Solving an Integral: Tips and Tricks for Evaluating ∫dx/(x√(x² - a²))

[insynC]

Homework Statement

Trying to evaluate the following integral:

∫dx/(x√(x² - a²))

The Attempt at a Solution

I think I'm missing something simple. I know:

∫dx/(x√(x² + a²)) = - 1/a arccsch|u/a| + C

&

∫dx/(x√(a² - x²)) = - 1/a arcsech(u/a) + C

But I'm not exactly sure how to manipulate my integral into one of these forms.

Any suggestions? Thanks

 

[The Dagda]

\frac{1}{x(x^2-a^2)^{\frac{1}{2}}}

Does that help?

 

[jgens]

Let x = au, then dx = adu. Can you take it from there?

 

[insynC]

It's just a standard integral for arcsec... :S don't know how I missed that.

Thanks for the help