general integration formula

Hi all,

Is there any general formula for calculating integrals of the type $\displaystyle \int{\frac{dx}{x\sqrt{x^2-a^2}}}$ other than $\displaystyle \frac{1}{a}arc\sec{\frac{|x|}{a}}+C$ (guess the function is not even included in LaTeX)? I was trying to figure it out and got something like $\displaystyle -\frac{1}{a}\arcsin{\frac{a}{|x|}}+C$ but I'm not sure if it's (always) correct and where absolute values should be put.

Thank you. (Smile)

EDIT:

Guess I got it: $\displaystyle -\frac{1}{|a|}\arcsin{\frac{|a|}{x}}+C$. Can someone confirm if it's correct? Thanks.