A calculus problem by Rudraksh Sisodia

Calculus Level 3

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

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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