The integral `int(1+x-1/x)e^(x+1/x)dx` is equal to (1) `(x-1)e^(x+1/x)+C` (2) `x e^(x+1/x)+C` (3) `(x+1)e^(x+1/x)+C` (4) `-x e^(x+1/x)+C`

Explanation

To solve the integral \( \int (1 + x - \frac{1}{x}) e^{(x + \frac{1}{x})} \, dx \), we will use substitution and integration techniques step by step.

### Step 1: Identify the substitution
Let \( t = x + \frac{1}{x} \). Then, we need to find \( dt \).