u=lnxu'= 1/xu'' = -1/x^2u'''= 2/x^3v = e^xv'=v''=v'''=e^x(uv)' =uv'+u'v(uv)'' = uv''+2u'v'+u''v(uv)''' = uv'''+3u'v''+3u''v'+u'''v=(lnx)e^x+ 3e^x/x- 3e^x/x^2 + 2e^x/x^3