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[tex]\int_{-\infty}^{\infty} {xe^{-x^{2}}dx}[/tex]

I noticed the function was even, so I then did this:

[tex]2\int_{0}^{\infty} {xe^{-x^{2}}dx}[/tex]

I attempted to do integration by parts:

[tex]u=e^{-x^{2}}, du=-2e^{-x^{2}}, dv=x, v=\frac{x^{2}}{2}[/tex]

which still left me with this at the end:

(I left out the bounds)

[tex]\frac{x^{2}}{2}(e^{-x^{2}} - \int_{}^{} {e^{-x^{2}}dx})[/tex]

and of course that integral can't be done. Doing parts the other way results with the same issue, and I don't see how a substitution could work. Thanks in advance for any help.

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# Homework Help: Improper Integral

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