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int(dx)/(xsqrt(x^(6)+1)) equals...

`int(dx)/(xsqrt(x^(6)+1))` equals

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
`I=int(dx)/(xsqrt(x^(6)+1))."Put "x^(6)+1=v^(2)`
`rArr" "6x^(5)dx=2vdv`
`therefore" "I=(1)/(2)int(v)/((v^(2)-1))dv`
`=(1)/(3)int(dv)/(v^(2)-1)=(1)/(6)log((sqrt(x^(6)+1)-1)/(sqrt(x^(6)+1)+1))+C`
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