\( \int_{0}^{\pi} \frac{x \sin x}{1+\cos ^{2} x} d x= \)....
\( \int_{0}^{\pi} \frac{x \sin x}{1+\cos ^{2} x} d x= \)
\( \mathrm{P} \)
(1) \( \frac{\pi^{2}}{4} \)
(2) \( \frac{\pi^{2}}{2} \)
(3) \( \frac{\pi^{2}}{2 \sqrt{2}} \)
(4) \( \frac{\pi^{2}}{4 \sqrt{2}} \)
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