\[ \int \frac {\left (10+e^x (2-2 x)+e^{x^2} \left (2-4 x^2\right )+8 \log (2)\right ) \log \left (\frac {4 x}{5+e^x+e^{x^2}-3 x+4 \log (2)}\right )}{5 x+e^x x+e^{x^2} x-3 x^2+4 x \log (2)} \, dx \]
Optimal antiderivative \[ \ln \! \left (\frac {x}{\ln \! \left (2\right )-\frac {3 x}{4}+\frac {5}{4}+\frac {{\mathrm e}^{x}}{4}+\frac {{\mathrm e}^{x^{2}}}{4}}\right )^{2} \]
command
Integrate[((10 + E^x*(2 - 2*x) + E^x^2*(2 - 4*x^2) + 8*Log[2])*Log[(4*x)/(5 + E^x + E^x^2 - 3*x + 4*Log[2])])/(5*x + E^x*x + E^x^2*x - 3*x^2 + 4*x*Log[2]),x]
Mathematica 13.1 output
\[ \int \frac {\left (10+e^x (2-2 x)+e^{x^2} \left (2-4 x^2\right )+8 \log (2)\right ) \log \left (\frac {4 x}{5+e^x+e^{x^2}-3 x+4 \log (2)}\right )}{5 x+e^x x+e^{x^2} x-3 x^2+4 x \log (2)} \, dx \]
Mathematica 12.3 output
\[ \log ^2\left (\frac {4 x}{e^x+e^{x^2}-3 x+5 \left (1+\frac {4 \log (2)}{5}\right )}\right ) \]