∫[(1+lnx)/(xlnx)^3]dx
=∫[(x/x+lnx)/(xlnx)^3]dx
=∫{[x(lnx)'+x'lnx]/(xlnx)^3dx
=∫[(xlnx)']/(xlnx)^3dx
=∫1/(xlnx)^3d(xlnx)
=(-1/2)(xlnx)^(-2)+C