# Integral of exponential + limit [closed]

Let $$f:\mathbb{R} - \{-5\}->\mathbb{R}$$, $$f(x)=(x-1)e^{-(1/(x+5))}$$. I have to calculate $$lim_{(n->\infty)}=n^2\int_{0}^{1}x^nf(x)dx$$.

I've tried using integration by parts, but i'm still stuck.

## closed as off-topic by Carlo Beenakker, fedja, YCor, David Handelman, GH from MOJul 11 at 22:36

• This question does not appear to be about research level mathematics within the scope defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.

• only the region near $x=1$ will contribute for large $n$, so you may replace $f(x)\mapsto (x-1)e^{-1/6}$ and find that the desired limit is $-e^{-1/6}$ --- I guess the question will be closed here, not research level math. – Carlo Beenakker Jul 11 at 21:08