(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

[tex] \int_{-\infty}^{\infty}e^{-x^2\over a} dx = \sqrt{\pi\over a} [/tex] [tex] a>0 [/tex]

3. The attempt at a solution

Can't seem to penetrate it, I thought about trying to isolate the second term with integration by parts.

[tex]\int_{-\infty}^{\infty} e^{x\over 2}e^{-x^2\over 2} dx = e^{x\over 2}\int e^{-x^2\over 2}dx - \int \frac{d}{dx}e^{x\over 2} \left[ \int e^{-x^2\over 2} dx \right] dx [/tex]

But I don't think there's any sensible way to put limits in on the RHS to eliminate those factors.

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# Improper integral with e^(-x/2)e^(-x^2/2). Realling annoying.

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