Products of Powers of Sines and Cosines

1 8 ˆ (3−4cos2x+cos4x)dx = 1 8 3x−2sin2x+ sin4x 4 +C Example 2. Even Products Evaluate ˆ sin4x cos6xdx This is not too difficult since 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 ... ................
................