Answer
\[ = \frac{{ - \cos \,\left( {{x^{10}}} \right)}}{{10}} + C\]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {{x^9}\sin {x^{10}}\,\,dx} \hfill \\
\hfill \\
set\,\,the\,\,substitution \hfill \\
\hfill \\
u = {x^{10}}\,\,\,\,then\,\,\,du = 10{x^9}dx \hfill \\
\hfill \\
therefore \hfill \\
\hfill \\
\int_{}^{} {{x^9}\sin {x^{10}}\,\,dx} = \,\frac{1}{{10}} \cdot \int_{}^{} {10{x^9}\sin {x^{10}}\,dx} \hfill \\
\hfill \\
apply\,\,the\,\,\,substitution \hfill \\
\hfill \\
\frac{1}{{10}} \cdot \int_{}^{} {\sin u\,du} \hfill \\
\hfill \\
integrate\,\, \hfill \\
\hfill \\
\frac{1}{{10}}\,\left( { - \cos \,u} \right) + C \hfill \\
\hfill \\
replace\,\,u\,\,with\,\,\,u = {x^{10}} \hfill \\
\hfill \\
= \frac{{ - \cos \,\left( {{x^{10}}} \right)}}{{10}} + C \hfill \\
\end{gathered} \]
