Integration of 1/(x^2-a^2) Using Substitution Method

[qw3x]

Homework Statement

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

Homework Equations

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 $x=asec(\theta)$?

 

[hunt_mat]

Try $x=a\cosh u$

 

[SammyS]

Homework Statement

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

Homework Equations

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 $x=asec(\theta)$?

Hello qw3x. Welcome to PF !

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