Integrate the functions $$\frac{x+2}{\sqrt{x^2+2x+3}}$$

Question

$\begin{array}{1 1} \sqrt{x^2+2x+3}+\log|(x+1)+\sqrt{x^2+2x+3}|+c \\ \sqrt{x^2+2x+3}-\log|(x+1)-\sqrt{x^2+2x+3}|+c \\ \sqrt{x^2+2x+3}-\log|(x+1)+\sqrt{x^2-2x-3}|+c \\ \sqrt{x^2-2x-3}-\log|(x+1)+\sqrt{x^2+2x+3}|+c \end{array}$