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Homework Help: Integral from 1 to infinity of 1 / xln(third root of x)

  1. Nov 14, 2007 #1
    1. The problem statement, all variables and given/known data

    Integral from 1 to infinity of 1 / xln(third root of x)

    2. Relevant equations

    n/a

    3. The attempt at a solution

    I tried to find if it diverged and then got lost after that

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 14, 2007 #2
    if it diverges then that's the final answer. But can you post your work? maybe you did a mistake. But I think it is supposed to diverge.
     
  4. Nov 14, 2007 #3
    well you see there bob im not too sure how to get started and what to do with the ln
     
  5. Nov 14, 2007 #4

    Dick

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    If you don't know what to do, then you don't know it diverges, right? Try a substitution u=ln(x).
     
  6. Nov 21, 2007 #5
    Dick: I did u = ln(x) and du = 1/x

    so int from 1 to 0 ln(third root of u)du

    = - in from 0 to 1 ln(third root of u)du

    I always mix up these substitutions.
     
  7. Nov 21, 2007 #6

    Gib Z

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    Note: [tex]\log_a b^x = x \log_a b[/tex] where a, b and x are real numbers, (a,b) > 0.
     
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