Abstract
Complex analysis is a branch of mathematics that studies complex numbers. Cauchy’s residue theorem is a very important theorem in complex integral calculus. Many researchers have studied and tried applying it in different academic fields. In this paper, we studied the residue theorem and used it to compute some complicated real-valued integrals that appeared to be difficult in computing in the domain of real numbers. This is done by first converting the real-valued function to a complex-valued function, obtain the residue of the function and then apply the residue theorem to obtain the value of the integral.