Evaluation of ʃcot x sin 2mx In(sin x/sina)dx, Etc.

Authors

Don Kirkham, Iowa State UniversityFollow

Document Type

Research

Abstract

For m = 1,2,... the following indefinite integrals are evaluated

⌠cot x sin 2mx dx, ⌠tan x sin 2mx dx,

⌠cot 2x sin 2mx dx, ⌠2 csc 2x sin 2mx dx,

⌠cot x sin 2mx ln(sin x/sin a)dx, ⌠tan x sin 2mx ln(sin x/sin a)dx,

2⌠cot 2x sin 2mx ln (sin x/ sin a) dx, 2 ⌠csc 2x sin 2mx ln (sin x/ sin a) dx.

Also, formulas are given for the last four expressions where f(x) replaces ln(sin x/sin a). Further, procedures for evaluating the above expressions are outlined when cos 2mx replaces sin 2mx. The need of the integrals arose in connection with Fourier series where singularities in the function to be developed had been removed.

Publication Date

1961

Journal Title

Proceedings of the Iowa Academy of Science

Volume

68

Issue

1

First Page

416

Last Page

426

Copyright

©1961 Iowa Academy of Science, Inc.

Language

en

File Format

application/pdf

Recommended Citation

Kirkham, Don (1961) "Evaluation of ʃcot x sin 2mx In(sin x/sina)dx, Etc.," Proceedings of the Iowa Academy of Science, 68(1), 416-426.
Available at: https://scholarworks.uni.edu/pias/vol68/iss1/58