calculus - Computing Integral of $frac{sin^n x}{x^n}$

How do you compute

$$\int_0^{\infty}\frac{\sin^n x}{x^n}dx$$ for every $n$? Thank you.

For $n=1$ it is widely known and for $n=2$ you might use Plancherel's formula. But I don't know how to do it for $n\geq3.$