# Integral of a gaussian

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1. May 11, 2015

### Ananthan9470

I need to evaluate ∫xp e-x2 eix dx from -∞ to ∞ Can someone please give me some pointers on how to do this? I am completely lost. I just need some hints or something.

2. May 12, 2015

### PeroK

Is this homework?

3. May 12, 2015

### Ananthan9470

No. I'm trying to learn quantum mechanics and this thing keeps popping up.

4. May 12, 2015

### PeroK

You'll get a better response if you post it in homework. Even if you're learning on your own, it still counts.

Can you integrate it without the complex exponential?

5. May 12, 2015

### mathman

To get you started, if p is even you need only cosx. If p is odd you need only isinx, where $e^{ix}=cosx+isinx$.
Next integrate by parts to reduce exponent from p to p-1, and continue until you get p = 0.
At the end you should have $\int_{-\infty}^{\infty}e^{-\frac{x^2}{2}}cosxdx$.

As an afterthought, it might be easier to start from
$\int_{-\infty}^{\infty}e^{-\frac{x^2}{2}}cosxdx$. Then integrate by parts to increase the exponent of x.

Last edited: May 13, 2015