The problem asks for the evaluation of the indefinite integral:

$\int e^{3x} \, dx$

Step 1: Recognize the Integral Formula

The integral of $e^{ax}$ with respect to $x$ is $\frac{1}{a}e^{ax} + C$, where $a$ is a constant.

Step 2: Apply the Formula

In this case, $a = 3$, so the integral becomes:

$\int e^{3x} \, dx = \frac{1}{3}e^{3x} + C$

Final Answer

The correct answer is:

$\boxed{\frac{1}{3}e^{3x} + C}$

Would you like to know more details or have any other questions?

Here are some related questions you might find interesting:

1. How would you integrate $\int e^{5x} \, dx$?
2. What is the general form of the integral of $e^{ax + b}$?
3. How does the constant $a$ affect the shape of the function $e^{ax}$?
4. What is the importance of the constant of integration $C$ in indefinite integrals?
5. Can you apply the substitution method to solve integrals like $\int e^{3x} \, dx$?

Tip: For exponential functions, always remember the integral formula $\int e^{ax} dx = \frac{1}{a}e^{ax} + C$. It will save you time on similar problems.