If $$\int \frac{1}{a^2 \sin^2 x + b^2 \cos^2 x} dx = \frac{1}{12} \tan^{-1}(3 \tan x) +$$ constant, then the maximum value of $$a \sin x + b \cos x$$, is :

A

$$\sqrt{40}$$

B

$$\sqrt{41}$$

C

$$\sqrt{39}$$

D

$$\sqrt{42}$$