Identities Involving Laplace Transforms and Fourier Transforms

In this chapter, our integration technique is based on the use of the Laplace and Fourier transform pairs, with surprising results. Combined with the method of interchanging the order of integration, the process has led to the derivation and utilization of Laplace transform pairs and Fourier transform pairs. Our results certainly contribute, if need be, to confirm the power of the Laplace and Fourier transforms as mathematical tools.