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The value of int(1)^(e^(2)) (dx)/(x(1+lo...

The value of `int_(1)^(e^(2)) (dx)/(x(1+logx)^(2))`is

A

`(2)/(3)`

B

`(1)/(3)`

C

`(3)/(2)`

D

`ln 2`

Text Solution

Verified by Experts

The correct Answer is:
A
Let ` l = int_(1)^(e^(2)) (dx)/(1+log x)^(2)`
Put ` 1+ log x = t`
` rArr 1/x dx = dt` ,
` :. L = int_(1)^(3) 1/(t^(2)) dt = [ -1/t]_(1)^(3) =2/3`
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