Typical Indefinite Integration 2

Calculus Level 3

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

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

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