\[ \int \frac {\left (-80-256 e^2-192 x\right ) \log (2)}{625 x^2+20480 e^6 x^2+1500 x^3+1200 x^4+320 x^5+e^4 \left (19200 x^2+15360 x^3\right )+e^2 \left (6000 x^2+9600 x^3+3840 x^4\right )} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{2}+\frac {\ln \left (2\right )}{5 \left (x +\frac {5}{4}+4 \,{\mathrm e}^{2}\right )^{2} x} \]
command
integrate((-256*exp(2)-192*x-80)*log(2)/(20480*x^2*exp(2)^3+(15360*x^3+19200*x^2)*exp(2)^2+(3840*x^4+9600*x^3+6000*x^2)*exp(2)+320*x^5+1200*x^4+1500*x^3+625*x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {16}{5} \, {\left (\frac {8 \, {\left (2 \, x + 16 \, e^{2} + 5\right )}}{{\left (4 \, x + 16 \, e^{2} + 5\right )}^{2} {\left (256 \, e^{4} + 160 \, e^{2} + 25\right )}} - \frac {1}{x {\left (256 \, e^{4} + 160 \, e^{2} + 25\right )}}\right )} \log \left (2\right ) \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________