\[ \int \frac {-e^{\frac {1+e^{21}+2 x}{x}} x+e^{\frac {1+e^{21}+2 x}{x}} \left (-1-e^{21}-x\right ) \log (x)}{x^3 \log ^2(x)} \, dx \]
Optimal antiderivative \[ \frac {{\mathrm e}^{\frac {{\mathrm e}^{21}+2 x +1}{x}}}{x \ln \left (x \right )} \]
command
Int[(-(E^((1 + E^21 + 2*x)/x)*x) + E^((1 + E^21 + 2*x)/x)*(-1 - E^21 - x)*Log[x])/(x^3*Log[x]^2),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \frac {e^{\frac {1+e^{21}}{x}+2}}{x \log (x)} \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \int \frac {-e^{\frac {1+e^{21}+2 x}{x}} x+e^{\frac {1+e^{21}+2 x}{x}} \left (-1-e^{21}-x\right ) \log (x)}{x^3 \log ^2(x)} \, dx \]________________________________________________________________________________________