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

`int (x^(2)+1)/(x^(4)+x^(2)+1)dx=`

A

`-(1)/(sqrt(3))Tan^(-1)((x^(2)-1)/(sqrt(3)x))+c`

B

`(1)/(sqrt(3))Tan^(-1)((sqrt(3)-x)/(sqrt(3)x))+c`

C

`(1)/(sqrt(2))Tan^(-1)((x^(2)-1)/(sqrt(3)x))+c`

D

`(1)/(sqrt(3))Tan^(-1)((x^(2)-1)/(sqrt(3)x))+c`

Text Solution

Verified by Experts

The correct Answer is:
D
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