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Math Help - integrate (e^-x)/(1+e^-x)

  1. #1
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    integrate (e^-x)/(1+e^-x)

    The answer is -ln(1+e^-x). I'm not real sure how it got there.
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  2. #2
    Super Member Matt Westwood's Avatar
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    Are you familiar with \int \frac {f'(x)}{f(x)} dx = \ln (f(x)) + C?
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  3. #3
    MHF Contributor
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    Have you considered:

    u = {whatever is in the denominator}

    ??
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  4. #4
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    We havn't been taught that rule Matt.

    And "u" substitution doesn't give me an ln. I doubt I'll be tested on this, but still wanted to know. Thanks Matt, the rule is something I need to know I guess.
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  5. #5
    Super Member Matt Westwood's Avatar
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    Okay then, substitute u = 1 + e^{-x}. Get du in terms of x and dx and see what happens.
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  6. #6
    Super Member Matt Westwood's Avatar
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    Quote Originally Posted by jebckr View Post
    We havn't been taught that rule Matt.

    And "u" substitution doesn't give me an ln. I doubt I'll be tested on this, but still wanted to know. Thanks Matt, the rule is something I need to know I guess.
    yes it does, you get -\int \frac 1 u du which is wot?
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  7. #7
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    ok, thanks. Got it.
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