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

Theorem

 * $\ds \int_0^\infty \frac {\sin p x \cos q x} x \rd x = \begin{cases} 0 & : p > q > 0 \\

\dfrac \pi 2 & : 0 < p < q \\ \dfrac \pi 4 & : p = q > 0 \end{cases}$