An evaluation of a class of singular integrals

Abstract:

      By means of residues and special integral loops, we give a general evaluation of the following kind of singular integrals:I(m,p,n)=∫₀^∞ (sin^mxcos^px) /xⁿdx,where m,n,p are all non-negative integers，m≥n> 0, and m，n are simultaneously odd or even.