\[ \int \frac {112+8 e^2+e (-60-14 x)+56 x+7 x^2}{64+4 e^2+e (-32-8 x)+32 x+4 x^2} \, dx \]
Optimal antiderivative \[ \left (2-\frac {x}{16+4 x -4 \,{\mathrm e}}\right ) \left (4+x \right )+\ln \left (\ln \left (5\right )\right ) \]
command
integrate((8*exp(1)^2+(-14*x-60)*exp(1)+7*x^2+56*x+112)/(4*exp(1)^2+(-8*x-32)*exp(1)+4*x^2+32*x+64),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {7}{4} \, x - \frac {e^{2} - 4 \, e}{4 \, {\left (x - e + 4\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________