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Integral of 3/x

  1. Jan 14, 2008 #1
    1. The problem statement, all variables and given/known data

    the integral of 3/x

    2. Relevant equations



    3. The attempt at a solution

    am i right in saying this is 3lnx
     
  2. jcsd
  3. Jan 14, 2008 #2

    Kurdt

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    Yes you are. Don't forget the arbitrary constant.
     
  4. Jan 14, 2008 #3

    Tom Mattson

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    And don't forget the absolute value bars. It's 3ln|x|+C.
     
  5. Jan 14, 2008 #4

    Kurdt

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    Indeed

    Welcome back Tom! :approve:
     
    Last edited: Jan 14, 2008
  6. Sep 7, 2009 #5
    Same question adding Limits of integration b=infinity a=0
     
  7. Sep 7, 2009 #6

    Hootenanny

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    Well, what do you think it is?
     
  8. Sep 7, 2009 #7
    rxtrejo - you asking a question?

    That would mean substituting the bounded values and find some 'area' within the limits you have given.
     
  9. Sep 7, 2009 #8

    Mark44

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    Not so fast. This is an improper definite integral that requires limits at both endpoints to evaluate.
     
  10. Sep 7, 2009 #9

    Mark44

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    IOW,
    [tex]3\int_0^{\infty} \frac{dx}{x}
    = 3\lim_{a \rightarrow 0_+}\int_a^{1} \frac{dx}{x}~+~ 3\lim_{b \rightarrow \infty}\int_1^{b} \frac{dx}{x}[/tex]

    I chose to split the first integral at 1. Any reasonable value could be used to divide the original interval into two subintervals.
     
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