EJMT Abstract

The study of some parametric integrals is presented with a combined approach of analytical development, the usage of a Computed Algebra System (CAS) and of the Online Encyclopedia of Integer Sequences. The paper runs around the analysis of the 2-parameter definite integral

$$I_n^{(p)}={\int }_0^{\frac{\pi }{4}}{x}^p{\tan }^{n}xdx$$

The methodology for the solution includes a) an analytical investigation for the study of the parametric integral, b) computations with a CAS of the integral for specific values of the parameter, c) investigation of the connection between the integral and special functions or mathematical constants, and d) derivation of a general algorithm for the complete computation of the parametric integral. Comparing the outputs of different kinds of software yields useful remarks about the understanding of the outputs, an important issue in mathematics education in a technology-rich environment.