Solve `int(sqrt(1+2x)-sqrt(1-2x))dx`

Explanation

To solve the integral \( \int (\sqrt{1+2x} - \sqrt{1-2x}) \, dx \), we will break it down into manageable steps.

### Step 1: Split the Integral
We can separate the integral into two parts:
\[ \int (\sqrt{1+2x} - \sqrt{1-2x}) \, dx = \int \sqrt{1+2x} \, dx - \int \sqrt{1-2x} \, dx \]

...