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