I=int(0)^(oo)(x)/((x^(2)+a^(2))^(2))dx...

`I=int_(0)^(oo)(x)/((x^(2)+a^(2))^(2))dx`

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

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int_(0)^(oo)(x^(2))/((x^(2)+a^(2))(x^(2)+b^(2)))dx=(pi)/(2(a+b))

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

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

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

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

Evaluate: int_(0)^(oo)(1)/((x^(2)+a^(2))(x^(2)+b^(2)))dx

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