One of Methods of Integrating by Parts in Indefinite Integral

Abstract

One of the parts "Differentiation and integration of a function of one variable" of higher mathematics, the section "Indefinite integral" is important for students of higher technical institutions. The paper considers an important method of integral calculus of the mathematical analysis of the higher mathematics course - one of the types of integration by parts. In many cases, we have to apply the method of integration by parts several times, the solution of the problem complicates. Therefore, the article considers a generalized version of the application of this method. The application of the shown formula allows to solve the problem more quickly. The rule of integration by parts is used in many cases. Integration by method of integration by parts has a number of peculiarities. It is necessary to take into account some remarks for applying the method of integration by parts. If the integrand is given by a product of a polynomial and an exponential or trigonometric function, then u is a polynomial, and if the integrand is given by a product of a polynomial and a logarithmic or inverse trigonometric function, thenu is the logarithmic or inverse trigonometric function. For integrating we must pay an attention on the efficiency of finding the integral of a function that is known or is faster depending on a more convenient way of integration.