\[ \int \frac {-27+e^6+e^4 (-9-3 x)-27 x-9 x^2-x^3+15 x^4+3 x^5+e^2 \left (27+18 x+3 x^2-5 x^4\right )}{-27+e^6+e^4 (-9-3 x)-27 x-9 x^2-x^3+e^2 \left (27+18 x+3 x^2\right )} \, dx \]
Optimal antiderivative \[ x -\frac {x^{5}}{\left (-{\mathrm e}^{2}+3+x \right )^{2}} \]
command
integrate((exp(2)^3+(-3*x-9)*exp(2)^2+(-5*x^4+3*x^2+18*x+27)*exp(2)+3*x^5+15*x^4-x^3-9*x^2-27*x-27)/(exp(2)^3+(-3*x-9)*exp(2)^2+(3*x^2+18*x+27)*exp(2)-x^3-9*x^2-27*x-27),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -x^{3} - 2 \, x^{2} e^{2} + 6 \, x^{2} - 3 \, x e^{4} + 18 \, x e^{2} - 26 \, x - \frac {5 \, x e^{8} - 60 \, x e^{6} + 270 \, x e^{4} - 540 \, x e^{2} + 405 \, x - 4 \, e^{10} + 60 \, e^{8} - 360 \, e^{6} + 1080 \, e^{4} - 1620 \, e^{2} + 972}{{\left (x - e^{2} + 3\right )}^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________