# Integrate 1/(x^2-a^2)

1. Mar 31, 2012

### qw3x

1. The problem statement, all variables and given/known data

$\int \frac{dx}{x^2-a^2}$

2. Relevant equations

3. The attempt at a solution

I've reached the answer, $\frac{1}{2a} ln |\frac{x-a}{x+a}| + C$ , using partial fractions, but my professor asks for the work using substitution. Now I know how to do this when there's a radical in the denominator, but would this also be a substitution $x=asec(\theta)$?

2. Mar 31, 2012

### hunt_mat

Try $x=a\cosh u$

3. Mar 31, 2012

### SammyS

Staff Emeritus
Hello qw3x. Welcome to PF !

$x=asec(\theta)$ should work fine. I think that leads to integrating csc(θ) .