Homework Help: Inverse laplace transofrm of natural logarithm

1. May 8, 2010

exidez

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

the inverse laplace transform of $$ln\frac{s+2}{s-5}$$ using the inverse Laplace transform of the derivative

2. Relevant equations

$$L^{-1}$${$$\frac{d^{n}}{ds^{n}}F(S)$$} = $$(-1)^{n}t^{n}f(t)$$

3. The attempt at a solution

the integral of $$ln\frac{s+2}{s-5}$$ 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. May 8, 2010

exidez

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 $$\frac{d}{ds}}F(S)$$ is the derivative of F(S) then $$\frac{d^{-1}}{ds^{-1}}F(S)$$ is the same as the integration of F(S) right?