∫(1+lnx)xlnx dx
=∫[xlnx+x(lnx )^2]dx
=∫xlnxdx+∫x(lnx )^2dx
=1/2∫lnxdx^2+1/2∫(lnx )^2dx ^2
=1/2x^2lnx-1/2∫xdx+1/2x^2(lnx)^2-∫xlnx dx
=1/2x^2(lnx)^2+C
∫(1+lnx)xlnx dx
=∫[xlnx+x(lnx )^2]dx
=∫xlnxdx+∫x(lnx )^2dx
=∫xlnx dx +1/2∫(lnx )^2dx ^2
=∫xlnx dx +1/2x^2(lnx)^2-∫xlnx dx
=1/2x^2(lnx)^2+C