Evaluate. \[ \int\left(12 x^{3}+5 x^{2}-3 x+3\right) d x \] $\int\left(12 x^{3}+5 x^{2}-3 x+3\right) d x=\square($ Type an exact answer. $)$

Step 1 ：Given the function \(f(x) = 12x^{3} + 5x^{2} - 3x + 3\), we are asked to find the integral of this function.

Step 2 ：We can use the power rule for integration, which states that the integral of \(x^n\) is \(\frac{1}{n+1}x^{n+1}\).

Step 3 ：Applying the power rule to each term in the function, we get \(\int f(x) dx = 3x^{4} + \frac{5}{3}x^{3} - \frac{3}{2}x^{2} + 3x\).

Step 4 ：However, when we integrate a function, we must also add a constant of integration, denoted by 'C'.

Step 5 ：Therefore, the integral of the function \(f(x) = 12x^{3} + 5x^{2} - 3x + 3\) is \(\boxed{3x^{4} + \frac{5}{3}x^{3} - \frac{3}{2}x^{2} + 3x + C}\).