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int 1/(xsqrt(x^4-1))dx...

`int 1/(xsqrt(x^4-1))dx`

A

`sec^(-1)x^(2)+C`

B

`(1)/(2)sec^(-1)x^(2)+C`

C

`"cosec"^(-1)x^(2)+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`:." "I=int(x)/(x^(2)sqrt(x^(4)-1))dx=(1)/(2)int(dt)/(t sqrt(t^(2)-1))`, where `x^(2)=t`.
`=(1)/(2)sec^(-1)t+C=(1)/(2)sec^(-1)x^(2)+C`.
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