`int (4e^(3x) +1)dx`

Explanation

To solve the integral \( \int (4e^{3x} + 1) \, dx \), we can break it down into two separate integrals:

1. **Separate the integral:**
\[ \int (4e^{3x} + 1) \, dx = \int 4e^{3x} \, dx + \int 1 \, dx \]

2. **Integrate \( \int 4e^{3x} \, dx \):**
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