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Trigonometric integration without trigonometric functions

Teaching Mathematics and its Applications, 2016
Teaching techniques of integration can be tedious and often uninspired. We present an obvious but underutilized approach for finding antiderivatives of various trigonometric functions using the complex exponential representation of the sine and cosine. The purpose goes beyond providing students an alternative approach to trigonometric integrals.
James Quinlan, Joseph Kolibal
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On Trigonometric Integrals

The Annals of Mathematics, 1947
whose coefficients are expressed by the very well known formulas. The tests we have at our disposal for the convergence or summability of Fourier series are perfectly satisfactory for applications of Fourier series. In a number of problems we come across series which are of the form (1.1.1) without necessarily being Fourier series.
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