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Seemingly simple integration

  1. Feb 25, 2009 #1
    The problem statement, all variables and given/known data

    I need to find the integral of 1/(x2 - 1) dx


    The attempt at a solution

    Double checking on an online integrator, it gave me an answer of

    1/2 [log(x-1) - log(x+1)]

    I would have expected

    log(x2-1)/2


    Does anyone know why it's the first one?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 25, 2009 #2

    Tom Mattson

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    Staff Emeritus
    Science Advisor
    Gold Member

    That's fine, but have you tried it? This integral can easily be done either by partial fractions or trig substitution.
     
  4. Feb 26, 2009 #3

    Mark44

    Staff: Mentor

    Why would you have expected this? Were you thinking that your integral looked like [itex]\int du/u?[/itex]
    If you were thinking along those lines, with u = x^2 - 1, you don't have anything remotely close to du to make this work.

    It is NOT true that
    [tex]\int \frac{dx}{f(x)} = ln |f(x)| + C[/tex]

    If you weren't thinking that, never mind...
     
  5. Feb 26, 2009 #4

    HallsofIvy

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    In any case, please try partial fractions and get back to us with the result.

    [tex]\frac{1}{x^2- 1}= \frac{1}{(x-1)(x+1)}= \frac{A}{x-1}+ \frac{B}{x+1}[/tex]

    What are A and B?
     
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