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How might I evaluate the integral $\int_{-\infty}^\infty {y\exp (-y^2)\over 1+y^2}dy$? I have tried integration by parts, but it seems to reach a dead end.

Wolfram Alpha's answer involved "Ei" which I am not expected to use. I reckon the problem is eliminated by the fact that limits are $\pm \infty$, but I am not sure how to do it. Thanks.

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up vote 3 down vote accepted

The integrand is an odd function, so the integral is zero.

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Very well-spotted!! Thanks! – Macleod Mar 6 '12 at 10:27
How often I let people know little tricks like this is absurd, in fact in stewart's calculus there is a separate chapter devoted to even and odd functions. I cannot give enough attention to knowledge like this – Triatticus May 26 '13 at 8:41

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