How to compute this integral? γ=−lim_{n→∞} ∫[0 to 1] {ln[n (1 − n-th-root{x}) ]} dx

[Win_odd Dhamnekar]

I want to integrate \(\displaystyle \gamma=-\lim_{n\to\infty} \displaystyle \int_0^1 \ln {\big[n(1-\sqrt[n]{x})\big]} dx\). But i could not get right answer which is \(\displaystyle
-\Gamma'{(1)}\)

If any member knows the correct answer, may reply this thread.