\[ \int \frac {x^m}{\left (a+b x^3\right )^3} \, dx \]
Optimal antiderivative \[ \frac {x^{1+m} \hypergeom \left (\left [3, \frac {1}{3}+\frac {m}{3}\right ], \left [\frac {4}{3}+\frac {m}{3}\right ], -\frac {b \,x^{3}}{a}\right )}{a^{3} \left (1+m \right )} \]
command
integrate(x**m/(b*x**3+a)**3,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {output too large to display} \]
Sympy 1.8 under Python 3.8.8 output \[ \text {Timed out} \]_____________________________________________________