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Here is a tough integral. Does anyone have any clever ideas?. I have tried all sorts of things, but make no real headway.

$\displaystyle \int_{0}^{\infty}\frac{e^{-x^{2}}\sin^{2}(x)}{x^{2}}dx$

Would residues be a consideration with this one?.

Thanks all.

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    It's not pretty, but maybe Taylor expand $\sin^2 x / x^2$ about $x=0$, which will contain even powers only of $x$, and then use 27 here?: http://mathworld.wolfram.com/GaussianIntegral.html2012-12-18

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