# Inverse laplace transform with complex inversion theorm

1. Sep 28, 2009

### oddiseas

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

Find the inverse laplace transform of In(1+1/s)

2. Relevant equations

3. The attempt at a solution

Using the complex inversion theorm, and the sum of the residues.

The only residue is at s=0. and it is a simple pole of degree one.

Therefore lim(s approaches 0)= s*In(1+1/s)e^st and since e^st at s=0 becomes 1, i get:

lim(s approaches 0)=s*In(1+1/s)

Now i have no idea what to do next. Usually i can find f(t) easily at this point but not with this function.

(note: i have already found the answer using a power series and the derivative property,(1-e^-t)/t) i am trying to figure out how to proceed next with this method.)

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