Evaluate `int e^(2x) sin 3x dx`.

Explanation

To evaluate the integral \( \int e^{2x} \sin(3x) \, dx \), we will use the method of integration by parts, also known as the ILET method (Inverse Logarithmic Algebraic Trigonometric Exponential). Here’s the step-by-step solution:

### Step 1: Set up the integral
Let:
\[ I = \int e^{2x} \sin(3x) \, dx \]

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