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\( \int \frac{x+\sqrt{x+1}}{x+2} d x \) is equal to
\( \mathrm{P} \)
(A) \( (x+1)-2 \sqrt{x+1}+2 \ln |x+2|-2 \tan ^{-1} \sqrt{x+1}+C \)
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(B) \( (x+1)+2 \sqrt{x+2}-2 \ell n|x+2|-2 \tan ^{-1} \sqrt{x+2}+C \)
(C) \( (x+1)+2 \sqrt{x+1}-2 \ell n|x+2|-2 \tan ^{-1} \sqrt{x+1}+C \)
(D) \( (x+1)+2 \sqrt{x+2}-2 \ell n|x+1|+2 \tan ^{-1} \sqrt{x+2}+C \)
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