https://file.aiquickdraw.com/mathbot/file/1725856105135d2c1hsb2.jpg

The integral shown in the image is:

\[
\int \frac{4 \, dx}{x^2 \sqrt{16x^2 - 9}}
\]

This is a problem that involves techniques of integration, possibly substitution to simplify the radical expression.

### Steps to Solve:
1. Factor the square root in terms of constants.
2. Apply substitution methods, particularly trigonometric substitution, since the term under the square root suggests a form related to a trigonometric identity.

Would you like a detailed step-by-step solution?

Here are 5 related questions for practice:
1. What is trigonometric substitution in integrals and when is it used?
2. How do you factor and simplify expressions under square roots?
3. What is the integral of basic trigonometric functions like \( \sec^2 \theta \)?
4. How does the chain rule apply in integrals involving substitution?
5. How do you verify your solution for integrals?

**Tip:** When you see a quadratic term inside a square root in integrals, think of trigonometric substitutions like \( x = \frac{3}{4} \sec \theta \) for terms involving \( x^2 - a^2 \).

Learn how to solve the integral ∫ 4 / [x^2 * sqrt(16x^2 - 9)] dx using trigonometric substitution. This detailed step-by-step solution applies key calculus concepts, including trigonometric identities and integration techniques. Ideal for students in undergraduate calculus.

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