please help...
integrate 1/Sqrt[ x^2-1]
If you don't want to use hyperbolic functions because you don't know them, an alternative is using the identity $\displaystyle \sec ^2 y = 1 + \tan ^2 y$ to substitute $\displaystyle x = \sec y$.
It won't be as easy as with the hyperbolic functions, but I assume you do know these basic trigonometric functions.