\[ \int \frac {A+B x^3}{x^4 \left (a+b x^3\right )^{5/2}} \, dx \]
Optimal antiderivative \[ \frac {-5 A b +2 B a}{9 a^{2} \left (b \,x^{3}+a \right )^{\frac {3}{2}}}-\frac {A}{3 a \,x^{3} \left (b \,x^{3}+a \right )^{\frac {3}{2}}}+\frac {\left (5 A b -2 B a \right ) \arctanh \left (\frac {\sqrt {b \,x^{3}+a}}{\sqrt {a}}\right )}{3 a^{\frac {7}{2}}}+\frac {-5 A b +2 B a}{3 a^{3} \sqrt {b \,x^{3}+a}} \]
command
integrate((B*x**3+A)/x**4/(b*x**3+a)**(5/2),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 \[ \text {Timed out} \]_____________________________________________________