It looks like you're asking about the integral of the function \(3\sqrt{x}\) with respect to \(x\). The expression can be written as:
\[ \int 3\sqrt{x} , dx \]
To solve this integral, we can rewrite \(\sqrt{x}\) as \(x^{1/2}\). Thus, the integral becomes:
\[ \int 3x^{1/2} , dx \]
Now we can apply the power rule for integration, which states that:
\[ \int x^n , dx = \frac{x^{n+1}}{n+1} + C \quad \text{for } n \neq -1 \]
In this case, \(n = \frac{1}{2}\), so \(n + 1 = \frac{3}{2}\). Therefore, we have:
\[ \int 3x^{1/2} , dx = 3 \cdot \frac{x^{3/2}}{\frac{3}{2}} + C = 3 \cdot \frac{2}{3} x^{3/2} + C = 2x^{3/2} + C \]
Thus, the integral is:
\[ \int 3\sqrt{x} , dx = 2x^{3/2} + C \]
where \(C\) is the constant of integration.