We discuss integrals with a linear function of sin or cos in the denominator of the integrand. We address the question of existence then exhibit a substitution which allows for use of the residue theorem to evaluate the integral.

Integrals of 1 over (a + b sin theta) and 1 over a + b cos theta) (MathsCasts)

These MathsCasts were produced by the mathematics support centres at Swinburne University, the University of Limerick and Loughborough University. They were part of a collaborative research project to develop high quality resources and investigate the effectiveness of MathsCasts to support mathematics learning. The full set of resources are available at http://commons.swin.edu.au/s/mathscasts MathsCasts are licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License

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Integrals of 1 over (a + b sin theta) and 1 over a + b cos theta) (MathsCasts)

Integrals of 1 over (a + b sin theta) and 1 over a + b cos theta) (MathsCasts)