Calculation of $\int_{1}^{\infty} \frac{\sin^2(\frac{ax}{2})}{x^p}dx$ for $1

I'm having trouble calculating$$\int_{1}^{\infty}\frac{\sin^{2}\left(ax/2\right)}{x^{p}}{\rm d}x\quad\mbox{for}\quad 1 < p < 3$$Could someone please help ?.

Everywhere I look I can only find that the integral converges as far as $p > 1$, but I cannot figure out why. Thanks for any help.