You mean

I presume?

There is a neat little trick to doing this.

First notice that the integrand is an even function. So

Now I am going to integrate

because it is simpler than the original.

Call the value of the integral

.

Then

where x and y are independent variables.

Now, define an xy plane. We are integrating over the whole of the xy plane. I am going to choose to do this with polar, rather than rectangular, coordinates. So define:

and

in the usual manner.

Then

and

. So...

The

integration is trivial:

Substitute

, then

, so

Thus

So finally:

-Dan