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Question

sin6x+cos6xsin2xcos2xdx=


Solution

Let I=sin6x+cos6xsin2xcos2xdx=(sin2x)3+(cos2x)3sin2x.cos2xdx=(sin2x+cos2x)(sin4xsin2xcos2x+cos4x)sin2x.cos2xdx=sin4xsin2xcos2xdx+cos4xsin2x.cos2xdxsin2xcos2xsin2x.cos2xdx=tan2xdx+cot2xdx1dx=(sec2x1)dx+(cosec2x1)dx1dx=sec2xdx+cosec2xdx3dxI=tanxcotx3x+C

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