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Could someone please help me to calculate the integral of:

$$\int_{-\infty}^{+\infty} \cos (at) e^{-bt^2} dt.$$

a and b both real, b>0.

I have tried integration by parts, but I can't seem to simplify it to anything useful. Essentially, I would like to arrive at something that looks like: 7.4.6 here: textbook result

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    yep! But... I can't seem to simplify it to anything useful. Essentially, I would like to arrive at something that looks like: 7.4.6 here http://people.math.sfu.ca/~cbm/aands/page_302.htm2012-09-04
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    You need to specify the domain.2012-09-04
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    Sorry. done now2012-09-04

2 Answers 2