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**Ulysses** Hi. Well, I've got this problem where the statement exhorts me to determinate the character of some improper integrals, and it begins with this one $\displaystyle \displaystyle\int_{-\infty}^{\infty}xe^{-x^2}dx$

I really don't know how to work this out. I think its not possible to integrate it, cause its not an elemental function. So I think I should use something, I know it converges to zero, cause I used mathematica to calculate it, but I don't know how to reason it, but maybe using something like the sandwich theorem for function, I mean squeezing it, knowing that integral is not bigger to some other one I could determinate its character. The other thing I thought watching at its graph was demonstrating that its symmetrical to the origin, so thats why it converges to zero. But I'm not sure.

Bye there. And thanks.