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[" Let "],[u=int(0)^(oo)(dx)/(x^(4)+7x^(...

[" Let "],[u=int_(0)^(oo)(dx)/(x^(4)+7x^(2)+1)" and "v=int_(0)^(oo)(x^(2)dx)/(x^(4)+7x^(2))],[" then: "]

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Let u=int_(0)^(oo)(dx)/(x^(4)+7x^(2)+1) and v=int_(0)^(x)(x^(2)dx)/(x^(4)+7x^(2)+1) then

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

int_(0)^(oo)(x^(2)+1)/(x^(4)+7x^(2)+1)dx=

int_(0)^(oo)(x^(2)+1)/(x^(4)+7x^(2)+1)dx=

int_(0)^(oo)(dx)/((1+x^(2))^(4))=

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

int_(0)^(oo) (dx)/((1+x^(2))^(4))=

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

int_(0)^(oo)e^(-x/2)dx

int_(0)^(oo)e^(-x/2)dx