Integral of Gaussian multiplied by cos(x)

Hey I have a problem that was in quantum mechanics, but is basically a math problem.

I need to solve the following integral:

http://mathworld.wolfram.com/images/...Equation10.gif

How do you achieve this result analytically?

I do know how to solve for the integral of the plain Gaussian by converting to polar coordinates, but I have no idea how to achieve this result.

Any Help would be appreciated!

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