Evaluation of specific integrals by differentiation

Abstract

Differentiation and integration (anti-differentiation) constitute one of the fundamental techniques used in higher mathematics. These operations are inverse of each other. While differentiation (to the extent of school mathematics) is relatively simple and straightforward, integration, in general, is a much more involving task. There are various classical methods to evaluate elementary integrals, e.g. substitution, integration by parts, partial fraction decomposition or more advanced techniques like the residue theorem, or Cauchy’s integral formula. The paper deals with some types of elementary functions whose integrals can be evaluated by intelligent guess and differentiation.