Answer
\[\frac{5}{4}{x^4} - 20{x^2} + C\]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {5x\,\left( {{x^2} - 8} \right)dx} \hfill \\
Simplifying\,\,the\,\,in\,tegrand\,\,and\,\,then \hfill \\
find\,\,the\,\,antiderivative \hfill \\
\int_{}^{} {\,\left( {5{x^3} - 40x} \right)dx} \hfill \\
Use\,\,the\,\,power\,\,rule \hfill \\
\int_{}^{} {{x^n}dx} = \frac{{{x^{n + 1}}}}{{n + 1}} + C \hfill \\
5\,\left( {\frac{{{x^4}}}{4}} \right) - 40\,\left( {\frac{{{x^2}}}{2}} \right) + C \hfill \\
Simplifying \hfill \\
\frac{5}{4}{x^4} - 20{x^2} + C \hfill \\
\end{gathered} \]
