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Homework Help: Improperly integrable

  1. Nov 1, 2009 #1
    1. The problem statement, all variables and given/known data

    For what p is f(x)=log^a(x)/x^p integrable from (1,infinity)?

    2. Relevant equations

    3. The attempt at a solution

    I'm not sure, maybe I can do some sort of inequality so that I can arrive at the comparison theorem for improper integrals.
  2. jcsd
  3. Nov 1, 2009 #2


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    Gold Member

    It's always integrable from (1,N) for N > 1. Find an expression for that integral, and then try letting [itex]N \rightarrow \infty[/itex]. For what [itex]p[/itex] does the limit exist?
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