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Improper Integral

  1. Sep 5, 2009 #1
    Is there any way to integrate
    [tex]\int dx/(xlogx)[/tex]

    within the limits 1 and n?

    If yes what is the result?
  2. jcsd
  3. Sep 5, 2009 #2
    Assuming that log x means ln x (if not a constant is just introduced), if you make the substitution u= ln x the integrand simplifies to du/u. However the limits are 0 to ln n, and so ln u would have to be evaluated at 0, which means the integral does not converge.
  4. Sep 5, 2009 #3
    Yes the integral doesn not converge . This can be seen without integrating - the function 1 / (x * ln x) goes to infinity at x = 1 , and also func is continous in the interval .. so the area under the curve is infinite
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