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The integral int(dx)/(x^(2)(x^(4)+1)^(3/...

The integral `int(dx)/(x^(2)(x^(4)+1)^(3//4))` equal

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
Let `l=int(dx)/(x^(2)(x^(4)+1)^((3)/(4)))=int(dx)/(x^(5)(1+(1)/(x^(4)))^((3)/(4)))`
Put `1+(1)/(x^(4))=t^(4)" "rArr" "-(4)/(x^(5))dx=4t^(3)dt`
`rArr" "(dx)/(x^(5))=-t^(3)dt`
`therefore" "l=int(-t^(3)dt)/(t^(3))=-intdt=-t+C=-(1+(1)/(x^(4)))^((1)/(4))+c`
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