积分:(lnx)^3/x^2dx
=积分:(lnx)^3d(-1/x)
=-(lnx)^3/x-积分:-1/xd(lnx)^3
=-(lnx)^3/x-积分:-3(lnx)^2/x^2dx
=-(lnx)^3/x+3积分:(lnx)^2d(-1/x)
=-(lnx)^3/x-3(lnx)^2/x+3积分:1/xd(lnx)^2
=-(lnx)^3/x-3(lnx)^2/x+3积分:2lnx/x^2dx
=-(lnx)^3/x-3(lnx)^2/x+3积分:2lnxd(-1/x)
=-(lnx)^3/x-3(lnx)^2/x-6lnx/x+3积分:2/xd(lnx)
=-(lnx)^3/x-3(lnx)^2/x-6lnx/x-6/x+C
(C是常数)
思路:连续用分部积分法