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I'm trying to find L^-1{ ln(1 + (1/s))}

I can see that there is an essential pole at s=0 (is this even right? The power series has an infinite amount of z^n's in the denominator..) and branch points at s=0 and s=-1.

So.. I've created a contour which excludes the branch cut from x=0 to x=-1

But then if I integrated around this contour, there are no singularities in my contour so by cauchys theorem won't my integral be equal to 0?...