- #1

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## Homework Statement

Use residues to evaluate the improper integral:

[tex]\int^{\infty}_{- \infty}[/tex] [tex]\frac{cos(x)dx}{(x^{2} + a^{2})(x^{2} + b^{2})}[/tex] = [tex]\frac{\pi}{a^{2} - b^{2}}[/tex] ( [tex]\frac{e^{-b}}{b}[/tex] - [tex]\frac{e^{-a}}{a}[/tex] )

## Homework Equations

a>b>0

## The Attempt at a Solution

If someone could just explain the concept of residues and how to apply them, that would be great. They give the answer, but you have to use residues to show how to get there. I've looked over my notes and through the book and I don't understand them at all.