A guide for using integration by parts: Pet-LoPo-InPo

Based on the tutorial cases accumulated in the past several years, by reclassifying the arithmetic functions (A) in LIATE into the polynomial function (P), the standard power function (Po), and the integer power function (nPo), a new guide, comprising three sub-guides, Pet, LoPo and InPo, or Pet-LoPo-InPo, is summarized in this note to guide practicing integration by parts. This new guide removes many incompatible combinations included in LIATE, rationalizes the relationship between the exponential and trigonometric functions in LIATE, and expands the coverage of the P-functions beyond the traditional definitions. Hence, the new guide can reduce potential confusions that students may experience in using LIATE for their practices of integration by parts. The advantages of this new guide are demonstrated by many worked examples in this note.