Evaluate ∫0π/2sinxcosx1+cos2xdx\int_{0}^{\pi/2} \frac{\sin x \cos x}{\sqrt{1+\cos^2 x}} dx∫0π/21+cos2xsinxcosxdx.
1−121 - \frac{1}{\sqrt{2}}1−21
2−1\sqrt{2} - 12−1
2−22 - \sqrt{2}2−2
2+1\sqrt{2} + 12+1