`int(2x)/((2x+1)^2)\ dx`

Explanation

To solve the integral \( \int \frac{2x}{(2x+1)^2} \, dx \), we can use a technique of rewriting the integrand to facilitate integration. Here’s a step-by-step solution:

### Step 1: Rewrite the Integrand
We can rewrite the integrand \( \frac{2x}{(2x+1)^2} \) by adding and subtracting 1 in the numerator:

\[ \frac{2x}{(2x+1)^2} = \frac{(2x + 1) - 1}{(2x + 1)^2} = \frac{2x + 1}{(2x + 1)^2} - \frac{1}{(2x + 1)^2} \]
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