Evaluate: `inte^x\ (logx+1/x)\ dx`

Explanation

To evaluate the integral \( I = \int e^x \left( \log x + \frac{1}{x} \right) dx \), we can follow these steps:

### Step 1: Identify the components
We notice that the integrand can be expressed as a sum of two functions: \( \log x \) and \( \frac{1}{x} \). We will try to express the integral in a form that allows us to use integration by parts.

### Step 2: Set up the function
Let \( f(x) = \log x \). Then, we can find its derivative:
\[
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