Evaluate: `inte^x\ (tanx+logsecx)\ dx`

Explanation

To evaluate the integral \( I = \int e^x \left( \tan x + \log(\sec x) \right) \, dx \), we can break it down into two parts:

1. \( I_1 = \int e^x \tan x \, dx \)
2. \( I_2 = \int e^x \log(\sec x) \, dx \)

### Step 1: Recognizing the Form
We notice that the integrand can be expressed in the form \( e^x f(x) + e^x f'(x) \). Here, we can let:
- \( f(x) = \log(\sec x) \)
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