13.1 Problem number 1309

$$\int \frac{x^{13/2}}{\sqrt{a+b{x}^5}}dx$$

Optimal antiderivative $$-\frac{a\mathrm{arctanh}\left(\frac{x^{\frac{5}{2}}\sqrt{b}}{\sqrt{b{x}^5+a}}\right)}{5b^{\frac{3}{2}}}+\frac{x^{\frac{5}{2}}\sqrt{b{x}^5+a}}{5b}$$

command

integrate(x**(13/2)/(b*x**5+a)**(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

$$\frac{\sqrt{a}{x}^{\frac{5}{2}}\sqrt{1+\frac{b{x}^5}{a}}}{5b}-\frac{a\mathrm{asinh}\left(\frac{\sqrt{b}{x}^{\frac{5}{2}}}{\sqrt{a}}\right)}{5b^{\frac{3}{2}}}$$