|The definite integral of LNX | from 1 / E to e | Math enthusiast | Mathematical art

|The definite integral of LNX | from 1 / E to e

∫（1/e,e）|lnx|dx=∫（1/e,1）-lnxdx+∫（1,e）lnxdx
∫lnxdx=∫lnxd(x)=xlnx-∫dx=xlnx-x+C
The original formula = x-xlnx (1 / E, 1) + xlnx-x (1, e) = (1-0-1 / E + 1 / eln1 / E) + (elne-e-0 + 1) = (1-2 / E) + 1 = 2-2 / E

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