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
SN - 1464-5211
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
IS - 6
ER -