\[ \int \frac {(a+b x)^{5/2} (A+B x)}{x^8} \, dx \]
Optimal antiderivative \[ \frac {b \left (A b -2 B a \right ) \left (b x +a \right )^{\frac {3}{2}}}{24 a \,x^{5}}+\frac {\left (A b -2 B a \right ) \left (b x +a \right )^{\frac {5}{2}}}{12 a \,x^{6}}-\frac {A \left (b x +a \right )^{\frac {7}{2}}}{7 a \,x^{7}}-\frac {5 b^{6} \left (A b -2 B a \right ) \arctanh \left (\frac {\sqrt {b x +a}}{\sqrt {a}}\right )}{1024 a^{\frac {9}{2}}}+\frac {b^{2} \left (A b -2 B a \right ) \sqrt {b x +a}}{64 a \,x^{4}}+\frac {b^{3} \left (A b -2 B a \right ) \sqrt {b x +a}}{384 a^{2} x^{3}}-\frac {5 b^{4} \left (A b -2 B a \right ) \sqrt {b x +a}}{1536 a^{3} x^{2}}+\frac {5 b^{5} \left (A b -2 B a \right ) \sqrt {b x +a}}{1024 a^{4} x} \]
command
integrate((b*x+a)**(5/2)*(B*x+A)/x**8,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 \[ \text {Timed out} \]_____________________________________________________