If $\int \large\frac{\log(t+\sqrt{1+t^2})}{\sqrt {1+t^2}}$$dt= \large\frac{1}{2}$$(g(t))^2+C$, Where C is a constant , then $g(2)$ is equal to :

Question

$\begin{array}{1 1} 2 \log(2+\sqrt 5) \\ \log (2+\sqrt 5) \\ \frac{1}{\sqrt 5 } \log(2+\sqrt 5) \\ \frac{1}{2} \log (2+\sqrt 5) \end{array} $