Question

∫x²lnxdx怎么求？要解答步骤！

Answer 1

原式=1/3∫lnxdx³
=1/3*x³lnx-1/3∫x³dlnx
=1/3*x³lnx-1/3∫x³*1/x dx
=1/3*x³lnx-1/3∫x²dx
=1/3*x³lnx-x³/9+C

Answer 2

∫x²lnxdx
=∫lnxd(x^3/3)
=x^3/3*lnx-∫(x^3/3)dlnx
=x^3/3*lnx-∫(x^2/3)dx
=x^3/3*lnx-x^3/9+c

Answer 3

分部积分
∫x²lnxdx
=1/3*∫lnxd(x^3)+c
=1/3*(x^3*lnx-∫x^3d(lnx)+c
=1/3(x^3*lnx-∫x²dx)+c
=1/3(x^3*lnx-1/3*x^3)+c
=1/3x^3(lnx-1/3) +c

Answer 4

分部积分吧
∫x²lnxdx=1/3∫Inxdx^3=1/3(Inx*x^3-∫x^3dInx)=1/3(Inx*x^3-∫x^2dx)=1/3Inx&x^3-1/9x^3+C

Answer 5

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