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