- #1
Gregg
- 459
- 0
Homework Statement
[tex]\int_{-\infty}^{\infty} e^{x\over 2}e^{-x^2\over 2} dx [/tex]
Homework Equations
[tex] \int_{-\infty}^{\infty}e^{-x^2\over a} dx = \sqrt{\pi\over a} [/tex] [tex] a>0 [/tex]
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.