\[ \int \frac {64+e^2 (40-40 x)-64 x+56 x^2}{64+25 e^4+e^2 (80-140 x)-224 x+196 x^2} \, dx \]
Optimal antiderivative \[ \frac {x}{1-\frac {5 \left ({\mathrm e}^{2}-2 x \right )}{2 \left (2 x -4\right )}} \]
command
integrate(((-40*x+40)*exp(2)+56*x^2-64*x+64)/(25*exp(2)^2+(-140*x+80)*exp(2)+196*x^2-224*x+64),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {2}{7} \, x + \frac {5 \, {\left (5 \, e^{4} - 12 \, e^{2} - 32\right )}}{49 \, {\left (14 \, x - 5 \, e^{2} - 8\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________