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

Explanation

To evaluate the integral \( \int e^x \left( \log x + \frac{1}{x} \right) dx \), we can break it down into two parts and use integration by parts. Let's go through the steps:

### Step 1: Break down the integral
We can separate the integral into two parts:
\[ \int e^x \left( \log x + \frac{1}{x} \right) dx = \int e^x \log x \, dx + \int e^x \frac{1}{x} \, dx \]

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