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The value of int(x^(2))/(1+x^(6))dx is e...

The value of `int(x^(2))/(1+x^(6))dx` is equal to

A

`x^(3)+C`

B

`(1)/(3)tan^(-1)(x^(3))+C`

C

`log(1+x^(3))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let `l=int(x^(2))/(1+x^(6))dx`
Put`" "x^(3)=t rArr x^(2)dx=(1)/(3)dt`
`therefore" "l=(1)/(3)int(1)/(1+t^(2))dt=(1)/(3)tan^(-1)t+C`
`=(1)/(3)tan^(-1)(x^(3))+C`
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