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

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March 22nd 2006, 04:50 AM
guess

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

please help...

integrate 1/Sqrt[ x^2-1]
March 22nd 2006, 05:07 AM
CaptainBlack

Quote:

Originally Posted by guess

please help...

integrate 1/Sqrt[ x^2-1]

Try the change of variable:

$\cosh(u)=x$

RonL
March 22nd 2006, 05:21 AM
guess

if there other method??
March 22nd 2006, 05:29 AM
CaptainBlack

Quote:

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:

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

and that:

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

RonL
March 22nd 2006, 05:35 AM
guess

it's because i haven got to learn about cosh...
March 22nd 2006, 07:28 AM
CaptainBlack

Quote:

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:

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

:cool:

RonL
March 22nd 2006, 07:37 AM
TD!

If you don't want to use hyperbolic functions because you don't know them, an alternative is using the identity $\sec ^2 y = 1 + \tan ^2 y$ to substitute $x = \sec y$ .

It won't be as easy as with the hyperbolic functions, but I assume you do know these basic trigonometric functions.
March 24th 2006, 06:24 AM
guess

Thanks Bro,

I solved it using the trigo function substitution

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