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int (x^2 -1 )/ (x^3 sqrt(2x^4 - 2x^2 +1)...

`int (x^2 -1 )/ (x^3 sqrt(2x^4 - 2x^2 +1))dx` is equal to

A

`2 sqrt(2-(2)/(x^(2))+(1)/(x^(4)))+c`

B

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

C

`(1)/(2) sqrt(2-(2)/(x^(2))+(1)/(x^(4)))+c`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Let `I=int((x^(2)-1)dx)/(x^(3)sqrt(2x^(4)-2x^(2)+1))` [dividing numerator and enominator by `x^(5)`]
`=int(((1)/(x^(3))-(1)/(x^(5)))dx)/(sqrt(2-(2)/(x^(2))+(1)/(x^(4))))`
`Put" "2-(2)/(x^(2))+(1)/(x^(4))=t`
`rArr ((4)/(x^(3))-(4)/(x^(5)))dx=dt`
`therefore I = (1)/(4)int(dt)/(sqrt(t))=(1)/(4)*(t^(1//2))/(1//2)+c`
`=(1)/(2)sqrt(2-(2)/(x^(2))+(1)/(x^(4)))+c`
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