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

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

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

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

int_(0)^(oo)(1)/(x+a)dx

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

int_(0)^(oo)(1)/(1+x)^(4)dx=

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

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

The value of int_(0)^(oo)(x)/((1+x)(x^(2)+1))dx is

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

Prove that: int_(0)^(oo) (x)/((1+x)(1+x^(2)))dx =(pi)/(4)