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Inverse laplace transofrm of natural logarithm

  1. May 8, 2010 #1
    1. The problem statement, all variables and given/known data

    the inverse laplace transform of [tex]ln\frac{s+2}{s-5}[/tex] using the inverse Laplace transform of the derivative

    2. Relevant equations


    [tex]L^{-1}[/tex]{[tex]\frac{d^{n}}{ds^{n}}F(S)[/tex]} = [tex](-1)^{n}t^{n}f(t)[/tex]

    3. The attempt at a solution

    the integral of [tex]ln\frac{s+2}{s-5}[/tex] I worked to be (s+2)ln(s+2)-(s+2) -(s-5)ln(s-5)+(s-5). So if this is F(S) then i still have no idea how to inverse it using the inverse Laplace transform of the derivative

    somehow i think im going down the wrong road... ?
     
    Last edited: May 8, 2010
  2. jcsd
  3. May 8, 2010 #2
    ok, i think i got it!

    i go the other way and make n = -1

    I have never seen this but just to clear this up: if [tex]\frac{d}{ds}}F(S)[/tex] is the derivative of F(S) then [tex]\frac{d^{-1}}{ds^{-1}}F(S)[/tex] is the same as the integration of F(S) right?
     
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