\[ \int \frac {-4 x+3 x^2+e^3 \left (2 x-x^2\right )+e^5 \left (4-12 x+13 x^2-6 x^3+x^4+e^6 \left (1-2 x+x^2\right )+e^3 \left (-4+10 x-8 x^2+2 x^3\right )\right )}{4-12 x+13 x^2-6 x^3+x^4+e^6 \left (1-2 x+x^2\right )+e^3 \left (-4+10 x-8 x^2+2 x^3\right )} \, dx \]
Optimal antiderivative \[ x \left (\frac {x^{2}}{\left (2-x -{\mathrm e}^{3}\right ) \left (x^{2}-x \right )}+{\mathrm e}^{5}\right ) \]
command
integrate((((x^2-2*x+1)*exp(3)^2+(2*x^3-8*x^2+10*x-4)*exp(3)+x^4-6*x^3+13*x^2-12*x+4)*exp(5)+(-x^2+2*x)*exp(3)+3*x^2-4*x)/((x^2-2*x+1)*exp(3)^2+(2*x^3-8*x^2+10*x-4)*exp(3)+x^4-6*x^3+13*x^2-12*x+4),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ x e^{5} + \frac {x e^{3} - 3 \, x - e^{3} + 2}{x^{2} + x e^{3} - 3 \, x - e^{3} + 2} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________