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What in the world?

  1. May 30, 2009 #1
    [tex]\frac{1}{2}\int \frac{dx}{x+1} = \frac{1}{2} \log(x+1)[/tex]

    [tex]\int \frac{dx}{2x+2} = \frac{1}{2} \log(2x+2)[/tex]

    Huh??
     
  2. jcsd
  3. May 30, 2009 #2

    Mute

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    Homework Helper

    Those are indefinite integrals, so they're only unique up to an additive constant. Notice:

    [tex]\frac{1}{2}\log(2x+2) = \frac{1}{2}\log(x+1) + \log\sqrt{2}[/tex]

    hence the two integrals differ only by a constant, and both are correct.
     
  4. May 30, 2009 #3
    Thought never crossed my mind. Thanks.
     
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