1. The problem is to find the integral of the function $3x$ with respect to $x$. 2. The formula for integrating a power function $x^n$ is: $$\int x^n dx = \frac{x^{n+1}}{n+1} + C$$ where $C$ is the constant of integration. 3. Here, the function is $3x$, which can be written as $3x^1$. 4. Applying the formula: $$\int 3x dx = 3 \int x^1 dx = 3 \cdot \frac{x^{1+1}}{1+1} + C = 3 \cdot \frac{x^2}{2} + C$$ 5. Simplifying: $$= \frac{3}{2} x^2 + C$$ 6. Therefore, the integral of $3x$ with respect to $x$ is: $$\frac{3}{2} x^2 + C$$ This means the area under the curve $3x$ is given by this expression plus a constant.