Thanks!
Well, the form of the integrand just screams "trig substitution" :
$\displaystyle tan( \theta ) = \frac{x^2 + 1}{x^2 - 1}$
The problem is that this attack is very messy. So messy that I decided to consult the "oracle" over on Mathematica's online integrator, which gave me a really messy answer. So messy that I am wondering if there isn't some typo in the problem?
-Dan