\[ \int \frac {-2 e^3+e^6 \left (-4 x+10 x^2\right )+e^6 \left (-2+20 x-50 x^2\right ) \log (4)}{x^2+2 e^3 x^3+e^6 x^4+\left (2 x-10 x^2+e^3 \left (4 x^2-20 x^3\right )+e^6 \left (2 x^3-10 x^4\right )\right ) \log (4)+\left (1-10 x+25 x^2+e^3 \left (2 x-20 x^2+50 x^3\right )+e^6 \left (x^2-10 x^3+25 x^4\right )\right ) \log ^2(4)} \, dx \]
Optimal antiderivative \[ \frac {2}{\left ({\mathrm e}^{-3}+x \right ) \left (\frac {x}{1-5 x}+2 \ln \left (2\right )\right )} \]
command
integrate((2*(-50*x^2+20*x-2)*exp(3)^2*log(2)+(10*x^2-4*x)*exp(3)^2-2*exp(3))/(4*((25*x^4-10*x^3+x^2)*exp(3)^2+(50*x^3-20*x^2+2*x)*exp(3)+25*x^2-10*x+1)*log(2)^2+2*((-10*x^4+2*x^3)*exp(3)^2+(-20*x^3+4*x^2)*exp(3)-10*x^2+2*x)*log(2)+x^4*exp(3)^2+2*x^3*exp(3)+x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {2 \, {\left (5 \, x e^{3} - e^{3}\right )}}{10 \, x^{2} e^{3} \log \left (2\right ) - x^{2} e^{3} - 2 \, x e^{3} \log \left (2\right ) + 10 \, x \log \left (2\right ) - x - 2 \, \log \left (2\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________