(sigh) I know I've seen how to do this before, but I can't find the notes!

The problem is this:

where a is real.

It is simple enough to show that the integral is equal to a real number, so

as an alternate formula.

Comparing two lines in the book I got this from the integral should be equal to

(For the case a = 0, the integral is simple and comes out to be equal to 2. Obviously I'm not worried about this case.)

Any takers? Thanks in advance.

-Dan