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Integral from e to infinity

  1. Feb 20, 2009 #1
    1. The problem statement, all variables and given/known data

    integral [from e to infinity of ] 67 / (x(ln(x))^3)

    read as the integral from e to infinity of

    67 divided by x times cubed lnx.


    2. Relevant equations



    3. The attempt at a solution



    i know it converges,

    but i got the value

    67/2
     
  2. jcsd
  3. Feb 21, 2009 #2
    Re: divergent/convergent

    And I would agree with you...

    Using the substitution [tex]u=\ln{x}[/tex], the integral

    [tex]\int_e^\infty \frac{1}{x(\ln{x})^3} \, dx[/tex]

    becomes

    [tex]-\frac{1}{2} \int_1^\infty \frac{1}{u^2} \, du.[/tex]
     
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