2. a) Calculate $\int \frac{\sin x+2 \cos x}{2 \sin x+\cos x} d x$, for $x \in\left(0, \frac{\pi}{2}\right)$;

b) Calculate $\int_{-1}^{1} \frac{x^{2}}{1+e^{x}} d x$.
2. a) $\int \frac{\sin x+2 \cos x}{2 \sin x+\cos x} d x=\frac{4}{5} \int \frac{2 \sin x+\cos x}{2 \sin x+\cos x} d x+\frac{3}{5} \int \frac{2 \cos x-\sin x}{2 \sin x+\cos x} d x=\frac{4}{5} x+\frac{3}{5} \ln |2 \sin x+\cos x|+C$;

b) Use the change of variable $y=-x$.