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Improper Integrals with u sub and integration by parts ?

  1. Apr 12, 2009 #1
    1. The problem statement, all variables and given/known data

    The integral from 1 to infinity of (lnx)/(x) dx

    2. Relevant equations
    U substitution and integration by parts

    3. The attempt at a solution
    Cant decide what to use as my "u" . . can any one help with this part ?

    -Jay J-
  2. jcsd
  3. Apr 12, 2009 #2


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    Gold Member

    this doesn't really require integration by parts, just a u-substitution:

    [tex]\int \frac{ln(x)}{x}=\int u du = \frac{1}{2}u+ C= \frac{1}{2}(ln(x))^2+C[/tex]

    here you take u = ln(x) and differentiate to get, du = 1/x dx.
  4. Apr 12, 2009 #3
    ok i understand the whole u substitution part but then i have to determine whether or not the integral is divergent or convergent and if its convergent i have 2 evaluate it . .. how would you do that ?

    -Jay J-
  5. Apr 12, 2009 #4


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    Homework Helper

    Evaluate the integral between x=0 and x=M and let M approach infinity. What do you conclude?
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