int \frac {x^{13/2}}{\sqrt {1+x^5}} \, dx \]

Optimal antiderivative \[ -\frac {\arcsinh \! \left (x^{\frac {5}{2}}\right )}{5}+\frac {x^{\frac {5}{2}} \sqrt {x^{5}+1}}{5} \]

command

integrate(x**(13/2)/(x**5+1)**(1/2),x)

Sympy 1.10.1 under Python 3.10.4 output

\[ \text {Exception raised: SystemError} \]

Sympy 1.8 under Python 3.8.8 output

\[ \frac {x^{\frac {5}{2}} \sqrt {x^{5} + 1}}{5} - \frac {\operatorname {asinh}{\left (x^{\frac {5}{2}} \right )}}{5} \]