Applications of complex variable residue theory to the evaluation solution of irrational definite integrals. II

摘要

Eight irrational definite integrals are proven to be zero using complex analysis. As in previous papers, the integrals are first expressed as contour integrals. By expanding binomially and collecting the contributions to the 1/Z term, the residue is found. In all eight cases, the residues are zero and hence the integrals are zero. It was not expected that all of the integrals would be zero. The result further illustrates the usefulness of this method to find exact values of extremely complex integrals. It is again concluded that this technique is widely applicable to whole classes of integrals not yet evaluated.