\[ \int \frac {-32-2592 e^8-630 x-10368 e^6 x-2340 x^2+5346 x^3-2592 x^4+e^4 \left (576+5670 x-15552 x^2\right )+e^2 \left (1152 x+11016 x^2-10368 x^3\right )}{64 x^3+5184 e^8 x^3+1296 x^4+20736 e^6 x^4+5409 x^5-11664 x^6+5184 x^7+e^4 \left (-1152 x^3-11664 x^4+31104 x^5\right )+e^2 \left (-2304 x^4-23328 x^5+20736 x^6\right )} \, dx \]
Optimal antiderivative \[ \frac {2}{\left (\frac {x}{x -\left (x +{\mathrm e}^{2}\right )^{2}+\frac {1}{9}}+8\right ) x^{2}} \]
command
integrate((-2592*exp(2)^4-10368*x*exp(2)^3+(-15552*x^2+5670*x+576)*exp(2)^2+(-10368*x^3+11016*x^2+1152*x)*exp(2)-2592*x^4+5346*x^3-2340*x^2-630*x-32)/(5184*x^3*exp(2)^4+20736*x^4*exp(2)^3+(31104*x^5-11664*x^4-1152*x^3)*exp(2)^2+(20736*x^6-23328*x^5-2304*x^4)*exp(2)+5184*x^7-11664*x^6+5409*x^5+1296*x^4+64*x^3),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {81 \, {\left (8 \, x + 16 \, e^{2} - 9\right )}}{32 \, {\left (72 \, x^{2} + 144 \, x e^{2} - 81 \, x + 72 \, e^{4} - 8\right )} {\left (9 \, e^{4} - 1\right )}} + \frac {9 \, x + 72 \, e^{4} - 8}{32 \, x^{2} {\left (9 \, e^{4} - 1\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________