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Determining what values a function converges at

  1. Feb 24, 2010 #1
    1. The problem statement, all variables and given/known data
    For what values of p and q does the integral

    dx / (x^p * (ln(x))^q) from 1 to infinity


    2. Relevant equations

    3. The attempt at a solution
    I have no idea how to start figuring this out. I've tried trig substitutions but can't find something that actually makes progress.
  2. jcsd
  3. Feb 24, 2010 #2
    You don't need to actually evaluate the integral of (find a primitive of) [tex]x^{-p} \log^{-q} x[/tex] for generic [tex]p[/tex] and [tex]q[/tex]. Instead, compare the growth behavior of this function to simpler functions whose integrals you know converge or diverge, and try to find critical values of [tex]p[/tex] and [tex]q[/tex] where the behavior changes.
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