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Finding the Improper integrals

  1. Oct 12, 2004 #1
    I am trying to find the integral of [ln(x)] / [sqrt(x)]. i tried doing it by u substitution but that failed. what is the easiest way to do it? Also, I evaulated the integral from 1 to infinity of [ln(x)]/x by treating as an improper integral.
    The way i did it was by setting up lim(as t->infinity) integral(1 to t) [ln(x)]/x. This correct, i got -1 so that means it diverges right? Or is my answer wrong?

    Thanks for your help!!!
  2. jcsd
  3. Oct 12, 2004 #2


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    Homework Helper

    I think you got to use integration by parts.
  4. Oct 13, 2004 #3
    k, i will try integrating by parts but am i right about the second integral?
  5. Oct 13, 2004 #4
    can anyone else help me out please?
  6. Oct 13, 2004 #5
    lnx = 2t
    x = e^2t
    taking sqrt on both sides,
    sqrt(x) = e^t
    1/2*sqrt(x) dx = e^t dt

    -- AI
  7. Oct 13, 2004 #6
    this may be a dumb question but whre is that from?

  8. Oct 14, 2004 #7
    oh i missed the word substitute ...
    -- AI
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