# Homework Help: Integration (maybe by parts)

1. Oct 20, 2012

### tomwilliam2

1. The problem statement, all variables and given/known data
$$\int \frac{x}{(1-x^2)} dx$$

2. Relevant equations

Integration by parts, by substitution, etc.

3. The attempt at a solution

I just can't remember how to begin this integration. I tried doing integration by parts, where
$$a(x) = x$$
$$a'(x) = 1$$
$$b(x) =$$
$$b'(x) = \frac{1}{(1-x^2)}$$
$$\int \frac{x}{(1-x^2)}dx = xb(x) - \int \frac{1}{(1-x^2)} dx$$

But couldn't work out what form b(x) should take.
Thanks in advance for any help

2. Oct 20, 2012

### Fightfish

If you have seen enough of these integrals, they can essentially done "by observation"

If not, substitution is a good method to use. Substitute $y = x^{2}$. Then $dy = 2x dx$
Then the integral becomes:
$$\int \frac{1}{2}\frac{1}{1-y}dy$$

Does that now look more doable?

Last edited: Oct 20, 2012
3. Oct 20, 2012

### HallsofIvy

Why not let u= 1- x^2 itself? Then du= -2xdx so that xdx= -(1/2)du do that
$-\frac{1}{2}\int \frac{du}{u}$

4. Oct 20, 2012

### tomwilliam2

Ah yes, thanks...that makes sense. I wasn't getting where the sqrt cam from in the first response.
Thanks to both of you

5. Oct 20, 2012

### Fightfish

Oops, typo, my bad.