Answer
\[4{y^4} + 3{y^3} - 3{y^2} + 3y + C\]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {\,\left( {16{y^3} + 9{y^2} - 6y + 3} \right)dy} \hfill \\
Extending\,\,using\,\,the\,\,sum\,\,and \hfill \\
difference\,\,rules \hfill \\
\int_{}^{} {13{y^3}dy} + \int_{}^{} {9{y^2}dy} - \int_{}^{} {6ydy} + \int_{}^{} {3dy} \hfill \\
Use\,\,the\,\,power\,\,rule \hfill \\
\int_{}^{} {{y^n}dy} = \frac{{{y^{n + 1}}}}{{n + 1}} + C \hfill \\
16\,\left( {\frac{{{y^4}}}{4}} \right) + 9\,\left( {\frac{{{y^3}}}{3}} \right) - 6\,\left( {\frac{{{y^2}}}{2}} \right) + 3y + C \hfill \\
Simplifying \hfill \\
4{y^4} + 3{y^3} - 3{y^2} + 3y + C \hfill \\
\end{gathered} \]
