If \( \int \frac{d x}{(x+2)\left(x^{2}+1\right)}=a \log \left|1+x^{...

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If \( \int \frac{d x}{(x+2)\left(x^{2}+1\right)}=a \log \left|1+x^{2}\right|+b \tan ^{-1} x+\frac{1}{5} \log |x+2|+C \), then
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W
(A) \( a=\frac{-1}{10}, b=\frac{-2}{5} \)
(B) \( a=\frac{1}{10}, b=-\frac{2}{5} \)
(C) \( a=\frac{-1}{10}, b=\frac{2}{5} \)
(D) \( a=\frac{1}{10}, b=\frac{2}{5} \)
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