Products of Powers of Sines and Cosines - Michigan State University

sin4x cos6x = sin2x 2 cos6x = 1−cos2x 2 cos6x = 1−2cos2x+cos4x cos6x =cos6x−2cos8x+cos10x Thus ˆ sin4x cos6xdx = ˆ cos6xdx−2 ˆ cos8xdx+ ˆ cos10xdx and we can proceed as before (to handle the odd powers that appear, see Example 3 below). For example, to integrate the last term above, we expand 32cos10x =(1+cos2x)5 =1+5cos2x+10cos22x ... ................
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