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∫x/CosxCosxDx

解: ∫x²cosxdx =∫x²d(sinx) =x²sinx-∫sinxd(x²) =x²sinx-2∫xsinxdx =x²sinx+2∫xd(cosx) =x²sinx+2xcosx-2∫cosxdx =x²sinx+2xcosx-2sinx +C

分部积分:原式=∫ x dsinx= =xsinx-∫ sinxdx =xsinx+cosx+C

∫xcos²xdx=∫x(1+cos2x)/2dx=1/2(∫xdx+∫xcos2xdx) =1/2(1/2x²+∫xcos2xdx) =1/2(1/2x²+1/2∫xdsin2x) =1/2(1/2x²+1/2(xsin2x-∫sin2xdx)) =1/2(1/2x²+1/2xsin2x+1/4cos2x)+C

这里直接进行凑微分即可, ∫x dx=∫0.5 d(x²) 所以得到 原积分=∫0.5cosx² d(x²) 而∫cost dt= sint 故解得原积分=0.5sinx² +C,C为常数

∫xcosxdx=∫xdsinx=xsinx-∫sinxdx=xsinx+cosx+C 你说的定积分就是把积分上下限带进去就可以了 希望对你有用

原式=∫xdsinx =xsinx-∫sinxdx =xsinx+cosx+C

解:xcosx/sin^3x =xcotxcsc^2x 原是=积分xcotxcsc^2xdx =-积分xcotxdcotx =-1/2积分xdcot^2x =-1/2(xcot^2x-积分cot^2xdx) =-1/2xcot^2x+1/2积分(csc^2x-1)dx =-1/2xcot^2x+1/2(积分csc^2xdx-积分1dx) =-1/2xcot^2x+1/2(-cotx-x)+C =-1/2xcot...

如图所示

∫cosxcos(x/2)dx =∫[2cos²(x/2)-1]cos(x/2)dx =∫2cos³(x/2)dx-∫cos(x/2)dx =4∫cos³(x/2)d(x/2)-2∫cos(x/2)d(x/2) =4∫cos²(x/2)dsin(x/2)-2sin(x/2) =4∫[1-sin²(x/2)]dsin(x/2)-2sin(x/2) =4sin(x/2)-4/3*sin³(x/2...

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