∫(0,1) xlnxdx
=1/2∫(0,1) lnxdx^2
=1/2x^2lnx(0,1)-1/2∫(0,1)x^2dlnx
=-1/2∫(0,1)x^2/xdx
=-1/4x^2(0,1)
=-1/4