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Homework Help: Integral of 1/(x*ln(x)) converging or diverging?

  1. May 4, 2006 #1
    In order to find the integral of 1/(x*ln(x)) dx, I tried using the substitution method where

    u = 1/x and dv = 1/ln(x) dx .

    Then du = ln(x) dx.

    However this is where I got stuck.

    What would v equal? Or is their another way I should be approaching this integral in order to find if it is diverging or converging and if converging, to what value?
  2. jcsd
  3. May 4, 2006 #2


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    Gold Member

    First of all, is it a definite integral? What are the limits of integration?

    Then, if u=1/x then du is not ln(x) dx. Why don't you try the substitution u=ln(x) and see what happens?
  4. May 4, 2006 #3
    My mistake and sorry for not mentioning the limits. Its an improper integral with lower limit 2 and upper limit infinity.

    I think I found the solution...


    int(1/u) du

    And then solve for the integral, with the lower limit being ln(2) and the upper limit being infinity.

    It ends up diverging, correct?
  5. May 5, 2006 #4


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    Yes, I think you're right.
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