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How would you solve this integral?

  1. Apr 16, 2009 #1
    how would you integrate the following, seemingly simple, function.

    f(x)=1/ln(x)

    what i tried to do was substitution
    t=ln(x)
    x=et
    dt=dx/x

    but from here i get to an integral of [tex]\int[/tex]((et)/(t))dt, no idea how to continue, tried integration in prts but keep going in cirlces, can anyone see how to do this?
     
  2. jcsd
  3. Apr 16, 2009 #2

    CompuChip

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    Science Advisor
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    When I plug it into Mathematica, I get
    LogIntegral[x]
    as the answer.

    So I think there is no closed form.
     
  4. Apr 16, 2009 #3
  5. Apr 16, 2009 #4
    My integral table has this, but it is a series solution.

    [tex] =ln(t)+t+{{t^2}\over{(2)\;2!}}+{{t^3}\over{(3)\;3!}} + ...[/tex]
     
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