We need to compute the integral:

\[
\int \frac{3}{x \sqrt{x^2 - 1}} \, dx
\]

This integral suggests the use of a trigonometric substitution because of the form \( \sqrt{x^2 - 1} \).

### Step 1: Use the substitution \( x = \sec(\theta) \)
We know that:
\[
\sec^2(\theta) - 1 = \tan^2(\theta)
\]
Thus, let:
\[
x = \sec(\theta) \quad \text{so} \quad dx = \sec(\theta) \tan(\theta) \, d\theta
\]
and:
\[
\sqrt{x^2 - 1} = \sqrt{\sec^2(\theta) - 1} = \tan(\theta)
\]

### Step 2: Rewrite the integral
Substitute \( x = \sec(\theta) \) and

Explore how to compute the integral of 3 / (x * sqrt(x^2 - 1)) using trigonometric substitution. This problem applies key calculus techniques such as trigonometric identities and the substitution x = sec(θ). Suitable for college-level calculus students.

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