We know the followings : 
$$\int_{0}^{\infty}\frac{{\sin}x}{x}dx=\int_{0}^{\infty}\frac{{\sin}^2x}{x^2}dx=\frac{\pi}{2},\int_{0}^{\infty}\frac{{\sin}^3x}{x^3}dx=\frac{3\pi}{8}.$$
Also, we can get
$$\int_{0}^{\infty}\frac{{\sin}^3x}{x^2}dx=\frac{3\log 3}{4},\int_{0}^{\infty}\frac{{\sin}^4x}{x^3}dx=\log 2.$$
Then, I got interested in their generalization. 
>**Question** : Letting $p,q\in\mathbb N$, can we simplify the following?
$$\int_{0}^{\infty}\frac{{\sin}^px}{x^q}dx$$

I don't have any good idea. Could you show me how to simplify this?

**Remark** : This question has been [asked previously on math.SE][1] without receiving any answers.


  [1]: http://math.stackexchange.com/questions/558014/can-we-simplify-int-0-infty-frac-sinpxxqdx