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Question regarding integrating (int(1/u))

  1. Dec 17, 2009 #1
    1. The problem statement, all variables and given/known data
    I'm confused about integrating something like [tex]\int[/tex][tex]\frac{1}{u}[/tex]
    Sometimes the answer seems to be ln|u| and sometimes just ln(u), and I wasn't sure why it is different from problem to problem. (after subbing u back in; I'm using the u-sub method)

    It looks like the answer should be very straight forward as I can't find an explanation, so I'm not seeing something. My only guess would be that the absolute value symbols are used only if a negative value of x could give a negative value for u when subbing back in, making the ln(blah) undefined (for my course anyways). Is this about right? Thanks.
    Last edited: Dec 17, 2009
  2. jcsd
  3. Dec 17, 2009 #2


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    Homework Helper

    Don't worry about it. The integral should be ln(|u|) because deriving that gives you 1/u for both u>0 and u<0. Sometimes, writing ln(u) works because (1) it's convenient and (2) it often works out in the end even if u is negative and the absolute value sign is ignored.
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