I am having trouble computing the following Laplace transform: $\frac {f(x)}{x}$.
From Wikipedia it should be equivalent to this: $\int_s^\infty F(\sigma) \,d\sigma$ .
What I've done so far is substitute in $-\int_s^\infty e^{-sx} ds$ for $\frac {e^{-sx}}{x}$.
After simplification I end up with this: $-\int_s^\infty F(s)\, ds$ where $F(s)$ is the Laplace transform of $f(x)$
I am unsure of how to simplify this further to get the result of Wikipedia.