\[ \int -\frac {84 e^2}{6480+80 e^2+360 x+5 x^2+e (1440+40 x)} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{2} \left (10+\frac {4}{\frac {5 x}{21}+\frac {60}{7}+\frac {20 \,{\mathrm e}}{21}}\right ) \]
command
integrate(-84*exp(2)/(80*exp(1)^2+(40*x+1440)*exp(1)+5*x^2+360*x+6480),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {84 \, e^{2}}{5 \, {\left (x + 4 \, e + 36\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________