Evaluate: `inte^x\ (tanx-logcosx)\ dx`

Explanation

To evaluate the integral \( I = \int e^x \left( \tan x - \log \cos x \right) \, dx \), we can use the method of integration by parts and properties of derivatives. Let's break it down step by step.

### Step 1: Identify \( f(x) \) and \( f'(x) \)

We want to express \( \tan x - \log \cos x \) in the form \( f'(x) + f(x) \). Let's choose:
- \( f(x) = -\log \cos x \)

Now, we need to find \( f'(x) \):
...