# Homework Help: Stuck on the following integral

1. Aug 25, 2006

### suspenc3

Hi, I am kinda stuck on the following integral:

$$\int\sqrt{\frac{1+x}{1-x}}dx$$

any hints?

2. Aug 25, 2006

### TD

If you let

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

The integral will become fraction of rationals, losing the square root.

3. Aug 25, 2006

### suspenc3

so are you saying to substitute that for x?

4. Aug 25, 2006

### suspenc3

or by making this substitution, the square root will be taken away

5. Aug 25, 2006

### neutrino

Or you could do the trig substitution $$x = \sin\theta$$

6. Aug 25, 2006

### TD

Yes, use that substitution to lose the square root.

I already solved for x as well, which allows you to easily find dx in terms of dy by differentiating both sides.