\[ \int \frac {240 x+768 x^4}{25-320 x^3+64 e^2 x^4+1024 x^6+e \left (80 x^2-512 x^5\right )+\left (-80 x^2-128 e x^4+512 x^5\right ) \log (4)+64 x^4 \log ^2(4)} \, dx \]
Optimal antiderivative \[ -\frac {3}{2 \ln \! \left (2\right )-{\mathrm e}-\frac {5}{8 x^{2}}+4 x} \]
command
Int[(240*x + 768*x^4)/(25 - 320*x^3 + 64*E^2*x^4 + 1024*x^6 + E*(80*x^2 - 512*x^5) + (-80*x^2 - 128*E*x^4 + 512*x^5)*Log[4] + 64*x^4*Log[4]^2),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \text {\$Aborted} \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \frac {24 x^2}{-32 x^3+8 x^2 (e-\log (4))+5} \]