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int(dx)/(xsqrt(x^(6)-1))=?...

int(dx)/(xsqrt(x^(6)-1))=?`

A

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

B

`(1)/(3)"cosec"^(-1)x^(3)+C`

C

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

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`I=int(x^(2))/(x^(3)sqrt(x^(6)-1))dx`.
`=(1)/(3)int(dt)/(tsqrt(t^(2)-2))`, where `x^(3)=t`
`=(1)/(3)sec^(-1)t+C=(1)/(3)sec^(-1)x^(3)+C`.
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