Rub-a-dub-dub, Find A Quick Sub

$\large \mathfrak{K}= \displaystyle\int_{e}^{2e}{ \frac{dz}{\ln{z^z}}}$ $\large =\displaystyle\int_{e}^{2e}{ \frac{dz}{z\ln{z}}}$ $\large =\displaystyle\int_{e}^{2e}{ \frac{d(\ln z)}{\ln{z}}}$ (Or it can be done by substituting $z=\ln t$ ) $\huge =\ln(\ln z) |_{e}^{2e}$ $\huge =\ln(\ln(2e))=\ln(\ln2+1)$ $\huge \therefore 2+1=\large\color{#456461}{\boxed{\color{#D61F06}{\Huge\boxed{\color{#007fff}{\textbf{3}}}}}}$