$$\int \left\{\frac{(\log x - 1)}{(1 + (\log x)^2)}\right\}^2 dx$$ is equal to

A

$$\frac{\log x}{(\log x)^2 + 1} + C$$

B

$$\frac{x}{x^2 + 1} + C$$

C

$$\frac{xe^x}{1 + x^2} + C$$

D

$$\frac{x}{(\log x)^2 + 1} + C$$