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How to evaluate this integral?

Let $b>0$. Evaluate the next value of integral:

$$\begin{equation} \int_{-\infty} ^{\infty} \dfrac{\cos x}{x^2 + b^2} \ dx \end{equation}$$

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    http://en.wikipedia.org/wiki/Residue_theorem#Example2012-04-21
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    Replace $\cos x$ by $\operatorname{Re} e^{ix}$.2012-04-21
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    yes, this integral is with the Cauchy's method of residues. I don't remenber. Long time, i did not see this.2012-04-21
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    I remembering doing this same exact integral in class. Wierd. The answer comes out as $\displaystyle\frac{\pi}{be^{b}}$ after you evaluate the residue at $x = ib$2012-04-22

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