How do you do this integral?

$\displaystyle \int \frac {x^2}{1+x^2} dx$

The original problem was $\displaystyle \int x tan^{-1}x$.

By doing integration by parts, I got $\displaystyle \int \frac {x^2}{1+x^2} dx$ as an integral later on.

But when I try integration by parts on this second integral, I end up having to evaluate $\displaystyle \int x tan^{-1}x$ again, and getting into a never-ending cycle is never a good idea.

Any ideas?