Two functions $f(x)$ and $g(x)$ are defined and differentiable on the set of all positive real numbers. $g(x)$ is the inverse function of $f(x)$, and $g'(x)$ is continuous on the set of all positive real numbers.\\
For all positive numbers $a$,
$$\int_1^a \frac{1}{g'(f(x))f(x)}\,dx = 2\ln a + \ln(a+1) - \ln 2$$
and $f(1) = 8$. Find the value of $f(2)$. [3 points]\\
(1) 36\\
(2) 40\\
(3) 44\\
(4) 48\\
(5) 52