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Among the methods used to solve indefinite integrals, students often face difficulties in applying the method of integration by parts. These challenges arise from the choice of functions to use as the finite factor and differential factor, as well as the subsequent calculations that such a choice entails. For example, integrals of a sinusoidal or exponential function multiplied by a polynomial of degree higher than one require repeated application of integration by parts. However, this process can be sped up by constructing a two-column table where the derivatives of the finite factor and the integrals of the differential factor are listed, and setting the calculations according to this table, as explained below. This alternative procedure is known as the Tabular Integration by Parts (TIBP) method. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to illustrate how the evaluation of the definite integral of real functions of real variables that exhibit particular symmetries can be simplified. The proposal will then be substantiated through some application rules. [ABSTRACT FROM AUTHOR]

This paper aims to show how the application of the generalised versions of Rolle's theorem allows the exact number of stationary points of a rational function to be determined, even if the rational function is a fraction which contains real and/or complex conjugate zeros of any multiplicity in both numerator and denominator. [ABSTRACT FROM AUTHOR]