Question

用分部积分法求∫lnxdx的不定积分

Answer 1

∫lnxdx=xlnx-∫xd(lnx)
=xlnx-∫1dx
=xlinx-x+C
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Answer 2

∫x^2*lnxdx=1/3*∫lnxdx^3=1/3*lnx*x^3-1/3*∫x^3*1/xdx=1/3*lnx*x^3-1/3*∫x^2dx=1/3*lnx*x^3-1/9*x^3+c