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Math Help - Integrating a hyperbolic.

  1. #1
    Super Member Showcase_22's Avatar
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    Integrating a hyperbolic.

    Does anyone know how to integrate:



    I've tried doing it in terms of e and I haven't really got anywhere.

    Please help!
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  2. #2
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    Quote Originally Posted by Showcase_22 View Post
    Does anyone know how to integrate:



    I've tried doing it in terms of e and I haven't really got anywhere.

    Please help!
    You can multiply it with \frac{tanh(x)}{tanh(x)}

    Remember that: (\text{sech(x)})' = -\text{sech(x)}\text{tanh(x)}

    tanh(x) = \sqrt{1-sech^2(x)}

    By substituting for u = sech(x), you will get a standard form in the end.
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  3. #3
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    Quote Originally Posted by Showcase_22 View Post
    Does anyone know how to integrate:



    I've tried doing it in terms of e and I haven't really got anywhere.

    Please help!
    = \int \frac{2}{e^x + e^{-x}} \, dx

    and the substitution u = e^x works just fine: \int \frac{2}{u^2 + 1} \, du \, ....
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  4. #4
    Super Member Showcase_22's Avatar
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    oh right. I think I tried turning it into partial fractions which is a very long and arduous process.

    cheers!
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