Evaluate `int_0^pi (xsinx)/(1+cos^2x)dx`

Explanation

To evaluate the integral \( I = \int_0^\pi \frac{x \sin x}{1 + \cos^2 x} \, dx \), we can use a symmetry property of definite integrals.

### Step-by-step Solution:

1. **Set up the integral**:
\[ I = \int_0^\pi \frac{x \sin x}{1 + \cos^2 x} \, dx \]
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