\[ \int \frac {-3+3 e^2-6 x-3 \log \left (9 e^6\right )}{x^2+e^4 x^2+2 x^3+x^4+e^2 \left (-2 x^2-2 x^3\right )+\left (2 x^2-2 e^2 x^2+2 x^3\right ) \log \left (9 e^6\right )+x^2 \log ^2\left (9 e^6\right )} \, dx \]
Optimal antiderivative \[ \frac {3}{\left (x +1-{\mathrm e}^{2}+\ln \left (9 \,{\mathrm e}^{6}\right )\right ) x} \]
command
integrate((-3*log(9*exp(3)^2)+3*exp(2)-6*x-3)/(x^2*log(9*exp(3)^2)^2+(-2*x^2*exp(2)+2*x^3+2*x^2)*log(9*exp(3)^2)+x^2*exp(2)^2+(-2*x^3-2*x^2)*exp(2)+x^4+2*x^3+x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {3}{x^{2} - x e^{2} + x \log \left (9 \, e^{6}\right ) + x} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________