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int[(x)^(1//3)-(1)/((x^())^(1//3))]dx is...

`int[(x)^(1//3)-(1)/((x^())^(1//3))]dx` is equal to `:`

A

`x^(4//3)-x^(2//3)+c`

B

`(4)/(3)x^(2//3)-(2)/(3)x^(2//3)+c`

C

`(3)/(4)x^(4//3)-(2)/(3)x^(1//3)+c`

D

`(3)/(4)(x)^(4//3)-(3)/(2)(x)^(2//3)+c`

Text Solution

Verified by Experts

The correct Answer is:
D
`intx^(1//3)dx-intx^(-1//3)dx=((x)^(1//3+1))/(((1)/(3)+1))-((x)^(-1//3+1))/((-(1)/(3)+1))+c`
`=(3)/(4)(x)^(4//3)-(3)/(2)(x)^(2//3)+c.`
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