求cosxcosx/2的不定积分
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先用积化和差公式,再求积分即可
cosxcosy=(1/2)[cos(x+y)+cos(x-y)]
∫[cosx*cos(x/2)]dx=1/2*∫[cos(x+x/2)+cos(x-x/2)]dx=1/2*∫[cos(3x/2)+cos(x/2)]dx=1/2*∫cos(3x/2)dx+1/2*∫cos(x/2)dxd(3x/2)=(3/2)dx,d(x/2)=(1/2)dx=1/2*2/3*∫cos(3x/2)d(3x/2)+1/2*2*∫cos(x/2)d(x/2)=1/3*sin(3x/2)+sin(x/2)+C=(1/3)sin(3x/2)+sin(x/2)+C
cosxcosy=(1/2)[cos(x+y)+cos(x-y)]
∫[cosx*cos(x/2)]dx=1/2*∫[cos(x+x/2)+cos(x-x/2)]dx=1/2*∫[cos(3x/2)+cos(x/2)]dx=1/2*∫cos(3x/2)dx+1/2*∫cos(x/2)dxd(3x/2)=(3/2)dx,d(x/2)=(1/2)dx=1/2*2/3*∫cos(3x/2)d(3x/2)+1/2*2*∫cos(x/2)d(x/2)=1/3*sin(3x/2)+sin(x/2)+C=(1/3)sin(3x/2)+sin(x/2)+C
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