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Math Help - integral

  1. #1
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    integral

    Integral of <br />
(e^x-e^-x)/(e^x+e^-x)<br />

    I have tried adding the conjugate to the top and bottom but don't know where to go from there. Should I continue that or try a different technique?
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  2. #2
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    Hello, stevo970!

    If you look at it the right way, it's easy . . .


    \int\frac{e^x-e^{-x}}{e^x+e^{-x}}\,dx

    Let u = the denominator.

    We have: . \begin{array}{ccc}u &=& e^x + e^{-x} \\ du &=& (e^x - e^{-x})\,dx \end{array}

    Hence, we have: . \int\frac{du}{u}

    Got it?

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  3. #3
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    wow ok thank you
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  4. #4
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    also noting that this is (sinh(x))/(cosh(x)) may make this become clearer
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