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The given integral is:

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

This integral looks similar to the standard form for arcsine, which is:

\[
\int \frac{1}{\sqrt{a^2 - x^2}} \, dx = \arcsin\left(\frac{x}{a}\right) + C
\]

Here, \( a^2 = 3 \), so \( a = \sqrt{3} \).

Thus, applying this formula, the solution to the integral is:

\[
\arcsin\left(\frac{x}{\sqrt{3}}\right) + C
\]

Where \( C \) is the constant of integration.

Would you like further clarification on any part of this solution? Here are some related questions for practice:

1. How do you integrate \( \int \frac{1}{\sqrt{4 - x^2}} \, dx \)?
2. What is the derivative of \( \arcsin\left(\frac{x}{a}\right) \)?
3. How would the integral change if the expression was \( \int \frac{1}{\sqrt{9 - x^2}} \, dx \)?
4. How do you recognize integrals that follow the arcsine pattern?
5. What happens if the integrand is \( \frac{1}{\sqrt{a^2 + x^2}} \) instead?

**Tip:** When integrating expressions involving square roots like \( \sqrt{a^2 - x^2} \), it's helpful to memorize standard integral forms like arcsine or arctangent functions.

Evaluate the integral ∫ (1 / √(3 - x^2)) dx. Use a capital C to denote an arbitrary constant of integration.

Learn how to evaluate the integral ∫ (1 / √(3 - x^2)) dx using the arcsine formula. This problem involves key concepts in integral calculus, specifically trigonometric integrals, and is suitable for students in undergraduate calculus courses.

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