Find LNX interval from 1 to E

Find LNX interval from 1 to E

The original formula = ∫ (1, e) lnxdx
=xlnx(1,e)-∫(1,e)xdlnx
=xlnx(1,e)-∫(1,e)x*1/xdx
=xlnx(1,e)-∫(1,e)dx
=(xlnx-x)(1,e)
=(e-e)-(0-1)
=1