\[ \int \frac {5-5 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (-x^2+\left (1-x-2 x^3+2 x^4\right ) \log (1-x)+(-1+x) \log (1-x) \log (50 x)\right )}{-25+25 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (10 x-10 x^2\right ) \log (1-x)+e^{\frac {2 \left (-x^3+\log (50 x)\right )}{x}} \left (-x^2+x^3\right ) \log ^2(1-x)} \, dx \]
Optimal antiderivative \[ \frac {x}{x \ln \! \left (1-x \right ) {\mathrm e}^{\frac {\ln \left (50 x \right )}{x}-x^{2}}-5} \]
command
Integrate[(5 - 5*x + E^((-x^3 + Log[50*x])/x)*(-x^2 + (1 - x - 2*x^3 + 2*x^4)*Log[1 - x] + (-1 + x)*Log[1 - x]*Log[50*x]))/(-25 + 25*x + E^((-x^3 + Log[50*x])/x)*(10*x - 10*x^2)*Log[1 - x] + E^((2*(-x^3 + Log[50*x]))/x)*(-x^2 + x^3)*Log[1 - x]^2),x]
Mathematica 13.1 output
\[ \text {\$Aborted} \]
Mathematica 12.3 output
\[ -\frac {e^{x^2} x}{5 e^{x^2}-50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)} \]