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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 [tex]\frac{(lnx)^2}{1+x^2}[/tex].

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 [tex]ln(r^2)+\theta^2[/tex] with r going to zero.

Can anybody tell me what I might be missing?