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" 16.सिद्ध कीजिए कि "int(0)^(oo)log(e)(x...

" 16.सिद्ध कीजिए कि "int_(0)^(oo)log_(e)(x+(1)/(x))(dx)/(1+x^(2))=pi log_(e)2

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Prove that : int_(0)^(oo) log (x+(1)/(x)). (dx)/(1+x^(2)) = pi log_(e) 2

int_(1)^(2) (log_(e) x)/(x^(2)) dx

int_(1)^(x)log_(e)[x]dx

int_(0)^(1)(log_(e)(1+x))/(1+x^(2))dx

int_(0)^(log 2)(e^(x))/(1+e^(x))dx=

int_(0)^(log 2)(e^(x))/(1+e^(x))dx=

int_(a=)^(oo)ln(x+(1)/(x))(dx)/(1+x^(2))dx=(pi)/(2)ln a then

" (2) "int_(1)^(2)(log e^(x))/(x^(2))dx

" "int(log_(e)x)/((1+x)^(2))dx