\[ \int \frac {x^4 \left (d^2-e^2 x^2\right )^p}{d+e x} \, dx \]
Optimal antiderivative \[ \frac {d^{4} \left (-e^{2} x^{2}+d^{2}\right )^{p}}{2 e^{5} p}-\frac {d^{2} \left (-e^{2} x^{2}+d^{2}\right )^{1+p}}{e^{5} \left (1+p \right )}+\frac {\left (-e^{2} x^{2}+d^{2}\right )^{2+p}}{2 e^{5} \left (2+p \right )}+\frac {x^{5} \left (-e^{2} x^{2}+d^{2}\right )^{p} \hypergeom \! \left (\left [\frac {5}{2}, 1-p \right ], \left [\frac {7}{2}\right ], \frac {e^{2} x^{2}}{d^{2}}\right ) \left (1-\frac {e^{2} x^{2}}{d^{2}}\right )^{-p}}{5 d} \]
command
integrate(x**4*(-e**2*x**2+d**2)**p/(e*x+d),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Timed out} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {output too large to display} \]