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l=inttan^(-1)""((1)/(x^(2)-x+1))dx is eq...

`l=inttan^(-1)""((1)/(x^(2)-x+1))dx` is equal to

A

`xtan^(-1)((1)/(x^(2)-x+1))+log_(e)""(x)/((2-x)sqrt(1+x^(2))sqrt(2x-x^(2)))+c`

B

`xcot^(-1)(x^(2)-x+1)+log_(e)""(x)/((2-x)sqrt(1+x^(2))sqrt(2x-x^(2)))+c`

C

`tan^(-1)((1)/(x^(2)-x+1))+c`

D

`xtan^(-1)""(1)/(x^(2)-x+1)-tan^(-1)(1-x)+(1)/(2)log""(x^(2)-2x+2)/(x^(2)+1)+c`

Text Solution

Verified by Experts

The correct Answer is:
D
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