On the Derivation of Some Reduction Formula through Tabular Integration by Parts

The study aimed to expose the application of the algorithm of the Tabular Integration by Parts (TIBP in the derivation of some reduction formula involving integrals of product of elementary functions. In the study, the existing algorithm of tabular integration by parts (TIBP) was modified by forming a table consisting of three columns namely: S column where alternating plus and minus signs are written, D column where f(x) and its successive derivatives are listed, and I column where g(x) and its successive antiderivative/integrals are listed. The modified algorithm of TIBP was then used to evaluate the reduction formula involving the integrals of the forms:axdxxn sin ,axdxxn cos ,axdxxn sinh ,axdxxn cosh ,dxex axn  ,anddxxx mn )(ln where n, m and a are any real number.

Keywords – elementary functions, integrals, reduction formula, tabular integration by parts