積分:(lnx)^3/x^2dx
=積分:(lnx)^3d(-1/x)
=-(lnx)^3/x-積分:-1/xd(lnx)^3
=-(lnx)^3/x-積分:-3(lnx)^2/x^2dx
=-(lnx)^3/x+3積分:(lnx)^2d(-1/x)
=-(lnx)^3/x-3(lnx)^2/x+3積分:1/xd(lnx)^2
=-(lnx)^3/x-3(lnx)^2/x+3積分:2lnx/x^2dx
=-(lnx)^3/x-3(lnx)^2/x+3積分:2lnxd(-1/x)
=-(lnx)^3/x-3(lnx)^2/x-6lnx/x+3積分:2/xd(lnx)
=-(lnx)^3/x-3(lnx)^2/x-6lnx/x-6/x+C
(C是常數(shù))
思路:連續(xù)用分部積分法