Explanation
Consider the given integral.
I=∫e1dxln(xx⋅ex)
I=∫e1dxlnxx+lnex
I=∫e1dxxlnx+xlne
I=∫e1dxxlnx+x
I=∫e1dxx(lnx+1)
Let t=lnx+1
dtdx=1x+0
dt=dxx
Therefore,
I=∫21dtt
I=[ln(t)]21
I=ln(2)−ln(1)
I=ln2
Hence, this is the answer.
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