\(\text{We have to solve the integral }I=\int 3^{-2x}dx\)

\(I=\int3^{-2x}dx\)

\(let\ -2x=t\)

\(-2dx=dt\)

\(dx=\frac{dt}{-2}\)

\(I=\frac{-1}{2}\int 3^tdt\)

\(I=\frac{-1}{2}(\frac{3^t}{\ln|3|})+C\)

\(I=\frac{-1}{2}(\frac{3^{-2x}}{\ln3})+C\)

\(I=\frac{-1}{2(\ln3.3^{2x})}+C\)

\(I=\int3^{-2x}dx\)

\(let\ -2x=t\)

\(-2dx=dt\)

\(dx=\frac{dt}{-2}\)

\(I=\frac{-1}{2}\int 3^tdt\)

\(I=\frac{-1}{2}(\frac{3^t}{\ln|3|})+C\)

\(I=\frac{-1}{2}(\frac{3^{-2x}}{\ln3})+C\)

\(I=\frac{-1}{2(\ln3.3^{2x})}+C\)