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int0^oo(pi/(1+pi^2x^2)-1/(1+x^2))logxdxi...

`int_0^oo(pi/(1+pi^2x^2)-1/(1+x^2))logxdxi se q u a lto` `-pi/21npi` (b) 0 `pi/21n2` (d) none of these

A

`-(pi)/2 In pi`

B

`0`

C

`(pi)/2 In 2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`int_(0)^(oo) ((pi)/(1+pi^(2)x^(2))-1/(1+x^(2)))log x dx`
`=int_(0)^(oo) ("log"(y/(pi))dy)/(1+y^(2))-int_(0)^(oo) (logx)/(1+x^(2))dx`
`=-int_(0)^(oo) (log pi)/(1+y^(2))dy=-(pi)/2 In pi`
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