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Evaluate: intx/(x^4+2x^2+3)dx...

Evaluate: `intx/(x^4+2x^2+3)dx`

Text Solution

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` I=int(x)/(x^(4)+2x^(2)+3)dx`
Let `x^(2)=t.`
` :. 2x dx=dt`
` :. I=(1)/(2)int(dt)/(t^(2)+2t+3)`
`=(1)/(2)int(dt)/((t+1)^(2)+2)`
`=(1)/(2)(1)/(sqrt(2))"tan"^(-1)(t+1)/(sqrt(2))+c`
`=(1)/(2sqrt(2))"tan"^(-1)(x^(2)+1)/(sqrt(2))+c`
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