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