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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.

Learn how to solve the indefinite integral ∫ e^{3x} dx step-by-step with a detailed explanation. This problem covers calculus concepts, including indefinite integration and exponential functions. Suitable for students in Grades 11-12.

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