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The value of the integral int0^oo(xlogx)...

The value of the integral `int_0^oo(xlogx)/((1+x^2)^2)dxi s` 0 (b) log 7 (c) 5 log 13 (d) none of these

A

`0`

B

`log7`

C

`5 log 13`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`I=int_(0)^(oo) (x log xdx)/((1+x^(2))^(2))`
Let `x=1/t`
`:. I=int_(oo)^(0)((1/t)log(1/t)(-1/(t^(2)))dt)/((1+1/(t^(2)))^(2))`
`=-int_(0)^(oo) (t logt)/((1+t^(2))^(2))dt=-1`
or `I=0`
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