b) Evaluate 

To evaluate the integral \(\int_{0}^\pi{}\frac{x\sin{x}}{1+\cos^2{x}}dx\), we can use integration by parts. 

Let's denote:
\[ u = x \quad \text{and} \quad dv = \frac{\sin{x}}{1+\cos^2{x}}dx \]

Then, we have:
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