# How to integrate $\int_{-\infty}^\infty {y\exp (-y^2)\over 1+y^2}dy$?

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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