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int(x^4-1)/(x^2sqrt(x^4+x^2+1))dx= sqr...

`int(x^4-1)/(x^2sqrt(x^4+x^2+1))dx=` `sqrt(x^2+1/(x^2)+1)+C` `(sqrt(x^4+x^2+1))/(x^2)+C` `(sqrt(x^4+x^2+1))/x+C` (d) none of these

A

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

B

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

C

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

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`I=int(x^(4)-1)/(x^(2)*xsqrt(x^(2)+(1)/(x^(2))+1))dx=int((x-(1)/(x^(3)))dx)/(sqrt(x^(2)+(1)/(x^(2))+1))`
Put `x^(2)+(1)/(x^(2))+1=t " or "2(x-(1)/(x^(3)))dx=dt`
` :. I=(1)/(2)int(dt)/(sqrt(t))=(1)/(2)*2sqrt(t)+C=sqrt(t)+C `
`=sqrt(x^(2)+(1)/(x^(2))+1)+C=(sqrt(x^(4)+x^(2)+1))/(x)+C`
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