\[ \int \frac {A+B x+C x^2}{(d+e x) \left (a+c x^2\right )^3} \, dx \]
Optimal antiderivative \[ \frac {-a \left (-A c e +B c d +a C e \right )+c \left (A c d +a B e -a C d \right ) x}{4 a c \left (a \,e^{2}+c \,d^{2}\right ) \left (c \,x^{2}+a \right )^{2}}+\frac {4 a^{2} e \left (A \,e^{2}-B d e +C \,d^{2}\right )+\left (a \left (-B e +C d \right ) \left (-3 a \,e^{2}+c \,d^{2}\right )+A c d \left (7 a \,e^{2}+3 c \,d^{2}\right )\right ) x}{8 a^{2} \left (a \,e^{2}+c \,d^{2}\right )^{2} \left (c \,x^{2}+a \right )}+\frac {e^{3} \left (A \,e^{2}-B d e +C \,d^{2}\right ) \ln \left (e x +d \right )}{\left (a \,e^{2}+c \,d^{2}\right )^{3}}-\frac {e^{3} \left (A \,e^{2}-B d e +C \,d^{2}\right ) \ln \left (c \,x^{2}+a \right )}{2 \left (a \,e^{2}+c \,d^{2}\right )^{3}}+\frac {\left (a \left (-B e +C d \right ) \left (-3 a^{2} e^{4}+6 a c \,d^{2} e^{2}+c^{2} d^{4}\right )+A c d \left (15 a^{2} e^{4}+10 a c \,d^{2} e^{2}+3 c^{2} d^{4}\right )\right ) \arctan \left (\frac {x \sqrt {c}}{\sqrt {a}}\right )}{8 a^{\frac {5}{2}} \left (a \,e^{2}+c \,d^{2}\right )^{3} \sqrt {c}} \]
command
integrate((C*x^2+B*x+A)/(e*x+d)/(c*x^2+a)^3,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 \[ \text {Timed out} \]