The vlaue of the integral int (0)^(2)(lo...

The vlaue of the integral `int _(0)^(2)(log (x ^(2) +2))/( (x+2)^(2))dx` is:

A

`(sqrt2)/(3) tan ^(-1)sqrt2+ (5)/(12) log 2- 1/4 log 3`

B

`(sqrt2)/(3) tan ^(-1)sqrt2- (5)/(12) log 2- 1/4 log 3`

C

`(sqrt2)/(3) tan ^(-1)sqrt2+ (5)/(12) log 2+ 1/4 log 3`

D

`(sqrt2)/(3) tan ^(-1)sqrt2- (5)/(12) log 2+ 1/4 log 3`

Text Solution

Verified by Experts

The correct Answer is:

D

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