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I need a little help with this question, please!

I have to evaluate the real convergent improper integrals using RESIDUE THEORY (vital that I use this), using the following contour:

$$\int\limits_0^\infty \frac{\log x} {(1+x^2)^2} dx$$

Using this contour:

enter image description here

$R>1$ and $r<1$

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    I edited. Is the expression correct?2012-03-07
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    @Bany I gave an answer using your contour, though I'm a bit late. I hope it helps!2016-01-15

3 Answers 3