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Integrate the curve (x)/(1+x^(4))...

Integrate the curve `(x)/(1+x^(4))`

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(2)"tan"^(-1)(x^(2))+c`
Let `I=int (xdx)/(1+x^(4))=(1)/(2)int(2x)/(1+(x^(2))^(2))dx`
Put `x^(2)=u rArr 2 xdx = du`
`therefore" "I=(1)/(2) int(du)/(1+u^(2))=-(1)/(2)tan^(-1)(u)+x=(1)/(2)tan^(-1)(x^(2))+c`
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