I know what I did wrong!
I used the wrong equation... (Dope!)
I was struggling with this forever, and all I had to do was look two pages back in my notes and grab the much easier equation to use.
For those who are curious, that equation would be:
dy/dx = 1/2 [ (1-x)^(-b/a) - (1-x)^(b/a) ]
Where a = b.
Integrating this is much easier than what I was trying to do.