I've been asking a lot of integral questions lately. :D This is the integral I'm trying to solve: $$\int \frac{\sqrt{1 - x^2} - 1}{x^2 - 1}dx$$

By replacing $x = \sin(u)$ (thus $dx = \cos(u)du$ and $u = \arcsin(x)$) I arrived at: $$\int \frac{\cos(u)}{\cos^2(u)}du - u + C$$

That fraction I think is $\sec(u)$, but we never learned about the secant function in school so I'd rather not use that. (Doesn't mean I don't want to know *how* to use it, I just want to be able to solve this some other way. :) )