\[ \int \frac {e^{15} \left (10-24 x+6 x^2\right )+e^{15} \left (-10+22 x-4 x^2\right ) \log (5)+e^{15} \left (-10+22 x-4 x^2\right ) \log (5-x)}{-5 x+6 x^2-x^3+\left (5 x-6 x^2+x^3\right ) \log (5)+\left (5 x-6 x^2+x^3\right ) \log (5-x)+\left (e^5 \left (-15 x+18 x^2-3 x^3\right )+e^5 \left (15 x-18 x^2+3 x^3\right ) \log (5)+e^5 \left (15 x-18 x^2+3 x^3\right ) \log (5-x)\right ) \log \left (\frac {-x+x^2}{-1+\log (5)+\log (5-x)}\right )+\left (e^{10} \left (-15 x+18 x^2-3 x^3\right )+e^{10} \left (15 x-18 x^2+3 x^3\right ) \log (5)+e^{10} \left (15 x-18 x^2+3 x^3\right ) \log (5-x)\right ) \log ^2\left (\frac {-x+x^2}{-1+\log (5)+\log (5-x)}\right )+\left (e^{15} \left (-5 x+6 x^2-x^3\right )+e^{15} \left (5 x-6 x^2+x^3\right ) \log (5)+e^{15} \left (5 x-6 x^2+x^3\right ) \log (5-x)\right ) \log ^3\left (\frac {-x+x^2}{-1+\log (5)+\log (5-x)}\right )} \, dx \]
Optimal antiderivative \[ \frac {x^{2}}{\left (x \ln \! \left (\frac {x^{2}-x}{\ln \left (5-x \right )+\ln \left (5\right )-1}\right )+x \,{\mathrm e}^{-5}\right )^{2}} \]
command
Integrate[(E^15*(10 - 24*x + 6*x^2) + E^15*(-10 + 22*x - 4*x^2)*Log[5] + E^15*(-10 + 22*x - 4*x^2)*Log[5 - x])/(-5*x + 6*x^2 - x^3 + (5*x - 6*x^2 + x^3)*Log[5] + (5*x - 6*x^2 + x^3)*Log[5 - x] + (E^5*(-15*x + 18*x^2 - 3*x^3) + E^5*(15*x - 18*x^2 + 3*x^3)*Log[5] + E^5*(15*x - 18*x^2 + 3*x^3)*Log[5 - x])*Log[(-x + x^2)/(-1 + Log[5] + Log[5 - x])] + (E^10*(-15*x + 18*x^2 - 3*x^3) + E^10*(15*x - 18*x^2 + 3*x^3)*Log[5] + E^10*(15*x - 18*x^2 + 3*x^3)*Log[5 - x])*Log[(-x + x^2)/(-1 + Log[5] + Log[5 - x])]^2 + (E^15*(-5*x + 6*x^2 - x^3) + E^15*(5*x - 6*x^2 + x^3)*Log[5] + E^15*(5*x - 6*x^2 + x^3)*Log[5 - x])*Log[(-x + x^2)/(-1 + Log[5] + Log[5 - x])]^3),x]
Mathematica 13.1 output
\[ \int \frac {e^{15} \left (10-24 x+6 x^2\right )+e^{15} \left (-10+22 x-4 x^2\right ) \log (5)+e^{15} \left (-10+22 x-4 x^2\right ) \log (5-x)}{-5 x+6 x^2-x^3+\left (5 x-6 x^2+x^3\right ) \log (5)+\left (5 x-6 x^2+x^3\right ) \log (5-x)+\left (e^5 \left (-15 x+18 x^2-3 x^3\right )+e^5 \left (15 x-18 x^2+3 x^3\right ) \log (5)+e^5 \left (15 x-18 x^2+3 x^3\right ) \log (5-x)\right ) \log \left (\frac {-x+x^2}{-1+\log (5)+\log (5-x)}\right )+\left (e^{10} \left (-15 x+18 x^2-3 x^3\right )+e^{10} \left (15 x-18 x^2+3 x^3\right ) \log (5)+e^{10} \left (15 x-18 x^2+3 x^3\right ) \log (5-x)\right ) \log ^2\left (\frac {-x+x^2}{-1+\log (5)+\log (5-x)}\right )+\left (e^{15} \left (-5 x+6 x^2-x^3\right )+e^{15} \left (5 x-6 x^2+x^3\right ) \log (5)+e^{15} \left (5 x-6 x^2+x^3\right ) \log (5-x)\right ) \log ^3\left (\frac {-x+x^2}{-1+\log (5)+\log (5-x)}\right )} \, dx \]
Mathematica 12.3 output
\[ \frac {e^{10}}{\left (1+e^5 \log \left (\frac {(-1+x) x}{-1+\log (-5 (-5+x))}\right )\right )^2} \]