A calculus problem by Rudraksh Sisodia

Calculus Level 3

ee20171x(1+1lnxlnxln(xlnx))dx\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 aln(blnb) a - \ln(b - \ln b) , where aa and bb are integers. Find the value of bab-a.

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