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If $\int \frac{f (x)}{x^{2} - x + 1} d x = \frac{3}{2} \log (x^{2} - x + 1) + \frac{1}{\sqrt{3}} \tan^{- 1} \frac{2 x - 1}{\sqrt{3}} + C$
then $f (x)$ is equal to

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detailed solution

Correct option is C

Differentiating both the sides w.r.t. x , we get f(x)x2−x+1=322x−1x2−x+1+1311+(2x-13)223=322x−1x2−x+1+12x2−x+1⇒f(x)=3x−1

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If ∫f(x)x2−x+1dx=32log⁡x2−x+1+13tan−1⁡2x−13+C then f(x) is equal to

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If $\int \frac{f (x)}{x^{2} - x + 1} d x = \frac{3}{2} \log (x^{2} - x + 1) + \frac{1}{\sqrt{3}} \tan^{- 1} \frac{2 x - 1}{\sqrt{3}} + C$
then $f (x)$ is equal to