\[ \begin{array}{l} \text { If } \int \frac{(x+2) d x}{\left(x^{2}+...
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\[
\begin{array}{l}
\text { If } \int \frac{(x+2) d x}{\left(x^{2}+3 x+3\right) \sqrt{(x+1)}} \\
=\frac{2}{\sqrt{3}}\left[\tan ^{-1}\left(\frac{f(x)+1}{\sqrt{3}}\right)+\tan ^{-1}\left(\frac{f(x)-1}{\sqrt{3}}\right)\right]+c
\end{array}
\]
\( \mathrm{P}^{147} \)
W then \( f(x) \) is equal to
(1) \( 2 \sqrt{x-1} \)
(2) \( 3 \sqrt{x+1} \)
(3) \( 3 \sqrt{x-1} \)
(4) \( 2 \sqrt{x+1} \)
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