Match the integrals of \( f(x) \) if
\begin{tabular}{|c|c|c|c|}
\hline & Column I & & Column II ....
Match the integrals of \( f(x) \) if
\( \mathrm{P} \)
\begin{tabular}{|c|c|c|c|}
\hline & Column I & & Column II \\
\hline (A) & \( f(x)=\frac{1}{\left(x^{2}+1\right) \sqrt{x^{2}+2}} \) & \( (\mathrm{P}) \) & \( \frac{x^{5}}{5\left(1-x^{4}\right)^{5 / 2}}+C \) \\
\hline (B) & \begin{tabular}{l}
\( f(x) \) \\
\( =\frac{1}{(x+2) \sqrt{x^{2}+6 x+7}} \)
\end{tabular} & (Q) & \( \sin ^{-1}\left(\frac{x+1}{(x+2) \sqrt{2}}+C\right) \) \\
\hline (C) & \begin{tabular}{l}
\( f(x) \) \\
\( =\frac{x^{4}+x^{8}}{\left(1-x^{4}\right)^{7 / 2}} \)
\end{tabular} & \( (\mathbf{R}) \) & \begin{tabular}{l}
\( -2 \sqrt{1-x}+\cos ^{-1} \sqrt{x} \) \\
\( +\sqrt{x} \sqrt{1-x}+C \)
\end{tabular} \\
\hline (D) & \( f(x)=\sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}} \) & \( (\mathbf{S}) \) & \( -\tan ^{1} \sqrt{1+2 / x^{2}}+C \) \\
\hline
\end{tabular}
\begin{tabular}{lllll}
(1) & \( \mathrm{R} \) & \( \mathrm{S} \) & \( \mathrm{Q} \) & \( \mathrm{P} \) \\
(2) & \( \mathrm{P} \) & \( \mathrm{Q} \) & \( \mathrm{S} \) & \( \mathrm{R} \) \\
(3) & \( \mathrm{S} \) & \( \mathrm{Q} \) & \( \mathrm{P} \) & \( \mathrm{R} \) \\
(4) & \( \mathrm{P} \) & \( \mathrm{Q} \) & \( \mathrm{S} \) & \( \mathrm{R} \)
\end{tabular}
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