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$\large \displaystyle\int_{e}^{e^{2010}} \dfrac{1}{x} \left(1+\frac{1-\ln x}{\ln x\ln(\frac{x}{\ln x})} \right) \, dx$

The integral above can be expressed as ${b-\ln (a- \ln a)}$, where $a$ and $b$ are integers.

Enter ${a-b}$ as your answer.

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