\[ \int \frac {(a+b x)^{3/2} (A+B x)}{x^6} \, dx \]
Optimal antiderivative \[ \frac {\left (A b -2 B a \right ) \left (b x +a \right )^{\frac {3}{2}}}{8 a \,x^{4}}-\frac {A \left (b x +a \right )^{\frac {5}{2}}}{5 a \,x^{5}}+\frac {3 b^{4} \left (A b -2 B a \right ) \arctanh \left (\frac {\sqrt {b x +a}}{\sqrt {a}}\right )}{128 a^{\frac {7}{2}}}+\frac {b \left (A b -2 B a \right ) \sqrt {b x +a}}{16 x^{3} a}+\frac {b^{2} \left (A b -2 B a \right ) \sqrt {b x +a}}{64 a^{2} x^{2}}-\frac {3 b^{3} \left (A b -2 B a \right ) \sqrt {b x +a}}{128 a^{3} x} \]
command
integrate((b*x+a)**(3/2)*(B*x+A)/x**6,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 \[ \text {Timed out} \]_____________________________________________________