\[ \int \frac {4 x-5 x^2-8 x^3+10 x^4+\left (-x+2 x^3\right ) \log (5)+\left (4 x-10 x^2+e^{x^2} (40-100 x-10 \log (5))-x \log (5)\right ) \log \left (e^{-x^2} \left (10 e^{x^2}+x\right )\right )}{10 e^{x^2}+x} \, dx \]
Optimal antiderivative \[ \left (4-5 x -\ln \! \left (5\right )\right ) \ln \! \left (10+x \,{\mathrm e}^{-x^{2}}\right ) x \]
command
Integrate[(4*x - 5*x^2 - 8*x^3 + 10*x^4 + (-x + 2*x^3)*Log[5] + (4*x - 10*x^2 + E^x^2*(40 - 100*x - 10*Log[5]) - x*Log[5])*Log[(10*E^x^2 + x)/E^x^2])/(10*E^x^2 + x),x]
Mathematica 13.1 output
\[ \int \frac {4 x-5 x^2-8 x^3+10 x^4+\left (-x+2 x^3\right ) \log (5)+\left (4 x-10 x^2+e^{x^2} (40-100 x-10 \log (5))-x \log (5)\right ) \log \left (e^{-x^2} \left (10 e^{x^2}+x\right )\right )}{10 e^{x^2}+x} \, dx \]
Mathematica 12.3 output
\[ -x (-4+5 x+\log (5)) \log \left (10+e^{-x^2} x\right ) \]