\[ \int \frac {3 x^2+3 x^4-e x^4}{1+6 x^2+4 x^3+9 x^4+e^2 x^4+12 x^5+4 x^6+e \left (-2 x^2-6 x^4-4 x^5\right )} \, dx \]
Optimal antiderivative \[ \frac {x}{\frac {1}{x^{2}}+3-{\mathrm e}+2 x} \]
command
integrate((-x^4*exp(1)+3*x^4+3*x^2)/(x^4*exp(1)^2+(-4*x^5-6*x^4-2*x^2)*exp(1)+4*x^6+12*x^5+9*x^4+4*x^3+6*x^2+1),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {x^{2} e - 3 \, x^{2} - 1}{2 \, {\left (2 \, x^{3} - x^{2} e + 3 \, x^{2} + 1\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________