\( 1 \leftarrow \quad \begin{array}{l}\text { Determine the following indefinite integral. } \\ \int(4 s+7)^{2} d s\end{array} \)

Calculate the integral \( \int(4s+7)^{2} ds \). Evaluate the integral by following steps: - step0: Evaluate using substitution: \(\int \left(4s+7\right)^{2} ds\) - step1: Use the substitution \(ds=\frac{1}{4} dt\) to transform the integral\(:\) \(\int \left(4s+7\right)^{2}\times \frac{1}{4} dt\) - step2: Simplify: \(\int \frac{\left(4s+7\right)^{2}}{4} dt\) - step3: Use the substitution \(t=4s+7\) to transform the integral\(:\) \(\int \frac{t^{2}}{4} dt\) - step4: Rewrite the expression: \(\int \frac{1}{4}t^{2} dt\) - step5: Use properties of integrals: \(\frac{1}{4}\times \int t^{2} dt\) - step6: Evaluate the integral: \(\frac{1}{4}\times \frac{t^{2+1}}{2+1}\) - step7: Simplify: \(\frac{1}{4}\times \frac{t^{3}}{3}\) - step8: Multiply the terms: \(\frac{t^{3}}{4\times 3}\) - step9: Multiply the terms: \(\frac{t^{3}}{12}\) - step10: Substitute back: \(\frac{\left(4s+7\right)^{3}}{12}\) - step11: Add the constant of integral C: \(\frac{\left(4s+7\right)^{3}}{12} + C, C \in \mathbb{R}\) The indefinite integral of \((4s+7)^{2}\) with respect to \(s\) is \(\frac{(4s+7)^{3}}{12} + C\), where \(C\) is an arbitrary constant.