Integral representation of Euler constan

[bbailey]

I am working on the integral representation of the Euler-Mascheroni constant and I can't seem to understand why the first of the two integrals is (1-exp(-u))lnu instead of just exp(-u)lnu. It is integrated over the interval from 1 to 0, as opposed to the second integral exp(-u)lnu which is integrated from 1 to infinity. I would appreciate any help on why the first integral is transformed from exp(-u)lnu to (1-exp(-u))lnu. thanks in advance

 

[jedishrfu]

You might your answer here

https://en.m.wikipedia.org/wiki/Euler–Mascheroni_constant

There's several ways of defining the constant.