Let $$g : (0, \infty) \to R$$ be a differentiable function such that $$\int \frac{x\cos x - \sin x}{e^x + 1} + \frac{g(x)e^x + 1 - xe^x}{(e^x + 1)^2} dx = \frac{xg(x)}{e^x + 1} + C$$, for all $$x > 0$$, where $$C$$ is an arbitrary constant. Then

A

$$g$$ is decreasing in $$\left(0, \frac{\pi}{4}\right)$$

B

$$g - g'$$ is increasing in $$\left(0, \frac{\pi}{2}\right)$$

C

$$g'$$ is increasing in $$\left(0, \frac{\pi}{4}\right)$$

D

$$g + g'$$ is increasing in $$\left(0, \frac{\pi}{2}\right)$$