- #1

utkarshakash

Gold Member

- 855

- 13

## Homework Statement

[itex]\displaystyle \int_0^{\infty} \dfrac{xlnx}{(1+x^2)^2} dx [/itex]

## Homework Equations

## The Attempt at a Solution

Integrating by parts and using ILATE rule

[itex]\left[ ln \dfrac{x}{\sqrt{1+x^2}} - \dfrac{lnx}{2(1+x^2)} \right] [/itex]

Now I find the limit as x tends to infinity and get 0. But how do I evaluate limit when x tends to zero.