Answer
\[16{t^{7/2}} + 4{t^{9/2}} + C\]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {{\,^{}}\left( {56{t^{5/2}} + 18{t^{7/2}}} \right)dt} \hfill \\
Use\,\,the\,\,sum\,\,and\,\,difference\,\,rules \hfill \\
\int_{}^{} {56{t^{5/2}}dt + \int_{}^{} {18{t^{7/2}}dt} } \hfill \\
Use\,\,the\,\,power\,\,rule \hfill \\
56\,\left( {\frac{{{t^{5/2 + 1}}}}{{5/2 + 1}}} \right) + 18\,\left( {\frac{{{t^{7/2 + 1}}}}{{7/2 + 1}}} \right) + C \hfill \\
56\,\left( {\frac{{{t^{7/2}}}}{{7/2}}} \right) + 18\,\left( {\frac{{{t^{9/2}}}}{{9/2}}} \right) + C \hfill \\
Simplifying \hfill \\
16{t^{7/2}} + 4{t^{9/2}} + C \hfill \\
\end{gathered} \]
