Let $$(2^{1-a} + 2^{1+a})$$, $$f(a)$$, $$(3^a + 3^{-a})$$ be in A.P. and $$\alpha$$ be the minimum value of  $$f(a)$$, Then the value of the integral $$\displaystyle\int_{\log_e(\alpha - 1)}^{\log_e(\alpha)} \frac{dx}{e^{2x} - e^{-2x}}$$ is equal to :

A

$$\frac{1}{2}\log_e\left(\frac{4}{3}\right)$$

B

$$\frac{1}{4}\log_e\left(\frac{4}{3}\right)$$

C

$$\frac{1}{2}\log_e\left(\frac{8}{5}\right)$$

D

$$\frac{1}{4}\log_e\left(\frac{8}{5}\right)$$