\[ \int \frac {(d+e x)^5}{\left (a+b x+c x^2\right )^3} \, dx \]
Optimal antiderivative \[ -\frac {e^{2} \left (-b e +2 c d \right ) \left (3 c^{2} d^{2}-b^{2} e^{2}-c e \left (-7 a e +3 b d \right )\right ) x}{c^{2} \left (-4 a c +b^{2}\right )^{2}}-\frac {\left (e x +d \right )^{4} \left (b d -2 a e +\left (-b e +2 c d \right ) x \right )}{2 \left (-4 a c +b^{2}\right ) \left (c \,x^{2}+b x +a \right )^{2}}-\frac {\left (e x +d \right )^{2} \left (8 a c e \left (2 a \,e^{2}+c \,d^{2}\right )-6 b c d \left (3 a \,e^{2}+c \,d^{2}\right )+b^{2} \left (-a \,e^{3}+7 c \,d^{2} e \right )-\left (-b e +2 c d \right ) \left (6 c^{2} d^{2}-b^{2} e^{2}-2 c e \left (-5 a e +3 b d \right )\right ) x \right )}{2 c \left (-4 a c +b^{2}\right )^{2} \left (c \,x^{2}+b x +a \right )}-\frac {\left (12 c^{5} d^{5}-b^{5} e^{5}+10 a \,b^{3} c \,e^{5}-30 a^{2} b \,c^{2} e^{5}-10 c^{4} d^{3} e \left (-4 a e +3 b d \right )+20 c^{3} d \,e^{2} \left (3 a^{2} e^{2}-3 a b d e +b^{2} d^{2}\right )\right ) \arctanh \! \left (\frac {2 c x +b}{\sqrt {-4 a c +b^{2}}}\right )}{c^{3} \left (-4 a c +b^{2}\right )^{\frac {5}{2}}}+\frac {e^{5} \ln \! \left (c \,x^{2}+b x +a \right )}{2 c^{3}} \]
command
integrate((e*x+d)**5/(c*x**2+b*x+a)**3,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Timed out} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {output too large to display} \]