Evaluate: `inte^xsecx\ (1+tanx)\ dx`

Explanation

To evaluate the integral \( I = \int e^x \sec x (1 + \tan x) \, dx \), we can follow these steps:

### Step 1: Rewrite the Integral
We start with the integral:
\[ I = \int e^x \sec x (1 + \tan x) \, dx \]
We can rewrite \( 1 + \tan x \) as \( \sec x + \tan x \):
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