Answer
\[ = \frac{1}{3}\sin \,\left( {3x} \right) + C\]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {\cos \,3xdx} \hfill \\
\hfill \\
set\,\,u = 3x\,\,\,\,\,then\,\,\,\,du = 3dx \hfill \\
and\,\,\,dx = \frac{{du}}{3} \hfill \\
\hfill \\
apply\,\,the\,\,\,substitution \hfill \\
\hfill \\
\int_{}^{} {\cos \,u\,\left( {\frac{{du}}{3}} \right) = \frac{1}{3}\int_{}^{} {\cos udu} } \hfill \\
\hfill \\
integrate\,\,\,use\,\,\,\int_{}^{} {\cos udu = \sin u + C} \hfill \\
\hfill \\
= \frac{1}{3}\sin u + C \hfill \\
\hfill \\
{\text{Replace }}u{\text{ with }}3x \hfill \\
\hfill \\
= \frac{1}{3}\sin \,\left( {3x} \right) + C \hfill \\
\hfill \\
\end{gathered} \]
