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Evaluate: int(dx)/(xsqrt(x^(6)-16))=...

Evaluate: `int(dx)/(xsqrt(x^(6)-16))=`

A

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

B

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

C

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

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`int(dx)/(xsqrt(x^(6)-16))=int(x^(2)dx)/(x^(3)sqrt(x^(6)-16))`
`=(1)/(3)int(dt)/(sqrt(t^(2)-16))" "("putting "x^(3)=t)`
`=(1)/(48)int(dt)/((1)/(4)sqrt((t^(2))/(16)-1))`
`=(1)/(12)sec.(t)/(4)+c`
`=(1)/(12)sec. (x^(3))/(4)+c`
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CENGAGE PUBLICATION-INDEFINITE INTEGRATION-Single Correct Answer Type
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