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int(x-x^5)^(1/5) / x^6 dx...

`int(x-x^5)^(1/5) / x^6 dx`

A

`(5)/(24)((1)/(x^(4))-1)^(6//5)+C`

B

`(5)/(24)(1-(1)/(x^(4)))^(6//5)+C`

C

`-(5)/(24)(1-(1)/(x^(4)))^(6//5)+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Let `I=int((x-x^(5))^(1//5))/(x^(6))dx=int((1)/(x^(4))-1)^(1//5)(1)/(x^(5))dx`
`rArrI=-(1)/(4)int((1)/(x^(4))-1)^(1//5)((-4)/(x^(5)))dx=-((1)/(x^())-1)^(1//5)d((1)/(x^(4))-1)`
`rArr I=-(5)/(24)((1)/(x^(4))-1)^(6//5)+C`
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