# Integral of a gaussian

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.

PeroK
Homework Helper
Gold Member
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.
Is this homework?

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

PeroK
Homework Helper
Gold Member
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?

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:
• Ananthan9470