∫x^(2)Inxdx=x^(2)Inx-∫1/x*x^(2)dx=x^2Inx-∫xdx=x^2Inx-(1/2)x^2+c这题貌似做错了.

Question

∫x^(2)Inxdx
=x^(2)Inx-∫1/x*x^(2)dx
=x^2Inx-∫xdx
=x^2Inx-(1/2)x^2+c
这题貌似做错了.

Answer 1

∫x^(2)Inxdx
=∫Inxd(x^3/3)
=(1/3)*(x^3*lnx-∫x^3d(lnx))
=(1/3)*(x^3*lnx-∫x^2dx)
=(1/3)*(x^3*lnx-x^3/3+C)