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Evaluate : int(x^(2)-4)/(x^(4)+9x^(2)+16...

Evaluate : `int(x^(2)-4)/(x^(4)+9x^(2)+16)dx`

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Verified by Experts

The correct Answer is:
5
`I=int(x^(2)-4)/(x^(4)+9x^(2)+16)dx`
Divide both numberator and denominator by `x^(2)`
`I=int((1-(4)/(x^(2))))/(x^(2)+9+(16)/(x^(2)))dx=int((1-(4)/(x^(2))))/((x+(4)/(x))^(2)+1)dx`
`"Put "u=x+(4)/(x),du=(1-(4)/(x^(2)))dx`
`I=int(du)/(u^(2)+1)=tan^(-1)(u)+B`
`=tan^(-1)(x+(4)/(x))+C`
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