Typical Indefinite Integration 2

Calculus Level 3

ln(x)ln(x)[ln(x)(ln(ln(x))+1)+1]xdx{ \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{(f(x))^{f(x)+1}}, then find the value of f(e)f(e).

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