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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 =...

这题利用公式求

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

先用积化和差公式变为简单三角函数,再用凑微分法计算。

∫[sinxsin(3x)]dx =∫½[cos(x-3x)-cos(x+3x)]dx =½∫[cos(-2x)-cos(4x)]dx =½∫[cos(2x)-cos(4x)]dx =½∫cos(2x)dx -½∫cos(4x)dx =¼∫cos(2x)d(2x)-⅛∫cos(4x)d(4x) =-¼sin(2x)+⅛sin(4x)+C 提示:先对

sinxsin2xsin3x=(sinxsin3x)sin2x=(cos2x-cos4x)sin2x=cos2xsin2x-cos4xsin2x =cos2xsin2x-(1/2)(sin2x-sin6x) ∫sinxsin2xsin3xdx=∫cos2xsin2xdx-(1/2)∫sin2xdx+(1/2)∫sin6xdx =(1/2)(sin2x)^2+(1/4)cos4x-(1/12)cos6x+C

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