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Improper Integrals - Infinite Intervals

  1. Feb 26, 2012 #1
    Improper Integrals -- Infinite Intervals

    1. The problem statement, all variables and given/known data

    Evaluate the integral.

    (from e to infinity) ∫(25/x(lnx)^3)dx

    2. Relevant equations


    3. The attempt at a solution

    I know that for evaluating improper integrals, you can take the limit as t approaches infinity of the given integral, but my problem is in evaluating the integral itself.

    25 comes out of the integrand, and so I'm left with dx/x(lnx)^3, and this is where I'm confused. I'm guessing integration by parts is necessary to properly evaluate this, but I'm not entirely sure. I tried setting u = (lnx)^-3, which gives me du=-3lnx/x*dx, but then I'm left with dv=xdx, so v=1/2x^2, but based on the solution, I don't believe I'm at all headed in the right direction.

    Any help would be greatly appreciated!
     
  2. jcsd
  3. Feb 27, 2012 #2

    ehild

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    Re: Improper Integrals -- Infinite Intervals


    Use the substitution u=ln(x) instead.


    ehild
     
  4. Feb 27, 2012 #3
    Re: Improper Integrals -- Infinite Intervals

    I did exactly that and it works out perfectly.

    Thanks a lot!
     
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