\[ \int \frac {-2 e^8+2 x^4}{e^{12}+x^3-3 x^4+3 x^5-x^6+e^8 \left (3 x-3 x^2\right )+e^4 \left (3 x^2-6 x^3+3 x^4\right )} \, dx \]
Optimal antiderivative \[ \ln \left (2 \ln \left (2\right )\right )+\left (\frac {x}{\left (1-x \right ) x +{\mathrm e}^{4}}-1\right )^{2} \]
command
integrate((-2*exp(4)^2+2*x^4)/(exp(4)^3+(-3*x^2+3*x)*exp(4)^2+(3*x^4-6*x^3+3*x^2)*exp(4)-x^6+3*x^5-3*x^4+x^3),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {2 \, x^{3} - x^{2} - 2 \, x e^{4}}{{\left (x^{2} - x - e^{4}\right )}^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int -\frac {2 \, {\left (x^{4} - e^{8}\right )}}{x^{6} - 3 \, x^{5} + 3 \, x^{4} - x^{3} + 3 \, {\left (x^{2} - x\right )} e^{8} - 3 \, {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{4} - e^{12}}\,{d x} \]________________________________________________________________________________________