Answer
\[4{u^{5/2}} - 4{u^{7/2}} + C\]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {\,\left( {10{u^{3/2}} - 14{u^{5/2}}} \right)du} \hfill \\
using\,\,the\,\,sum\,\,and\,difference\,\,rules \hfill \\
\int_{}^{} {10{u^{3/2}}du - \int_{}^{} {14{u^{5/2}}du} } \hfill \\
Find\,\,the\,\,antiderivative\,\,\,use\,\,the\,\, \hfill \\
power\,\,\,rule \hfill \\
\int_{}^{} {{x^n}dx} = \frac{{{x^{n + 1}}}}{{n + 1}} + C \hfill \\
Then \hfill \\
10\,\left( {\frac{{{u^{3/2 + 1}}}}{{3/2 + 1}}} \right) - 14\,\left( {\frac{{{u^{5/2 + 1}}}}{{5/2 + 1}}} \right) + C \hfill \\
10\,\left( {\frac{{{u^{5/2}}}}{{5/2}}} \right) - 14\,\left( {\frac{{{u^{7/2}}}}{{7/2}}} \right) + C \hfill \\
Simplifying \hfill \\
4{u^{5/2}} - 4{u^{7/2}} + C \hfill \\
\hfill \\
\end{gathered} \]
