\[ \int \frac {-432-288 x-81 x^3+3 e^{12} x^3-81 x^4-27 x^5-3 x^6+e^8 \left (-27 x^3-9 x^4\right )+e^4 \left (144+81 x^3+54 x^4+9 x^5\right )}{-27 x^3+e^{12} x^3-27 x^4-9 x^5-x^6+e^8 \left (-9 x^3-3 x^4\right )+e^4 \left (27 x^3+18 x^4+3 x^5\right )} \, dx \]
Optimal antiderivative \[ -\frac {8}{\left (x +x \left (\frac {x}{3}-\frac {{\mathrm e}^{4}}{3}\right )\right )^{2}}+3 x \]
command
integrate((3*x^3*exp(4)^3+(-9*x^4-27*x^3)*exp(4)^2+(9*x^5+54*x^4+81*x^3+144)*exp(4)-3*x^6-27*x^5-81*x^4-81*x^3-288*x-432)/(x^3*exp(4)^3+(-3*x^4-9*x^3)*exp(4)^2+(3*x^5+18*x^4+27*x^3)*exp(4)-x^6-9*x^5-27*x^4-27*x^3),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ 3 \, x - \frac {72}{{\left (x^{2} - x e^{4} + 3 \, x\right )}^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________