TY - JOUR

T1 - Integrating rational functions of sine and cosine using the rules of Bioche

AU - Stewart, Seán M.

N1 - Generated from Scopus record by KAUST IRTS on 2022-09-15

PY - 2022/1/1

Y1 - 2022/1/1

N2 - For integrals consisting of rational functions of sine and cosine a set of little known rules known as the Bioche rules are considered. The rules, which consist of testing the differential form of the integral for invariance under one of three simple substitutions (Formula presented.), and (Formula presented.), allow one to decide which of the three trigonometric substitutions of: (Formula presented.), or (Formula presented.) would be most appropriate for finding the integral. In seeking to not only bring these simple rules to the attention of a wider audience, formal justification of the rules is provided and two examples illustrating the use of the rules given.

AB - For integrals consisting of rational functions of sine and cosine a set of little known rules known as the Bioche rules are considered. The rules, which consist of testing the differential form of the integral for invariance under one of three simple substitutions (Formula presented.), and (Formula presented.), allow one to decide which of the three trigonometric substitutions of: (Formula presented.), or (Formula presented.) would be most appropriate for finding the integral. In seeking to not only bring these simple rules to the attention of a wider audience, formal justification of the rules is provided and two examples illustrating the use of the rules given.

UR - https://www.tandfonline.com/doi/full/10.1080/0020739X.2021.1912841

UR - http://www.scopus.com/inward/record.url?scp=85104809712&partnerID=8YFLogxK

U2 - 10.1080/0020739X.2021.1912841

DO - 10.1080/0020739X.2021.1912841

M3 - Article

VL - 53

SP - 1688

EP - 1700

JO - International Journal of Mathematical Education in Science and Technology

JF - International Journal of Mathematical Education in Science and Technology

SN - 0020-739X

IS - 6

ER -