I used contour integration and the Pac-Man contour to find I(a), unaware that by substitution I could make it look like that integral I asked about.
You and simplependulum are too good. I give up. (Clapping)
The only other thing I see wrong in your first solution is what you substituted back in for dx. But even if you did that correctly, you would still get the negative of what you should get. So what else is wrong?
So that's where the negative was hiding. Sneaky bastard.
EDIT: I was referring to the negative; not you.
This one I worked out without using contour integration.
I can generalize my solution, which doesn't rely on the previous problem.
reverse the order the integration and let
EDIT: On second thought, it's really not that interesting. Nevermind.