If \( \int \frac{x(x-1)}{\left(x^{2}+1\right)(x+1) \sqrt{x^{3}+x^{2...

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If \( \int \frac{x(x-1)}{\left(x^{2}+1\right)(x+1) \sqrt{x^{3}+x^{2}+x}} d x \)
\( \mathrm{P} \)
W \( =\frac{1}{2} \log _{e}\left|\frac{\sqrt{f(x)}-1}{\sqrt{f(x)}+1}\right|-\tan ^{-1} \sqrt{f(x)}+C \), then
The value of \( f(1) \) is
(1) 1
(2) 2
(3) 3
(4) 4
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