1. **State the problem:** We need to find the indefinite integral of the function $ (3 - x)^2 $ with respect to $ x $. 2. **Recall the formula:** The integral of a function $ f(x) $ is given by $ \int f(x) \, dx $. For polynomials, we can expand and integrate term by term. 3. **Expand the integrand:** $$ (3 - x)^2 = 3^2 - 2 \cdot 3 \cdot x + x^2 = 9 - 6x + x^2 $$ 4. **Rewrite the integral:** $$ \int (3 - x)^2 \, dx = \int (9 - 6x + x^2) \, dx $$ 5. **Integrate term by term:** $$ \int 9 \, dx = 9x $$ $$ \int (-6x) \, dx = -6 \cdot \frac{x^2}{2} = -3x^2 $$ $$ \int x^2 \, dx = \frac{x^3}{3} $$ 6. **Combine the results:** $$ 9x - 3x^2 + \frac{x^3}{3} + C $$ 7. **Final answer:** $$ \int (3 - x)^2 \, dx = 9x - 3x^2 + \frac{x^3}{3} + C $$ This is the antiderivative of the given function, where $ C $ is the constant of integration.