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Math Help - Integration Check

  1. #1
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    Integration Check

    I attempted to solve this on my own...please let me know if I am correct

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

    my answer:
     <br />
e^x-e^{-x}+c<br />

    Thank you.
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  2. #2
    Moo
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    Hello,

    Note that the numerator is the derivative of the denominator. So you have something in the form u'/u. Thus the integral would give \ln(e^x-e^{-x})+c
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  3. #3
    Super Member Random Variable's Avatar
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    The following is completely unnecessary, but true:

     \int \frac{e^{x}+e^{-x}}{e^{x}-e^{-x}} \ dx = \int \coth{x} \ dx = \ln ({\sinh {x}}) + C = \ln \Big(\frac{e^{x}-e^{-x}}{2}\Big) + C = \ln (e^{x}-e^{-x}) + B
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