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Integral of (lnx)/(4x)

  1. Dec 6, 2012 #1

    939

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

    I am lost as to what to do here.

    2. Relevant equations

    Integral of (lnx)/(4x)

    3. The attempt at a solution

    let u = lnx
    let du = (1/x)dx

    (u)/(4x) dx...

    But then howdo you make 4x disappear in the equation? Typically I did it by making du = something in the equation I want to take out, but how can you make 1/x = 4x?
     
  2. jcsd
  3. Dec 6, 2012 #2

    Mute

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    Your integral is

    $$\int dx~\frac{\ln x}{4x},$$
    and you made the substitution u = ln x, so that du = dx/x, so you need to replace the dx in the integral with dx = x du. What happens to the 1/x in the integral then?
     
  4. Dec 6, 2012 #3
    du = 1/x dx sooo

    u/4 du...........b/c.....(1/4)*(ln(x)/x) dx
     
  5. Dec 6, 2012 #4

    Dick

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    Sure, u/4 du. Integrate that.
     
  6. Dec 6, 2012 #5

    Mark44

    Staff: Mentor

    And it would be a good idea to pull out that 1/4 right away so that you're working with this integral:
    $$ \frac{1}{4} \int \frac{ln(x) dx}{x}$$
     
  7. Dec 7, 2012 #6
    u = lnx, du = (1/x) dx

    [itex]\frac{1}{4}[/itex]∫u du

    Then apply power rule...
     
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