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int(x^(2))/(sqrt(x^(6)-1))dx=?...

`int(x^(2))/(sqrt(x^(6)-1))dx=?`

A

`(1)/(2) log |x^(3)+sqrt(x^(6)-1)|+C`

B

`(1)/(3) log |x^(3)+sqrt(x^(6)-1)|+C`

C

`(1)/(3) log |x^(3)-sqrt(x^(6)-1)|+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Put `x^(3) = t and 3x^(2)dx=dt.` then
`I=(1)/(3)int (dt)/(sqrt(t^(2)-1))=(1)/(3)log |t+sqrt(t^(2)-1)|+C=(1)/(3)log |x^(3)+sqrt(x^(6)-1)|+C.`
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