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

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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.
Original languageEnglish (US)
Pages (from-to)1688-1700
Number of pages13
JournalInternational Journal of Mathematical Education in Science and Technology
Issue number6
StatePublished - Jan 1 2022
Externally publishedYes

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


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