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Question

Find the integrals of the functions sin3x+cos3xsin2xcos2x

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Solution

sin3x+cos3xsin2xcos2x=sin3xsin2cos2x+cos3xsin2xcos2x
=sinxcos2x+cosxsin2x
=tanxsecx+cotxcosecx
sin3x+cos3xsin2xcos2xdx=(tanxsecx+cotxcosecx)dx
=secxcosecx+C

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