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Differential Equation Involving Natural Log.

  1. Sep 26, 2011 #1
    1. The problem statement, all variables and given/known data
    Calculate the following:
    [itex]\int^{-4}_{-6} (x^-1+5x)dx[/itex]


    2. Relevant equations



    3. The attempt at a solution
    I've worked this down to
    [itex]ln(-4) + 5(-4) - ln(-6) - 5(-6)
    =ln(-4)-ln(-6)+10[/itex]
    The answer to the left half (the ln parts) of the equation is undefined, and the right is 10..
    So... undefined + 10? I'm unsure what to say the definite answer is....

    Thank you for any help.
     
  2. jcsd
  3. Sep 26, 2011 #2

    LCKurtz

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    The antiderivative is

    [tex]\int \frac 1 x\,dx = \ln |x|+C[/tex]

    The absolute value signs matter when x < 0.
     
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