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

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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