`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
`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
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Correct Answer - 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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