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What is int (x^(4) -1)/(x^(2) sqrt(x^(4)...

What is `int (x^(4) -1)/(x^(2) sqrt(x^(4) + x^(2) + 1)) dx` equal to ?

A

`sqrt((x^(4)+x^(2)+1)/(x))+C`

B

`(x^(2))/(sqrt(x^(4)+x^(2)+1))+C`

C

`x(x^(4)+x^(2)+1)^(3//2)+C`

D

`(sqrt(x^(4)+x^(2)+1))/(x)+C`

Text Solution

Verified by Experts

The correct Answer is:
D
`int(x^(4)-1)/(x^(2)(x^(4)+x^(2)+1)^(1//2))dx=int(2x^(4)+x^(2)-(x^(4)+x^(2)+1))/(x^(2)sqrt(x^(4)+x^(2)+1))dx`
`=int((x(4x^(3)+2x))/(2sqrt(x^(4)+x^(2)+1))-sqrt(x^(4)+x^(2)+1))/(x^(2))`
`=int(d)/(dx)((sqrt(x^(4)+x^(2)+1))/(x))dx=(sqrt(x^(4)+x^(2)+1))/(x)+C`
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