limit of integral

[Vali]

I need to find the limit from the picture.I have no idea how to start.Some ideas?

 

[Deleted member 4993]

I need to find the limit from the picture.I have no idea how to start.Some ideas?

Does your problem look like this:

\(\displaystyle \displaystyle{\lim_{n \to \infty}\left [ n \cdot \int_0^1 \dfrac{x^n}{x^2+2}dx\right ]}\)

 

[Vali]

Yes, I forgot "dx".

 

[Deleted member 4993]

Yes, I forgot "dx".

Did you try "integration by parts"?

x^n/(x^2+2) = x^(n-1) * x/(x^2+1)

 

[Vali]

I did it, thank you for the response!