# Thread: How Do I integrate 1/Sqrt[ x^2-1]

1. ## How Do I integrate 1/Sqrt[ x^2-1]

integrate 1/Sqrt[ x^2-1]

2. Originally Posted by guess

integrate 1/Sqrt[ x^2-1]
Try the change of variable:

$\displaystyle \cosh(u)=x$

RonL

3. if there other method??

4. Originally Posted by guess
if there other method??
Why would you want another method, this change of variable makes the
problem trivial.

All you need to know is that:

$\displaystyle (\cosh(x))^2-(\sinh(x))^2=1$

and that:

$\displaystyle \frac{d}{dx} \cosh(x)=\sinh(x)$

RonL

5. it's because i haven got to learn about cosh...

6. Originally Posted by guess
it's because i haven got to learn about cosh...
My good friend Mephistopheles suggests that I recommend that you try the
substitution:

$\displaystyle \frac{e^u+e^{-u}}{2}=x$

RonL

7. 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.

8. Thanks Bro,

I solved it using the trigo function substitution