Answer
\[ = \frac{{\,{{\left( {\sin \theta } \right)}^{11}}}}{{11}} + C\]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {{{\sin }^{10}}\theta \cos \theta dx} \hfill \\
\hfill \\
set\,\,the\,\,substitution \hfill \\
\hfill \\
u = \sin \theta \,\,\,\,\,\,\,\,then\,\,\,\,\,\,\,du = \cos \theta d\theta \hfill \\
\hfill \\
apply\,\,the\,\,\,substitution \hfill \\
\hfill \\
\int_{}^{} {{{\sin }^{10}}\theta \cos \theta dx} = \int_{}^{} {{u^{10}}du} \hfill \\
\hfill \\
integrate\,\, \hfill \\
\hfill \\
= \frac{{{u^{11}}}}{{11}} + C \hfill \\
\hfill \\
replace\,\,u\,\,with\,\,\,u = \sin \theta \hfill \\
\hfill \\
= \frac{{\,{{\left( {\sin \theta } \right)}^{11}}}}{{11}} + C \hfill \\
\hfill \\
\end{gathered} \]
