# Thread: Integral question relating to arctan...

1. ## Integral question relating to arctan...

How do you do this integral?

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

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

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

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

Any ideas?

2. $\frac{x^2}{x^2+1} = \frac{x^2+1-1}{x^2+1} = \frac{x^2+1}{x^2+1} - \frac{1}{x^2+1} = 1 - \frac{1}{x^2+1}$

now integrate

3. That's a really neat solution. Thanks!