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int((x^(4)-x)^(1//4))/(x^(5))dx is equal...

`int((x^(4)-x)^(1//4))/(x^(5))dx` is equal to

A

`(4)/(15)(1-(1)/(x^(3)))^(5//4)+C`

B

`(4)/(5)(1-(1)/(x^(3)))^(5//4)+C`

C

`(4)/(15)(1+(1)/(x^(3)))^(5//4)+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Let `l=int((x^(4)-x)^(1//4))/(x^(5))dx=int(x(1-(1)/(x^(3)))^(1//4))/(x^(5))dx`
`=int((1-(1)/(x^(3)))^(1//4))/(x^(4))dx`
Put `1-(1)/(x^(3))=t^(4) rArr (3)/(x^(4))dx= 4t^(3)dt`
`therefore" "l=(4)/(3)int t.t^(3)dt=(4)/(3).((t^(5))/(5))+C=(4)/(!5)(1-(1)/(x^(3)))^(5//4)+C`
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