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I'm very rusty with calculus, and I was hoping someone would be willing to help me with the following definite integral:

$$\int_b^{\infty} \frac{\cos(ax)}{1+x^2} dx$$

$$b>0$$

Thanks in advance.

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    This does it in Mathematica, but it ain't pretty: Integrate[Cos[a*x]/(1 + x^2), {x, b, Infinity}, Assumptions -> {b > 0, a > 0}] // FullSimplify2012-04-25
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    I'm thinking curiosity's going to win and I'm going to end up looking in a table of integrals to see if this is in there.2012-04-25
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    Thanks for trying everyone.2012-04-25

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