Typical Indefinite Integration 2

Calculus Level 3

$\int \dfrac{\ln(x)^{\ln(x)}\left [\ln(x)\left (\ln(\ln(x))+1 \right )+1\right]}{x} \, dx$

Ignoring the constant of integration, if the integral above can be expressed as ${(f(x))^{f(x)+1}}$ , then find the value of $f(e)$ .