\[ \int \frac {e^{12} \left (-e^5+e^{10} \left (-1-x^2\right )\right )}{1+e^5 \left (2+2 x-2 x^2\right )+e^{10} \left (1+2 x-x^2-2 x^3+x^4\right )} \, dx \]
Optimal antiderivative \[ \frac {{\mathrm e}^{12}}{x -\frac {{\mathrm e}^{-5}+1}{x}-1} \]
command
integrate(((-x^2-1)*exp(5)^2-exp(5))*exp(12)/((x^4-2*x^3-x^2+2*x+1)*exp(5)^2+(-2*x^2+2*x+2)*exp(5)+1),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {x e^{17}}{x^{2} e^{5} - x e^{5} - e^{5} - 1} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int -\frac {{\left ({\left (x^{2} + 1\right )} e^{10} + e^{5}\right )} e^{12}}{{\left (x^{4} - 2 \, x^{3} - x^{2} + 2 \, x + 1\right )} e^{10} - 2 \, {\left (x^{2} - x - 1\right )} e^{5} + 1}\,{d x} \]________________________________________________________________________________________