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For integral int f(x- a/x)*(1+a/x^(2))dx...

For integral `int f(x- a/x)*(1+a/x^(2))dx`, put `x-a/x=t`
For integral `int f(x+a/x)*(1-(a)/(x^(2)))dx`, put `x+a/x =t`
For integral `int f(x^(2)-(a)/(x^(2)))*(x+(a)/(x^(3)))dx`, put `x^(2)-(a)/(x^(2))=t`
For integral `int f(x^(2)+(a)/(x^(2)))*(x-(a)/(x^(3)))dx`, put `x^(2)+(a)/(x^(2))=t`
many integrands can be brought into above forms by suitable reductions or transformations .
`int(x^(4)-2)/(x^(2)sqrt(x^(4)+x^(2)+2))dx`

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
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