JEE maths#9

Calculus Level 3

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

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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