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int(x^2)/(sqrt(x^6-a^6))dx...

`int(x^2)/(sqrt(x^6-a^6))dx`

A

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

B

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

C

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

D

None of these

Text Solution

Verified by Experts

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