# Homework Help: Seemingly simple integration

1. Feb 25, 2009

### abite

The problem statement, all variables and given/known data

I need to find the integral of 1/(x2 - 1) dx

The attempt at a solution

Double checking on an online integrator, it gave me an answer of

1/2 [log(x-1) - log(x+1)]

I would have expected

log(x2-1)/2

Does anyone know why it's the first one?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 25, 2009

### Tom Mattson

Staff Emeritus
That's fine, but have you tried it? This integral can easily be done either by partial fractions or trig substitution.

3. Feb 26, 2009

### Staff: Mentor

Why would you have expected this? Were you thinking that your integral looked like $\int du/u?$
If you were thinking along those lines, with u = x^2 - 1, you don't have anything remotely close to du to make this work.

It is NOT true that
$$\int \frac{dx}{f(x)} = ln |f(x)| + C$$

If you weren't thinking that, never mind...

4. Feb 26, 2009

### HallsofIvy

In any case, please try partial fractions and get back to us with the result.

$$\frac{1}{x^2- 1}= \frac{1}{(x-1)(x+1)}= \frac{A}{x-1}+ \frac{B}{x+1}$$

What are A and B?