I know what the Laplace Transform of a function
$\exp(-x(t))$
is, where $x(t)$ is positive for all $t$. Is there any way to calculate what the Laplace Transform of
$\frac{1}{1-\exp(-x(t))}$
is?
I have tried with the geometrical series, but then I still do not know how to calculate the Laplace Transform of
$\exp(-kx(t))$,
which occurs in the formula (for $k=2,3,...$). One can assume that the function $x(t)$ is "enough nice" if this is needed (i.e. differentiable, continuous or what is necessary).