If \( f(x) \) is a quadratic expression such that \( f(0)=f(1) \) \( =3 f(2)=-3 \), then \( \int....

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If \( f(x) \) is a quadratic expression such that \( f(0)=f(1) \)
\( =3 f(2)=-3 \), then \( \int \frac{f(x)}{x^{3}-1} d x= \)
\( \mathrm{P} \)
(1) \( -\log _{e}|x-1|+\log _{e}\left(x^{2}+x+1\right)+\frac{2}{\sqrt{3}} \operatorname{Tan}^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c \)
(2) \( \log _{e}|x-1|+\log _{e}\left(x^{2}+x+1\right)+\frac{1}{\sqrt{3}} \operatorname{Tan}^{-1}\left(\frac{x+1}{\sqrt{3}}\right)+c \)
(3) \( \log _{e}\left(x^{2}+x+1\right)+\log _{e}|x|+\frac{2}{\sqrt{3}} \operatorname{Tan}^{-1}\left(\frac{2 x+3}{\sqrt{3}}\right)+c \)
(4) \( \log _{e}\left|x^{3}+x^{2}+x\right|+\frac{2}{\sqrt{3}} \operatorname{Tan}^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c \)


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