1. The problem asks to find the Stammfunktion (antiderivative) of the function $f(x) = \frac{3}{8}(x - 2)^2$. 2. Recall the power rule for integration: $$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$$ where $C$ is the constant of integration. 3. Apply the rule to $f(x)$: $$\int \frac{3}{8}(x - 2)^2 \, dx = \frac{3}{8} \int (x - 2)^2 \, dx$$ 4. Use substitution: let $u = x - 2$, so $du = dx$. 5. Then the integral becomes: $$\frac{3}{8} \int u^2 \, du = \frac{3}{8} \cdot \frac{u^{3}}{3} + C = \frac{3}{8} \cdot \frac{(x - 2)^3}{3} + C$$ 6. Simplify the coefficient: $$\frac{3}{8} \cdot \frac{1}{3} = \frac{1}{8}$$ 7. Therefore, the Stammfunktion is: $$F(x) = \frac{1}{8} (x - 2)^3 + C$$ This function $F(x)$ is the antiderivative of $f(x)$, representing the area under the curve of $f(x)$ plus a constant $C$.