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Integral with /ln(x)

  1. Apr 7, 2009 #1
    sorry that i do not know the correct english terminology, hope you understand

    i need to look into tis integral
    [tex]\int[/tex]dx/ln(x) (from 0 to 1)

    and say if it comes to a number or to infinity or what, dont necessarily have to gve the answer as a number, can either comapre it to another simpler function or work out the integral.

    if F(x)<G(x) and G(x) collects to an actual number than so will F(x), etc
    again, hope im clear and understood
     
  2. jcsd
  3. Apr 7, 2009 #2

    Dick

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    Clearly the only place you could have a problem with convergence is near x=1. Find something to compare with in a small interval near x=1, think about the tangent line to the curve y=ln(x) there.
     
  4. Apr 8, 2009 #3
    i cannot find such a function of x that is always bigger or always smaller than 1/lnx. could you please show me
     
  5. Apr 8, 2009 #4

    Dick

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    It doesn't have to be always bigger or always smaller. It only has to be bigger or smaller where it counts. Can you find f(x) so that 1/|f(x)|<1/|ln(x)| only on the interval [0.9,1] and 1/|f(x)| diverges over that interval? Make f a linear function. What is the tangent to y=ln(x) at x=1?
     
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