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Evaluate int(1)/(x^(2)(x^(4)+1)^(3//4))...

Evaluate `int(1)/(x^(2)(x^(4)+1)^(3//4))dx`

A

`((x^(4)+1)/(x^(4)))^(1//4)+c`

B

`(x^(4)+1)^(1//4)+c`

C

`-(x^(4)+1)^(1//4)+c`

D

`-((x^(4)+1)/(x^(4)))^(1//4)+c`

Text Solution

Verified by Experts

The correct Answer is:
D
` I=int(dx)/(x^(2)(x^(4)+1)^(3//4))`
` int(dx)/(x^(5)(1+(1)/(x^(4)))^(3//4))`
`"Let "1+(1)/(x^(4))=t^(4)`
`implies (-4)/(x^(5))dx=4t^(3)dt " or " (dx)/(x^(5))=-t^(3)dt`
` :. I=int(-t^(3)dt)/(t^(3))=-t+c=-(1+(1)/(x^(4)))^(1//4)+c`
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