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`(2)/(3)``(1)/(3)``(3)/(2)``ln 2`

Answer :

ASolution :

Let ` l = int_(1)^(e^(2)) (dx)/(1+log x)^(2)` <br> Put ` 1+ log x = t` <br> ` rArr 1/x dx = dt` ,<br> ` :. L = int_(1)^(3) 1/(t^(2)) dt = [ -1/t]_(1)^(3) =2/3`