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

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

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(sqrt3)tan^(-1)(x-1//x)/(sqrt3)-(2)/(sqrt3)tan^(-1)((2x^(2)+1)/(sqrt3))+C`
`int((x-1)^(2))/(x^(4)+x^(2)+1)dx`
`=int(x^(2)+1)/(x^(4)+x^(2)+1)dx-int(2x)/(x^(4)+x^(2)+1)dx`
`=int(1+(1)/(x^(2)))/((x-(1)/(x))^(2)+3)dx-int(2x)/((x^(2)+(1)/(2))^(2)+(3)/(4))dx`
`=(1)/(sqrt3)tan^(-1).(x-1//x)/(sqrt3)-(2)/(sqrt3)tan^(-1)((2x^(2)+1)/(sqrt3))+C`
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