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

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

    please help...

    integrate 1/Sqrt[ x^2-1]
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by guess
    please help...

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

    \cosh(u)=x

    RonL
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  3. #3
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    if there other method??
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  4. #4
    Grand Panjandrum
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    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:

    <br />
(\cosh(x))^2-(\sinh(x))^2=1<br />

    and that:

    <br />
\frac{d}{dx} \cosh(x)=\sinh(x)<br />

    RonL
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  5. #5
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    it's because i haven got to learn about cosh...
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  6. #6
    Grand Panjandrum
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    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:

    <br />
\frac{e^u+e^{-u}}{2}=x<br />



    RonL
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  7. #7
    TD!
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    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.
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  8. #8
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    Thanks Bro,

    I solved it using the trigo function substitution
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