ABSTRACT
Over the years, we have seen a great many elegant and striking integral problems and clever solutions published in the Monthly. Most of them contain mathematical ingenuities. In this chapter, we select 15 of these irresistible integrals. In presenting the combination of approaches required to evaluate these integrals, we have tried to follow the most interesting route to the results and endeavored to highlight connections to other problems and to more advanced topics. It is interesting to see the range of mathematical approaches this chapter exploits. These evaluations provide nice application of infinite series, gamma and beta functions, parametric differentiation and integration, Laplace transforms and contour integration.
