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

Question

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.