Evaluate: `inte^(a x)cosb x\ dx`

Explanation

To evaluate the integral \( I = \int e^{ax} \cos(bx) \, dx \), we will use integration by parts. Let's go through the steps one by one.

### Step 1: Identify Functions for Integration by Parts
We will use the integration by parts formula:
\[ \int u \, dv = uv - \int v \, du \]
Let:
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