A guide for using integration by parts: <i>Pet-LoPo-InPo</i>

William Guo; William Guo

doi:10.3934/era.2022182

Electronic Research Archive

2022, Volume 30, Issue 10: 3572-3585. doi: 10.3934/era.2022182

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Technical note

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

William Guo ^,

School of Engineering and Technology, Central Queensland University, Bruce Highway, North Rockhampton, QLD 4702, Australia

Received: 16 April 2022 Revised: 15 June 2022 Accepted: 10 July 2022 Published: 28 July 2022

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.
- integration by parts,
- combinative integrands,
- LIATE,
- LIPTE,
- Pet-LoPo-InPo
Citation: William Guo. A guide for using integration by parts: Pet-LoPo-InPo[J]. Electronic Research Archive, 2022, 30(10): 3572-3585. doi: 10.3934/era.2022182

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Abstract

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.

References

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