\[ \int \frac {50 x^2+20 x^3-10 x^4+e^4 \left (-100 x-30 x^2\right )+e^2 \left (-100 x^2-40 x^3\right )+\left (-10 x^2-4 x^3+2 x^4+e^4 \left (20 x+6 x^2\right )+e^2 \left (20 x^2+8 x^3\right )\right ) \log (9)}{e^8+4 e^6 x+x^2-2 x^3+x^4+e^4 \left (-2 x+6 x^2\right )+e^2 \left (-4 x^2+4 x^3\right )} \, dx \]
Optimal antiderivative \[ \frac {2 \left (2 \ln \left (3\right )-5\right ) x^{2} \left (5+x \right )}{\left (x +{\mathrm e}^{2}\right )^{2}-x} \]
command
integrate((2*((6*x^2+20*x)*exp(2)^2+(8*x^3+20*x^2)*exp(2)+2*x^4-4*x^3-10*x^2)*log(3)+(-30*x^2-100*x)*exp(2)^2+(-40*x^3-100*x^2)*exp(2)-10*x^4+20*x^3+50*x^2)/(exp(2)^4+4*x*exp(2)^3+(6*x^2-2*x)*exp(2)^2+(4*x^3-4*x^2)*exp(2)+x^4-2*x^3+x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ 4 \, x \log \left (3\right ) - 10 \, x + \frac {2 \, {\left (6 \, x e^{4} \log \left (3\right ) - 28 \, x e^{2} \log \left (3\right ) - 15 \, x e^{4} + 70 \, x e^{2} + 12 \, x \log \left (3\right ) + 4 \, e^{6} \log \left (3\right ) - 12 \, e^{4} \log \left (3\right ) - 30 \, x - 10 \, e^{6} + 30 \, e^{4}\right )}}{x^{2} + 2 \, x e^{2} - x + e^{4}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________