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

Explanation

To solve the integral \( \int (\sqrt{1 + 2x} - \sqrt{1 - 2x}) \, dx \), we can break it down into two separate integrals. Here’s a step-by-step solution:

### Step 1: Separate the Integral
We start by separating the integral into two parts:

\[ \int (\sqrt{1 + 2x} - \sqrt{1 - 2x}) \, dx = \int \sqrt{1 + 2x} \, dx - \int \sqrt{1 - 2x} \, dx \]
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