I = \int_{0}^{\frac{\pi}{2}} \frac{[\frac{1}{2}(sinx+cosx+1)-\frac{1}{2}(cosx-sinx) - \frac{1}{2}]dx}{1+sinx+cosx} \\ \\ I = \int_{0}^{\frac{\pi}{2}}\frac{dx}{2} - \int_{0}^{\frac{\pi}{2}}\frac{cosx-sin x}{2(sinx+cosx+1)}dx - \int_{0}^{\frac{\pi}{2}} \frac{dx}{2(sin x + cosx+1)} \\ \\ I =...