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

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

Text Solution

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`int(x^(2))/((x^(2)+1)(x^(2)+4))dx=(1)/(3)int[(4)/(x^(2)+4)-(1)/(x^(2)+1)]dx`
`= -(1)/(3)int(1)/(x^(2)+1)dx+(4)/(3)int(1)/(x^(2)+4)dx`
`= -(1)/(3)tan^(-1)x+(4)/(3)xx(1)/(2)tan^(-1)((x)/(2))+C`
`= -(1)/(3)tan^(-1)x+(2)/(3)tan^(-1)((x)/(2))+C`
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