If \( A=\int_{0}^{\pi} \frac{\cos x}{(x+2)^{2}} d x \), then \( \int_{0}^{\frac{\pi}{2}} \frac{\...
If \( A=\int_{0}^{\pi} \frac{\cos x}{(x+2)^{2}} d x \), then \( \int_{0}^{\frac{\pi}{2}} \frac{\sin 2 x}{(x+1)} d x \) is equal to
\( \mathrm{P} \)
(A) \( \frac{1}{\pi+2}-A \)
(B) \( \frac{1}{2}+\frac{1}{\pi+2}-A \)
(C) \( \frac{1}{2}-\frac{1}{\pi+2}-A \)
(D) \( \frac{1}{2}+\frac{1}{\pi+2}+A \)
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