$\int_0^\pi \frac{x \sin x}{1 + \cos^2 x} \, dx$ equals:
Step-by-Step Solution
Key Concept: Apply $\int_0^\pi f(x) \, dx = \int_0^\pi f(\pi - x) \, dx$ to replace $x$ by $\pi - x$, add the two forms, and reduce the problem to an integral free of $x$.
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Correct Answer: (1)