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

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

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`I=int(x^(2)+1)/(x^(4)+1)dx = int(1+(1)/(x^(2)))/(x^(2)+(1)/(x^(2)))dx=int(1+(1)/(x^(2)))/((x-(1)/(x))^(2)+2)dx`
Let `x-(1)/(x)=t " or " d(x-(1)/(x))=dt " or " (1+(1)/(x^(2)))dx=dt`
`:. I=int(dt)/(t^(2)+(sqrt(2))^(2))=(1)/(sqrt(2))tan^(-1)((t)/(sqrt(2)))+C`
`=(1)/(sqrt(2))tan^(-1)((x-1//x)/(sqrt(2)))+C`
`=(1)/(sqrt(2))tan^(-1)((x^(2)-1)/(sqrt(2)x))+C`
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