\[ \int \frac {\left (-384 x-768 x^2-384 x^3\right ) \log (x)+\left (-384 x-1664 x^2-2304 x^3-1536 x^4-512 x^5\right ) \log ^2(x)+\left (512 x^2+1536 x^3+1536 x^4+512 x^5\right ) \log (x) \log \left (2 x+e^5 x\right )}{-27+\left (108 x+108 x^2\right ) \log \left (2 x+e^5 x\right )+\left (-144 x^2-288 x^3-144 x^4\right ) \log ^2\left (2 x+e^5 x\right )+\left (64 x^3+192 x^4+192 x^5+64 x^6\right ) \log ^3\left (2 x+e^5 x\right )} \, dx \]
Optimal antiderivative \[ \frac {4 \ln \! \left (x \right )^{2}}{\left (\frac {3}{\left (4+4 x \right ) x}-\ln \! \left (x \left ({\mathrm e}^{5}+2\right )\right )\right )^{2}} \]
command
Integrate[((-384*x - 768*x^2 - 384*x^3)*Log[x] + (-384*x - 1664*x^2 - 2304*x^3 - 1536*x^4 - 512*x^5)*Log[x]^2 + (512*x^2 + 1536*x^3 + 1536*x^4 + 512*x^5)*Log[x]*Log[2*x + E^5*x])/(-27 + (108*x + 108*x^2)*Log[2*x + E^5*x] + (-144*x^2 - 288*x^3 - 144*x^4)*Log[2*x + E^5*x]^2 + (64*x^3 + 192*x^4 + 192*x^5 + 64*x^6)*Log[2*x + E^5*x]^3),x]
Mathematica 13.1 output
\[ \text {\$Aborted} \]
Mathematica 12.3 output
\[ -\frac {4 \left (-3+4 x \log \left (2+e^5\right )+4 x^2 \log \left (2+e^5\right )\right ) \left (-3+4 x \log \left (2+e^5\right )+4 x^2 \log \left (2+e^5\right )+8 x (1+x) \log (x)\right )}{\left (3-4 x (1+x) \log \left (\left (2+e^5\right ) x\right )\right )^2} \]