please help...

integrate 1/Sqrt[ x^2-1]

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- Mar 22nd 2006, 04:50 AMguessHow Do I integrate 1/Sqrt[ x^2-1]
please help...

integrate 1/Sqrt[ x^2-1] - Mar 22nd 2006, 05:07 AMCaptainBlackQuote:

Originally Posted by**guess**

$\displaystyle \cosh(u)=x$

RonL - Mar 22nd 2006, 05:21 AMguess
if there other method??

- Mar 22nd 2006, 05:29 AMCaptainBlackQuote:

Originally Posted by**guess**

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 - Mar 22nd 2006, 05:35 AMguess
it's because i haven got to learn about cosh...

- Mar 22nd 2006, 07:28 AMCaptainBlackQuote:

Originally Posted by**guess**

substitution:

$\displaystyle

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

$

:cool:

RonL - Mar 22nd 2006, 07:37 AMTD!
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. - Mar 24th 2006, 06:24 AMguess
Thanks Bro,

I solved it using the trigo function substitution