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4 int (sqrt(a^(6)+x^(8)))/(x) dx is equa...

`4 int (sqrt(a^(6)+x^(8)))/(x) dx` is equal to

A

`sqrt(a^(6)+x^(8))+(a^(3))/(2)In|(sqrt(a^(6)+x^(8))+a^(3))/(sqrt(a^(6)+x^(8))-a^(3))|+c`

B

`a^(6)In|(sqrt(a^(6)+x^(8))-a^(3))/(sqrt(a^(6)+x^(8))+a^(3))|+c`

C

`sqrt(a^(6)+x^(8))+(a^(3))/(2)In|(sqrt(a^(6)+x^(8))-a^(3))/(sqrt(a^(6)+x^(8))+a^(3))|+c`

D

`a^(6)In|(sqrt(a^(6)+x^(8))+a^(3))/(sqrt(a^(6)+x^(8))-a^(3))|+c`

Text Solution

Verified by Experts

The correct Answer is:
C
Putting `a^(6)+x^(8)=t^(2),` we get
`I=int (t^(2))/(t^(2)-a^(6))dt=t+(a^(3))/(2)In|(t-a^(3))/(t+a^(3))|+C`
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