# Thread: Integration by Parts Help

1. ## Integration by Parts Help

Hey everybody,

My class is learning integration by substitution and integration by parts right now, and I'm having a lot of trouble with them.

Right now, I need to find the antiderivative of $[(x^2)/(x^2 + 1)]dx$.

I've tried letting $u = x^2$ and $dv = [1/(x^2 + 1)]dx$, but I don't know if that's correct, because now I'm stuck at a weird place where I have to find the antiderivative of $[x arctan(x)]dx$, and I don't think we're supposed to have to do that much at this level.

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

3. Or, in order to use integation by parts, write the integral as
$\int x\left(\frac{x}{x^2+ 1}\right)dx$
and let u= x, $dv= \frac{x}{x^2+1}dx$.