\[ \int \frac {A+B x^3}{(e x)^{5/2} \left (a+b x^3\right )^{3/2}} \, dx \]
Optimal antiderivative \[ -\frac {2 A}{3 a e \left (e x \right )^{\frac {3}{2}} \sqrt {b \,x^{3}+a}}-\frac {2 \left (2 A b -B a \right ) \left (e x \right )^{\frac {3}{2}}}{3 a^{2} e^{4} \sqrt {b \,x^{3}+a}} \]
command
integrate((B*x**3+A)/(e*x)**(5/2)/(b*x**3+a)**(3/2),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ A \left (- \frac {2}{3 a \sqrt {b} e^{\frac {5}{2}} x^{3} \sqrt {\frac {a}{b x^{3}} + 1}} - \frac {4 \sqrt {b}}{3 a^{2} e^{\frac {5}{2}} \sqrt {\frac {a}{b x^{3}} + 1}}\right ) + \frac {2 B}{3 a \sqrt {b} e^{\frac {5}{2}} \sqrt {\frac {a}{b x^{3}} + 1}} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________