Evaluate the integral I=∫0πxsinx1+cos2x dxI = \int_{0}^{\pi} \frac{x \sin x}{1 + \cos^2 x} \, dxI=∫0π1+cos2xxsinxdx.
π24\frac{\pi^2}{4}4π2
π22\frac{\pi^2}{2}2π2
π28\frac{\pi^2}{8}8π2
π26\frac{\pi^2}{6}6π2