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## Homework Statement

Solve

[tex] \int_{0}^{\infty} \frac{x^2}{(x^2+1)(x^2+4)} dx [/tex]

works here

http://www.codecogs.com/latex/eqneditor.php

using residues

## Homework Equations

## The Attempt at a Solution

Can I use residues here?

The contour intergral will be a quarter of a circle in the first quadrant and lines along the positive x- and y- axis of

[tex] \frac{z^2}{(z+i)(z-i)(x+2i)(z-2i)} [/tex]

But can I use Cauchy's Residue Theorem when I get divide by 0 in the contour? i and 2i is on the contour.

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