The value of the integral $$\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\left(\frac{32\cos^4 x}{1 + e^{\sin x}}\right)dx$$ is:

A

$$4\pi + 2$$

B

$$3\pi + 8$$

C

$$3\pi + 4$$

D

$$4\pi + 3$$