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

`4int(sqrt(a^6+x^8))/x dx` is equal to (a)`sqrt(a^6+x^8)+(a^3)/2ln|(sqrt(a^6+x^8)+a^3)/(sqrt(a^6+x^8)-a^3)|+c` (b) `a^6ln|(sqrt(a^6+x^8)-a^3)/(sqrt(a^6+x^8)+a^3)|+c` (c)`sqrt(a^6+x^8)+(a^3)/2ln|(sqrt(a^6+x^8)-a^3)/(sqrt(a^6+x^8)+a^3)|+c` (d) `a^6ln|(sqrt(a^6+x^8)+a^3)/(sqrt(a^6+x^8)-a^3)|+c`

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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