\begin{equation}
\int \frac{-\sin{3t}\times9\sec^2{3t}}{3} \,dt\\
= \int \frac{-3sin{3t}}{cos^2{3t}} \,dt\\
=\int \frac{1}{cos^2{3t}} \,d(cos{3t})\\
\end{equation}
let m=cos3t
\begin{equation}
\int \frac{1}{cos^2{3t}} \,d(cos{3t})\\
=\int \frac{1}{cos^2{3t}} \,dm\\
=\int \frac{1}{m^2}\,dm\\
=\frac{-1}{m}\\
=\frac{-1}{cos3t}\\
\end{equation}
