Cannot find the limit of this integral I am trying to find the limit of the following integral as $n$ grows to infinity.
$$\int_1^{ n+1 }\frac { \ln x }{ x^n } \, dx $$
However, when I am doing an integration by parts, the result looks ugly. It is not in a simple form from which, I think, one can find the limit in a simple way (indeterminate form, I mean).
So there should be a trick in there to find the limit.
Can someone help me on this one please?
Regards,

Let $u=\ln x$ and $dv=x^{-n}\,dx$. Then $du=\frac{1}{x}\,dx$ and we can take $v=\frac{1}{-n+1}x^{-n+1}$.
The second integration will be easy. 
Remark: One can avoid some of the complications by noting the fact that for $x\ge 1$ we have $0\le \ln x\le x-1$.  
