CVRC8

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Show that \int _{0}^{\infty }\left\{\prod _{{k=1}}^{n}{\frac  {\sin(\phi _{k}x)}{x}}\right\}\left\{\prod _{{j=1}}^{m}\cos(a_{j}x)\right\}{\frac  {\sin(ax)}{x}}\ dx={\frac  {\pi }{2}}\phi _{1}\phi _{2}\ldots \phi _{n}\,,   if \phi _{1},\phi _{2},\ldots ,\phi _{n},a_{1},a_{2},\ldots ,a_{m}\, are real, a\, is positive and a>\sum _{{k=1}}^{n}|\phi _{k}|+\sum _{{j=1}}^{m}|a_{j}|.