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Math Help - integral help

  1. #1
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    integral help

    ok, so i have to integrate (e^x-e^-x)/(e^x+e^-x). any ideas on how to solve this problem?
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  2. #2
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    Let {\color{red}u = e^x + e^{-x}} \ \Rightarrow \ {\color{blue}du = \left(e^x - e^{-x} \right)dx}

    So your integral becomes: \int \frac{{\color{blue}e^x-e^{-x}}}{{\color{red}e^x + e^{-x}}} \ {\color{blue} dx} = \cdots
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    Put the bottom equal to u. Take its derivative. It's going to equal the top. You will thus conclude that it is ln(denominator)
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  4. #4
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    ok, kewl. i see wat i did wrong now. i differentiated e^-x wrong. forgot that it was negative. thanks guys, really appreciate it.
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  5. #5
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    Quote Originally Posted by needhelp101 View Post
    ok, so i have to integrate (e^x-e^-x)/(e^x+e^-x). any ideas on how to solve this problem?
    Or, you might recognise the definition of a familiar hyperbolic function and hence a standard integral ....
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  6. #6
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    solution of the integral

    Your (E^x-E^(-x))/(E^x+E^(-x)) equals Tanh[x]. And its integral is Ln[Cosh[x]]. Please visit one of most powerful math engines:
    http://integrals.wolfram.com/index.jsp
    All the best. Marek.
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