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.
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.