The integral $$\int_0^{\pi} \frac{(x+3)\sin x}{1 + 3\cos^2 x} dx$$ is equal to :

A

$$\frac{\pi}{\sqrt{3}}(\pi + 1)$$

B

$$\frac{\pi}{\sqrt{3}}(\pi + 2)$$

C

$$\frac{\pi}{3\sqrt{3}}(\pi + 6)$$

D

$$\frac{\pi}{2\sqrt{3}}(\pi + 4)$$