∫x²cosx/3dx怎么解?

    ∫x²cosx/3dx怎么解?

  答: 分部积分
先算cosxdx=dsinx
=1/3∫x^2dsinx
然后∫udv=uv-∫vdu
=1/3x^2sinx-1/3∫sinxdx^2
=1/3x^2sinx-2/3∫xsinxdx
=1/3x^2sinx+2/3∫xdcosx
=1/3x^2sinx+2/3xcosx-2/3∫cosxdx
=1/3x^2sinx+2/3xcosx-2/3sinx