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$\large \int_e^{e^{2017}} \dfrac1x \left(1 + \dfrac{1-\ln x}{\ln x \cdot \ln \left( \frac x{\ln x} \right)} \right) \, dx$

The integral above can be expressed as $a - \ln(b - \ln b)$, where $a$ and $b$ are integers. Find the value of $b-a$.

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