Answer
\[\frac{8}{3}{v^{3/2}} - \frac{6}{5}{v^{5/2}} + C\]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {\,\left( {4\sqrt v - 3{v^{3/2}}} \right)dv} \hfill \\
Write\,\,\sqrt v \,\,as\,\,{v^{1/2}} \hfill \\
\int_{}^{} {\,\left( {4{v^{1/2}} - 3{v^{3/2}}} \right)dv} \hfill \\
Use\,\,the\,\,power\,\,rule \hfill \\
\int_{}^{} {{v^n}dx} = \frac{{{v^{n + 1}}}}{{n + 1}} + C \hfill \\
4\,\left( {\frac{{{v^{3/2}}}}{{3/2}}} \right) - 3\,\left( {\frac{{{v^{5/2}}}}{{5/2}}} \right) + C \hfill \\
Simplifying \hfill \\
\frac{8}{3}{v^{3/2}} - \frac{6}{5}{v^{5/2}} + C \hfill \\
\end{gathered} \]
