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.