Answer
\[6{x^{5/2}} + \frac{4}{3}{x^{3/2}} + C\]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {\,\left( {15x\sqrt x + 2\sqrt x } \right)dx} \hfill \\
Write\,\,\sqrt x \,\,\,as\,\,{x^{1/2}} \hfill \\
\int_{}^{} {\,\left( {15x{x^{1/2}} + 2{x^{1/2}}} \right)dx} \hfill \\
Multiplying \hfill \\
\int_{}^{} {\,\left( {15{x^{3/2}} + 2{x^{1/2}}} \right)dx} \hfill \\
Find\,\,the\,\,antiderivative\,\,\,use\,\,the\,\, \hfill \\
power\,\,\,rule \hfill \\
\int_{}^{} {{x^n}dx} = \frac{{{x^{n + 1}}}}{{n + 1}} + C \hfill \\
15\,\left( {\frac{{{x^{5/2}}}}{{5/2}}} \right) + 2\,\left( {\frac{{{x^{3/2}}}}{{3/2}}} \right) + C \hfill \\
Simplifying \hfill \\
6{x^{5/2}} + \frac{4}{3}{x^{3/2}} + C \hfill \\
\end{gathered} \]
