Evaluate `int_(0)^(pi)(xsinx)/((1+cos^(2)x))dx`.

Explanation

To evaluate the integral \( I = \int_{0}^{\pi} \frac{x \sin x}{1 + \cos^2 x} \, dx \), we can use the property of definite integrals that states:

\[ \int_{a}^{b} f(x) \, dx = \int_{a}^{b} f(a + b - x) \, dx \]

In this case, \( a = 0 \) and \( b = \pi \). Therefore, we can write:

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