integration - Integrate $I(t)=int_0^infty left( frac{sin tx}{x} right)^n,mathrm d x$

How to integrate the following:
$$I(t)=\int_0^\infty \left( \frac{\sin tx}{x} \right)^n\,\mathrm d x$$

I tried to using the Laplace transform:

$$\begin{align} \mathcal{L}\left[I(t)\right]=\int_0^\infty \mathcal L\left[\left( \frac{\sin tx}{x} \right)^n\right]\,\mathrm d x \end{align}$$

but I don't know what to do then.