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sin3xsin2xDx等于多少

由cos5x=cos(3x+2x) =cos3xcos2x-sin3xsin2x ① cosx=cos(3x-2x) =cos3xcos2x+sin3xsin2x ② ②-①得 cosx-cos5x=2sin3xsin2x 即sin3xsin2x=1/2(cosx-cos5x) 则sin3xsin2xdx=[1/2(cosx-cos5x)]dx =1/2cosxdx-1/2cos5xdx =1/2sinx-1/2*1/5sin5x =...

积化和差∫sinxsin2xsin3xdx=1/2∫(cosx-cos3x)sin3xdx=1/2∫cosxsin3xdx-1/2∫cos3xsin3xdx=1/4∫(sin2x+sin4x)dx-1/4∫sin6xdx=-1/8cos2x-1/16cos4x+1/24cos6x+C数学软件验算:

先用积化和差公式变为简单三角函数,再用凑微分法计算。

先做积化和差: 2sin3x*cos2x=sin5x+sinx 下面就简单了,直接化为正弦函数的积分

这题利用公式求

😁

2)3)4)答案同楼上, 1)∫xsin2xdx=(-1/2)∫xdcos2x=(-1/2)xcos2x+(1/2)∫cos2xdx=(-1/2)xcos2x+(1/4)sin2x+C 2)∫xlnxdx=(1/2)∫lnxdx^2=(1/2)x^2lnx-(1/2)∫xdx=(1/2)x^2lnx-(1/4)x^2+C 3)∫arccosxdx=xarccosx-∫-xdx/√(1-x^2) =xarctanx-(1/2)d...

∫ (x^3+2x-1) dx =(1/4)x^4+x^2 -x + C

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