1. Find an antiderivative of the function $2x$. 2. The formula for the antiderivative of $x^n$ where $n \neq -1$ is: $$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$$ where $C$ is the constant of integration. 3. Applying this formula to $2x = 2x^1$: $$\int 2x \, dx = 2 \int x^1 \, dx = 2 \cdot \frac{x^{1+1}}{1+1} + C = 2 \cdot \frac{x^2}{2} + C = x^2 + C$$ 4. So, an antiderivative of $2x$ is: $$x^2 + C$$ 5. To check, differentiate $x^2 + C$: $$\frac{d}{dx}(x^2 + C) = 2x$$ which matches the original function. Final answer: $x^2 + C$