Answer
\[ = \frac{1}{4}\,\sec \,\,4w\,\, + C\]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {\sec \,4w\tan 4w\,dw} \hfill \\
\hfill \\
set\,\,u = 4w\,\,\,\,\,\,\,\,then\,\,\,\,\,du = 4dw \hfill \\
\hfill \\
therefore \hfill \\
\hfill \\
= \frac{1}{4}\int_{}^{} {\sec \,\,u\,\,\tan u\,\,du} \hfill \\
\hfill \\
integrate\,\, \hfill \\
\hfill \\
= \frac{1}{4}\sec \,\,u\,\, + C \hfill \\
\hfill \\
replace\,\,u\,\,with\,\,\,u = 4w \hfill \\
\hfill \\
= \frac{1}{4}\,\sec \,\,4w\,\, + C \hfill \\
\end{gathered} \]
