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

qw3x

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

[itex]\int \frac{dx}{x^2-a^2}[/itex]

2. Relevant equations



3. The attempt at a solution

I've reached the answer, [itex]\frac{1}{2a} ln |\frac{x-a}{x+a}| + C[/itex] , 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 [itex]x=asec(\theta)[/itex]?

hunt_mat

Try [itex]x=a\cosh u[/itex]

SammyS

Hello qw3x. Welcome to PF !

[itex]x=asec(\theta)[/itex] should work fine. I think that leads to integrating csc(θ) .