\( \int ( 5 s + 6 ) ^ { 2 } d s = \square \)

To evaluate the integral: \[ \int (5s + 6)^2 \, ds \] **Step 1: Use Substitution** Let \( u = 5s + 6 \). Then, the derivative of \( u \) with respect to \( s \) is: \[ \frac{du}{ds} = 5 \quad \Rightarrow \quad ds = \frac{du}{5} \] **Step 2: Rewrite the Integral in Terms of \( u \)** Substitute \( u \) and \( ds \) into the integral: \[ \int u^2 \cdot \frac{du}{5} = \frac{1}{5} \int u^2 \, du \] **Step 3: Integrate** \[ \frac{1}{5} \int u^2 \, du = \frac{1}{5} \cdot \frac{u^3}{3} + C = \frac{u^3}{15} + C \] **Step 4: Substitute Back \( u = 5s + 6 \)** \[ \frac{(5s + 6)^3}{15} + C \] **Final Answer:** \[ \int (5s + 6)^2 \, ds = \frac{(5s + 6)^3}{15} + C \] Where \( C \) is the constant of integration.