\[ \int \frac {x^3}{\left (a+\frac {c}{x^2}+\frac {b}{x}\right ) (d+e x)^2} \, dx \]
Optimal antiderivative \[ -\frac {\left (2 a d +b e \right ) x}{a^{2} e^{3}}+\frac {x^{2}}{2 a \,e^{2}}+\frac {d^{5}}{e^{4} \left (a \,d^{2}-e \left (b d -c e \right )\right ) \left (e x +d \right )}+\frac {d^{4} \left (3 a \,d^{2}-e \left (4 b d -5 c e \right )\right ) \ln \left (e x +d \right )}{e^{4} \left (a \,d^{2}-e \left (b d -c e \right )\right )^{2}}+\frac {\left (b^{4} d^{2}-2 b^{3} c d e +4 a b \,c^{2} d e +a \,c^{2} \left (a \,d^{2}-c \,e^{2}\right )-b^{2} c \left (3 a \,d^{2}-c \,e^{2}\right )\right ) \ln \left (a \,x^{2}+b x +c \right )}{2 a^{3} \left (a \,d^{2}-e \left (b d -c e \right )\right )^{2}}+\frac {\left (b^{5} d^{2}-2 b^{4} c d e +8 a \,b^{2} c^{2} d e -4 a^{2} c^{3} d e +a b \,c^{2} \left (5 a \,d^{2}-3 c \,e^{2}\right )-b^{3} c \left (5 a \,d^{2}-c \,e^{2}\right )\right ) \arctanh \left (\frac {2 a x +b}{\sqrt {-4 a c +b^{2}}}\right )}{a^{3} \left (a \,d^{2}-e \left (b d -c e \right )\right )^{2} \sqrt {-4 a c +b^{2}}} \]
command
integrate(x^3/(a+c/x^2+b/x)/(e*x+d)^2,x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \text {output too large to display} \]
Fricas 1.3.7 via sagemath 9.3 output \[ \text {Timed out} \]