\[ \int \frac {x^2+e^{10} x^2-2 x^3+2 x^4+x^6+e^{-147+x} \left (-1+e^5 (-1+x)+x-3 x^2+x^3\right )+e^5 \left (2 x^2+2 x^4\right )}{x^2+e^{10} x^2+2 x^4+x^6+e^5 \left (2 x^2+2 x^4\right )} \, dx \]
Optimal antiderivative \[ \frac {x +{\mathrm e}^{x -147}}{\left (1+x^{2}+{\mathrm e}^{5}\right ) x}+x \]
command
integrate((((-1+x)*exp(5)+x^3-3*x^2+x-1)*exp(x-147)+x^2*exp(5)^2+(2*x^4+2*x^2)*exp(5)+x^6+2*x^4-2*x^3+x^2)/(x^2*exp(5)^2+(2*x^4+2*x^2)*exp(5)+x^6+2*x^4+x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {x^{6} e^{147} + 2 \, x^{4} e^{152} + 2 \, x^{4} e^{147} + 2 \, x^{3} e^{147} + x^{2} e^{157} + 2 \, x^{2} e^{152} + x^{2} e^{147} + 2 \, x^{2} e^{x} + 2 \, x e^{152} + 2 \, x e^{147} + 2 \, e^{\left (x + 5\right )} + 2 \, e^{x}}{x^{5} e^{147} + 2 \, x^{3} e^{152} + 2 \, x^{3} e^{147} + x e^{157} + 2 \, x e^{152} + x e^{147}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \mathit {sage}_{0} x \]________________________________________________________________________________________