\[ \int \frac {(c+d x)^{5/2}}{x^4 (a+b x)} \, dx \]
Optimal antiderivative \[ -\frac {c \left (d x +c \right )^{\frac {3}{2}}}{3 x^{3} a}-\frac {2 \left (-a d +b c \right )^{\frac {5}{2}} \arctanh \left (\frac {\sqrt {b}\, \sqrt {d x +c}}{\sqrt {-a d +b c}}\right ) \sqrt {b}}{a^{4}}+\frac {\left (-5 a^{3} d^{3}+30 a^{2} b c \,d^{2}-40 a \,b^{2} c^{2} d +16 b^{3} c^{3}\right ) \arctanh \left (\frac {\sqrt {d x +c}}{\sqrt {c}}\right )}{8 a^{4} \sqrt {c}}+\frac {c \left (-3 a d +2 b c \right ) \sqrt {d x +c}}{4 a^{2} x^{2}}-\frac {\left (11 a^{2} d^{2}-18 a b c d +8 b^{2} c^{2}\right ) \sqrt {d x +c}}{8 a^{3} x} \]
command
integrate((d*x+c)**(5/2)/x**4/(b*x+a),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 \[ \text {Timed out} \]_____________________________________________________