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Logs and antiderivatives

  1. Feb 11, 2009 #1
    S (x+2)/(x^2+4x) dx

    I've been learning about natural logs and their properties but at this answer I get befuddled at how to work it out. I think perhaps substitution, and some properties with logs but I am very weak in logs...Didn't do well in it when I was in algebra.
    I want to know how to do this equation, although I know it has this as an answer:


    Thanks for any help.
  2. jcsd
  3. Feb 11, 2009 #2

    Tom Mattson

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    Staff Emeritus
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    You think rightly. Now take a stab at choosing the right substitution. There aren't that many choices available, so this shouldn't be too hard.
  4. Feb 11, 2009 #3
    hmmm ok lets see u = x^2+4x --> du=2x+4 --> du/2=x+2

    makes the equation

    1/2 S du/U but 1/u means ln|u| though right? why is it a log?
  5. Feb 11, 2009 #4


    Staff: Mentor

    That's the right substitution, but you're missing something in du.
    u = x^2 + 4x ==> du = (2x + 4)dx

    [tex]\int du/u = ln |u| + C[/tex]
    An antiderivative of 1/u is ln |u | because the derivative of ln |u| is 1/u. It's a sort of inverse relationship, similar to the relationship between the equations y = ln(x) and x = e^y.
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