I have the following expression: $$\int_0^\infty f(x)e^{-sx}dx=\frac{1}{(K^M-e^{-sM})^{\frac{a}{M}}}$$ where $a$, $M$ and $K$ are positive constants. Is it possible to find the expression for $f(x)$ through the inverse Laplace transform? I tried but I got lost with the computations.
Thank you very much.