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int((x^2+1))/(x^4+7x^2+1)dx...

`int((x^2+1))/(x^4+7x^2+1)dx`

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`I=int frac{(x^{2}+1) d x}{x^{4}+7 x^{2}+1}`
`I=int frac{x^{2}(1+frac{1}{x^{2}}) d x}{x^{2}(x^{2}+7+frac{1}{x^{2}})}`
`I=int frac{(1+frac{1}{x^{2}}) d x}{(x^{2}+7+frac{1}{x^{2}})}`
`I=int frac{(1+frac{1}{x^{2}}) d x}{(x^{2}+frac{1}{x^{2}}+7)}` ...
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int(x^(2)+1)/(x^(4)-x^(2)+1)dx= . . .

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The value of int((x^(2)+1))/((x^(4)-x^(2)+1)cot^(-1)(x-(1)/(x)))dx will be

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