\[ \int \frac {3+2 x+3 x^2+e \left (-6+2 x-32 x^2+6 x^3\right )+e^2 \left (3-4 x+32 x^2-24 x^3+3 x^4\right )}{1+e (-2+2 x)+e^2 \left (1-2 x+x^2\right )} \, dx \]
Optimal antiderivative \[ x \left (3+x +x^{2} \left (\frac {10 x}{x -x^{2}-{\mathrm e}^{-1} x}+1\right )\right ) \]
command
integrate(((3*x^4-24*x^3+32*x^2-4*x+3)*exp(1)^2+(6*x^3-32*x^2+2*x-6)*exp(1)+3*x^2+2*x+3)/((x^2-2*x+1)*exp(1)^2+(-2+2*x)*exp(1)+1),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ {\left (x^{3} e^{6} - 9 \, x^{2} e^{6} - 7 \, x e^{6} + 10 \, x e^{5}\right )} e^{\left (-6\right )} - \frac {10 \, {\left (e^{3} - 3 \, e^{2} + 3 \, e - 1\right )} e^{\left (-2\right )}}{x e - e + 1} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________