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int(root3(x))(root5(1+root3(x^(4))))dx ...

`int(root3(x))(root5(1+root3(x^(4))))dx` is equal to

A

`(1+x^((3)/(4)))^((6)/(5))+C`

B

`(1+x^((4)/(3)))^((6)/(5))+C`

C

`(5)/(8)(1+x^((4)/(3)))^((6)/(5))+C`

D

`(1)/(6)(1+x^((4)/(3)))^(6)+C`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `l=int(root3(x))(root5(1+root3(x^(4))))dx`
Put `root3(x)^(4)=t rArr (4)/(3).root3x dx=dt`
`therefore" "l=(3)/(4)int(root5(1+t))dt=(3)/(4)[((1+t)^((1)/(5)+1))/((1)/(5)+1)]+C`
`=(5)/(8)[(1+root3(x)^(4))^(6//5)]+C`
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