improper integrals - Laplace transform:$int_0^infty frac{sin^4 x}{x^3} , dx $

I have a trouble with a integral:
Using this Laplace trasform equation:
$$\begin{align}

\int_0^\infty F(u)g(u) \, du & = \int_0^\infty f(u)G(u) \, du \\[6pt]
L[f(t)] & = F(s) \\[6pt]
L[g(t)] & = G(s)
\end{align}$$

Applying to compute this integral:

$$I = \int_0^\infty \frac{\sin^4 x}{x^3} \, dx $$