Let \( f(x) \) be a polynomial function of degree 2 \( \mathrm{P} \...

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Let \( f(x) \) be a polynomial function of degree 2
\( \mathrm{P} \) satisfying

W
\[
\int \frac{f(x)}{x^{3}-1} d x=\ln \left|\frac{x^{2}+x+1}{x-1}\right|+\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+C \text {, }
\]
where \( C \) is indefinite integration constant.
The value of \( f(1) \) is equal to:
(1) 1
(2) 2
(3) -1
(4) -3
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