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

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

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`I =int(x^(2)-1)/((x^(2)+1)sqrt(x^(4)+1))dx`
`=int(x^(2)(1-1//x^(2)))/(x^(2)(x+1//x)sqrt(x^(2)+1//x^(2)))dx`
`=int((1-1//x^(2))dx)/((x+1//x)sqrt((x+1//x)^(2)-2))`
Putting `x+1//x=t,` we have `I=int(dt)/(t sqrt(t^(2)-2)).`
Again putting `t^(2)-2=y^(2), 2tdt=2ydy,`
`I=int(ydy)/((y^(2)+2)y)=(1)/(sqrt(2))"tan"^(-1)(y)/(sqrt(2))=(1)/(2)"tan"^(-1)sqrt(x^(2)+1//x^(2))/(sqrt(2))+c.`
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