∫[1--->e] ln²x dx
=xln²x-∫[1--->e] 2xlnx*(1/x) dx
=xln²x-2∫[1--->e] lnx dx
=xln²x-2xlnx+2∫[1--->e] x*(1/x)dx
=xln²x-2xlnx+2∫[1--->e] 1dx
=xln²x-2xlnx+2x [1--->e]
=e-2e+2e-2
=e-2