∫(lnx)^3/x^2dx
=-∫(lnx)^3d(1/x)
=-(lnx)^3/x+∫(1/x)d(lnx)^3
=-(lnx)^3/x+∫(1/x)*3(lnx)^2*1/xdx
=-(lnx)^3/x+∫(1/x^2)*3(lnx)^2dx
=-(lnx)^3/x-∫3(lnx)^2d(1/x)
=-(lnx)^3/x-3(lnx)^2/x+∫(1/x^2)*6(lnx)dx
=-(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