\[ \int \frac {240 x+768 x^4}{25-320 x^3+64 e^2 x^4+1024 x^6+e \left (80 x^2-512 x^5\right )+\left (-80 x^2-128 e x^4+512 x^5\right ) \log (4)+64 x^4 \log ^2(4)} \, dx \]
Optimal antiderivative \[ -\frac {3}{2 \ln \left (2\right )-{\mathrm e}-\frac {5}{8 x^{2}}+4 x} \]
command
integrate((768*x^4+240*x)/(256*x^4*log(2)^2+2*(-128*x^4*exp(1)+512*x^5-80*x^2)*log(2)+64*x^4*exp(1)^2+(-512*x^5+80*x^2)*exp(1)+1024*x^6-320*x^3+25),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {24 \, x^{2}}{32 \, x^{3} - 8 \, x^{2} e + 16 \, x^{2} \log \left (2\right ) - 5} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________