xcos3x的积分
求xCOS3x的不定积分。积分变量为x -
∫ xcos3x dx = (1/3)∫ xcos3x d(3x)= (1/3)∫ x dsin3x = (1/3)xsin3x - (1/3)∫ sin3x dx = (1/3)xsin3x - (1/3)(1/3)∫ sin3x d(3x)= (1/3)xsin3x - (1/9)(-cos3x) + C = (1/3)xsin3x + (1/9)cos3x + C 等会说。
∫ xcos3x dx =(1/3)∫ xdsin3x =(1/3)x.sin3x -(1/3)∫sin3x dx =(1/3)x.sin3x +(1/9)cos3x + C
∫ xcos3x dx = (1/3)∫ xcos3x d(3x)= (1/3)∫ x dsin3x = (1/3)xsin3x - (1/3)∫ sin3x dx = (1/3)xsin3x - (1/3)(1/3)∫ sin3x d(3x)= (1/3)xsin3x - (1/9)(-cos3x) + C = (1/3)xsin3x + (1/9)cos3x + C 等会说。
∫ xcos3x dx =(1/3)∫ xdsin3x =(1/3)x.sin3x -(1/3)∫sin3x dx =(1/3)x.sin3x +(1/9)cos3x + C
=1/3xsin3x-1/3∫sin3xdx =1/3xsin3x+1/9cos3x (0,π/2)=(-π/6+0)-(0+1/9)=-π/6-1/9
=(1/3)∫xdsin3x =(1/3)xsin3x-(1/3)∫sin3xdx =(1/3)xsin3x+(1/9)cos3x ∫[0,π]xcos3x =-π/3-1/9-1/9=-π/3-2/9
数学的微积分 求这题的不定积分 fxcos3xdx 是微分符号 -
解∫xcos3xdx=(1/3)*∫xdsin3x=(1/3)*x*sin3x-(1/3)*∫sin3xdx =(1/3)*x*sin3x-(1/3)*(1/3)*(-cos3x)+C =(1/3)*x*sin3x+(1/9)*(cos3x)+C
∫xcos3xdx =(1/3)∫xdsin3x =(1/3)xsin3x-(1/3)∫sin3xdx =(1/3)xsin3x+(1/9)cos3x ∫[0,π]xcos3x =-π/3-1/9-1/9=-π/3-2/9
怎么求xcos3x的原函数 -
(sin3x/3)' = cos3x 原式=xsin3x/3 - 积分（sin3x/3）xsin3x/3+cos3x/9+C
根据三倍角公式(cosx)^3=[cos(3x)+3cosx]/4 所以原式=∫x[cos(3x)+3cosx]/4dx =∫xcos(3x)/4dx+∫3cosx/4dx =1/12*∫xd[sin(3x)]+3/4*sinx =1/12*[xsin(3x)-∫sin(3x)dx]+3/4*sinx =1/12*xsin(3x)+1/36*cos(3x)+3/4*sinx+C 后面会介绍。
∫xcos3xdx怎么做? -
用分部积分简单地说，根据积的微分法则，∫(u'v+uv')dx=uv 令u=x,v=sin3x/3, 则∫xcos3xdx=(xsin3x)/3-(-cos3x/9)
∫cos3xdx =∫(cos3x)/3 d3x =(sin3x)/3+C