# Find a $F(s)$ such that the inverse Laplace transform of $(1-s)^n F(s)$ exists for all $n$ on $s\in (0,1)$ and $\int f(x) dx=1$

I am looking for a function $$f(t)$$ with the Laplace transform $$F(s)$$ such that $$G(s)=(1-s)^n F(s)$$ has the inverse Laplace transform for all non-negative integers $$n$$. Moreover, I want $$\int f(t)dt=1$$.