\[ \int \frac {a+b x^2+c x^4}{\left (d+e x^2\right )^{11/2}} \, dx \]
Optimal antiderivative \[ \frac {a x}{d \left (e \,x^{2}+d \right )^{\frac {9}{2}}}+\frac {\left (8 a e +b d \right ) x^{3}}{3 d^{2} \left (e \,x^{2}+d \right )^{\frac {9}{2}}}+\frac {\left (c \,d^{2}+2 e \left (8 a e +b d \right )\right ) x^{5}}{5 d^{3} \left (e \,x^{2}+d \right )^{\frac {9}{2}}}+\frac {4 e \left (c \,d^{2}+2 e \left (8 a e +b d \right )\right ) x^{7}}{35 d^{4} \left (e \,x^{2}+d \right )^{\frac {9}{2}}}+\frac {8 e^{2} \left (c \,d^{2}+2 e \left (8 a e +b d \right )\right ) x^{9}}{315 d^{5} \left (e \,x^{2}+d \right )^{\frac {9}{2}}} \]
command
integrate((c*x**4+b*x**2+a)/(e*x**2+d)**(11/2),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 \[ \text {Timed out} \]_____________________________________________________