∫sin(5x)sin(7x)dx=

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∫sin(5x)sin(7x)dx=

∫sin(5x)sin(7x)dx=
∫sin(5x)sin(7x)dx=

∫sin(5x)sin(7x)dx=
∫sin(5x)sin(7x)dx
=(1/2)∫[cos(5x-7x)+cos(5x+7x)]dx
=(1/2)∫[cos(2x)+cos(12x)]dx
=(1/2)[(1/2)sin2x+(1/12)sin12x]
=(1/4)sin2x+(1/24)sin12x

如下