Consider the following for the next two (02) items that follow:

Given that $\int \frac{3 \cos x + 4 \sin x}{2 \cos x + 5 \sin x} dx = \frac{\alpha x}{29} + \frac{\beta}{29} \ln |2 \cos x + 5 \sin x| + c$

What is the value of $\beta$ ?

Consider the following for the next two (02) items that follow:

Let $f(x) = \frac{x}{\ln x}; (x > 1)$

Consider the following statements :
1. $f(x)$ is increasing in the interval $(e, \infty)$
2. $f(x)$ is decreasing in the interval $(1, e)$
3. $9 \ln 7 > 7 \ln 9$
Which of the statements given above are correct ?

Consider the following for the next two (02) items that follow:

Let $f(x) = \frac{x}{\ln x}; (x > 1)$

Consider the following statements :
1. $f''(e) = \frac{1}{e}$
2. $f(x)$ attains local minimum value at $x = e$
3. A local minimum value of $f(x)$ is $e$
Which of the statements given above are correct ?

Consider the following for the next two (02) items that follow:

Let $f(x)$ and $g(x)$ be two functions such that $g(x) = x - \frac{1}{x}$ and $f \circ g(x) = x^3 - \frac{1}{x^3}$.

What is $g[f(x) - 3x]$ equal to?