\[ \int \frac {(a+b x)^{3/2} (A+B x)}{x^5} \, dx \]
Optimal antiderivative \[ \frac {\left (3 A b -8 B a \right ) \left (b x +a \right )^{\frac {3}{2}}}{24 x^{3} a}-\frac {A \left (b x +a \right )^{\frac {5}{2}}}{4 a \,x^{4}}-\frac {b^{3} \left (3 A b -8 B a \right ) \arctanh \left (\frac {\sqrt {b x +a}}{\sqrt {a}}\right )}{64 a^{\frac {5}{2}}}+\frac {b \left (3 A b -8 B a \right ) \sqrt {b x +a}}{32 a \,x^{2}}+\frac {b^{2} \left (3 A b -8 B a \right ) \sqrt {b x +a}}{64 a^{2} x} \]
command
integrate((b*x+a)**(3/2)*(B*x+A)/x**5,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 \[ \text {Timed out} \]_____________________________________________________