The equation you've written involves an integral that results in a square root function. Let's denote the integral as:

$\int f(x) \, dx = \sqrt{g(x) + 3}$

To solve this, we need to find the function $f(x)$ such that when integrated, the result is $\sqrt{g(x) + 3}$.

Step 1: Differentiate the Result

Assume the antiderivative is given by:

$F(x) = \sqrt{g(x) + 3}$

The derivative of this with respect to $x$ gives the integrand $f(x)$. Using the chain rule, we differentiate:

$f(x) = \frac{d}{dx} \left( \sqrt{g(x) + 3} \right)$

This simplifies to:

$f(x) = \frac{1}{2\sqrt{g(x) + 3}} \cdot g'(x)$

Thus, the integrand $f(x)$ must be of the form:

$f(x) = \frac{g'(x)}{2\sqrt{g(x) + 3}}$

Now, if you know the specific form of $g(x)$, we can determine $f(x)$ explicitly. Otherwise, this is the general form of the integrand.

Would you like more details or clarification on this process?

Related Questions:

1. How do you compute integrals involving square roots?
2. What is the chain rule in calculus, and how is it applied here?
3. Can you provide a concrete example with a specific $g(x)$?
4. What techniques are used to solve non-elementary integrals?
5. How do you determine $g(x)$ from a given $f(x)$?
6. What are the common forms of integrals that involve roots?
7. Can partial fractions be applied in similar cases?
8. How does substitution help in integrating complex functions?

Tip: Always differentiate your answer to check if your integration was correct.