0
$\begingroup$

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.

1 Answers 1

3

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

  • 0
    How often I let people know little t$r$icks like this is absu$r$d, i$n$ fact in stewart's calculus there is a separate chapter devoted to even and odd functions. I cannot give enough attention to knowledge like this2013-05-26