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Homework Help: Convergence of the following integral

  1. Apr 11, 2009 #1
    i need to prove that the following converges or diverges

    [tex]\int[/tex][tex]\frac{ln(x)dx}{\sqrt[3]{x}(x+1)}[/tex] (from 1-∞)

    what i have been trying to do is find a function that is either:
    g(x)>f(x); g(x) converges
    g(x)<f(x); g(x) diverges

    but i have not been able,
    is there any other way to solve this, or could you please show me a similar function that is one of the 2, if possible could you show how you reached your g(x)

    thank you
  2. jcsd
  3. Apr 12, 2009 #2


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    Hi Dell! :smile:

    have you tried ∫ ln(x)/x4/3 dx ?
  4. Apr 12, 2009 #3
    i thought of that, but what do i know about ln(x)/x^4/3, i would ideally liked to have taken it as my gx and said lim fx/gx=1 therefore f(x) behaves like ln(x)/x^4/3, how can i fin out if ln(x)/x^4/3 converges/diverges, do i have to integrate it? if so is there a simpler way than integration in parts? if not, is there not a simpler function you can think of
  5. Apr 12, 2009 #4


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    D'uh! :rolleyes:

    you'd think so, wouldn't you?

    get on with it!!
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