Integral (dx)/(sqrt(x² - 16))

Here are the solutions to the integration problems.

2. (i) $\int \frac{dx}{\sqrt{x^2 - 16}}$
This integral is of the form $\int \frac{dx}{\sqrt{x^2 - a^2}}$.
Here, $a^2 = 16$, so $a = 4$.
The formula for this type of integral is $\ln|x + \sqrt{x^2 - a^2}| + C$.
Substituting $a=4$:

$$\int \frac{dx}{\sqrt{x^2 - 16}} = \ln|x + \sqrt{x^2 - 16}| + C$$

The final answer is $\boxed{\ln|x +