\[ \int \frac {(a+b x)^n}{x^{5/2}} \, dx \]
Optimal antiderivative \[ -\frac {2 \left (b x +a \right )^{n} \hypergeom \left (\left [-\frac {3}{2}, -n \right ], \left [-\frac {1}{2}\right ], -\frac {b x}{a}\right ) \left (1+\frac {b x}{a}\right )^{-n}}{3 x^{\frac {3}{2}}} \]
command
integrate((b*x+a)**n/x**(5/2),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ - \frac {2 a^{n} {{}_{2}F_{1}\left (\begin {matrix} - \frac {3}{2}, - n \\ - \frac {1}{2} \end {matrix}\middle | {\frac {b x e^{i \pi }}{a}} \right )}}{3 x^{\frac {3}{2}}} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________