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Math Help - Integrating to produce a log function

  1. #1
    Junior Member
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    Integrating to produce a log function

    Hey everyone, just wondering whats the difference when I integrate:
    \int\dfrac{1}{-x+1}\,dx
    it be integrated in 2 ways
    -\int\dfrac{1}{x-1}=-ln(x-1)

    OR

    -\int\dfrac{-1}{-x+1}\,dx=-ln(-x+1)

    are those 2 solutions different? or is there some log manipulation to make
    -ln(x-1)\text{be the same as} -ln(-x+1)
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  2. #2
    MHF Contributor

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    Tejas
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    as you can see, -ln(x-1), and -ln(-x+1) have different domains.

    the first function is only defined for x > 1, and the second is only defined for x < 1.

    to circumvent these difficulties, one often sees the antiderivative as -ln|x-1|, which is defined for all x ≠ 1.
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  3. #3
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    ah ok i get what you mean now. Thanks for the help
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