Wow. I just tried an online integral calculator (no idea how accurate, it's at

Online Integral Calculator ), and the result it spat out, given the form above was that it cold not be integrated. But, when I removed the

substitution, and let a=1, was:

based on whether

was positive or negative. But, it gave no suggestion as to how that was all computed. I am not one to look a gift horse in the mouth, but since I started trying to figure these integrals out solely for the excuse to play with math, I'd rather not include a 'wave magic wand *here*' step.

Any ideas how this came about? Of course, this is all moot if I am integrating from 0 to 2

, as all the arctan terms become 0.

Matt