A small problem with a complex integral

[krishna mohan]

Hi...

I have an integral over a contour. The contour is a semicircle with vanishing radius around the origin and situated in the upper half plane.

The integrand is $$\frac{(lnx)^2}{1+x^2}$$.

The integral is supposed be zero.


I don't see how. Taking the modulus and letting the radius go to zero, I find that the denominator goes to 1 and the numerator is of the form $$ln(r^2)+\theta^2$$ with r going to zero.

Can anybody tell me what I might be missing?

 

[tiny-tim]

hi krishna!

but the arc-length is πr, so you multiply by that

 

[krishna mohan]

Yep..thanks a lot tiny tim!