We use the complex exponential to integrate e^(ax) times cos(bx) or sin(bx) as real and imaginary parts of the same integral. Integration by parts is thereby avoided.

Using complex exponentials to integrate exponential times cos or sin function (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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Using complex exponentials to integrate exponential times cos or sin function (MathsCasts)

Using complex exponentials to integrate exponential times cos or sin function (MathsCasts)