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int(0)^(oo)(log(1+x^(2)))/(1+x^(2))dx...

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

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int_(0)^(oo)((ln(1+x^(2)))/(1+x^(2)))dx .

Evaluate int_(0)^(a)((log(1+ax))/(1+x^(2))dx)

int_(0)^(oo)(x logx)/((1+x^(2))^(2)) dx=

int_(0)^(oo)(x logx)/((1+x^(2))^(2)) dx=

" 8."int_(0)^(oo)(log x)/(1+x^(2))dx

Let A=int_(0)^(oo)(log x)/(1+x^(3))dx Then find the value of int_(0)^(oo)(x log x)/(1+x^(3))dx in terms of A

STATEMENT-1 : int_(0)^(oo)(dx)/(1+e^(x))=ln2-1 STATEMENT-2 : int_(0)^(oo)(sin(tan^(-1)))/(1+x^(2))dx=pi STATEMENT-3 : int_(0)^(pi^(2)//4)(sinsqrt(x))/(sqrt(x))dx=1

STATEMENT-1 : int_(0)^(oo)(dx)/(1+e^(x))=ln2-1 STATEMENT-2 : int_(0)^(oo)(sin(tan^(-1)))/(1+x^(2))dx=pi STATEMENT-3 : int_(0)^(pi^(2)//4)(sinsqrt(x))/(sqrt(x))dx=1