用分部积分法求 不定积分[(lnx)³/x²]dx

∫[(lnx)^3/x^2]dx
=-∫(lnx)^3d(1/x)
=-(lnx)^3/x +3∫[(lnx)^2/x^2]dx
=-(lnx)^3/x -3∫[(lnx)^2d(1/x)
=-(lnx)^3/x -3(lnx)^2/x - 6∫lnxd(1/x)
=-(lnx)^3/x -3(lnx)^2/x - 6lnx/x + 6∫(1/x^2) dx
=-(lnx)^3/x -3(lnx)^2/x - 6lnx/x - 6/x + C