∫sin(6x)sin(2x)dx=?
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∫sin(6x)sin(2x)dx=?
∫sin(6x)sin(2x)dx=?
∫sin(6x)sin(2x)dx=?
利用积化和差公式
cos(6x+2x)=cos8x=cos6xcos2x-sin6xsin2x
cos(6x-2x)=cos4x=cos6xcos2x+sin6xsin2x
cos4x-cos8x=2sin6xsin2x
∫sin6xsin2xdx=∫1/2(cos4x-cos8x)dx
=1/2∫cos4xdx-1/2∫cos8xdx
=1/8∫cos4xd4x-1/16∫cos8xd8x
=1/8sin4x-1/16sin8x+C
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