Integral to Infinity of Sine p x Sine q x over x Squared

Theorem

 * $\ds \int_0^\infty \frac {\sin p x \sin q x} {x^2} \rd x = \begin {cases} \dfrac {\pi p} 2 & : 0 < p \le q \\

\dfrac {\pi q} 2 & : p \ge q > 0 \end {cases}$