JEE maths#9

Calculus Level 3

ee20101x(1+1lnxlnxln(xlnx))dx \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 bln(alna){b-\ln (a- \ln a)}, where aa and bb are integers.

Enter ab{a-b} as your answer.


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