\[ \int \frac {3 x^2+8 x^3+x^4+e^2 \left (5+2 x-x^2\right )+e^6 \left (e^2 x^2+2 x^3\right )}{1+8 x+18 x^2+e^{12} x^2+8 x^3+x^4+e^6 \left (2 x+8 x^2+2 x^3\right )} \, dx \]
Optimal antiderivative \[ \frac {\left (5+x \right ) {\mathrm e}^{2}+x^{2}}{{\mathrm e}^{6}+4+x +\frac {1}{x}} \]
command
integrate(((x^2*exp(2)+2*x^3)*exp(3)^2+(-x^2+2*x+5)*exp(2)+x^4+8*x^3+3*x^2)/(x^2*exp(3)^4+(2*x^3+8*x^2+2*x)*exp(3)^2+x^4+8*x^3+18*x^2+8*x+1),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ x + \frac {x e^{12} - x e^{8} + 8 \, x e^{6} + x e^{2} + 15 \, x + e^{6} - e^{2} + 4}{x^{2} + x e^{6} + 4 \, x + 1} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________