# Evaluate the following integrals. Include absolute values only when needed. int 3^{-2x}dx

Question
Integrals
Evaluate the following integrals. Include absolute values only when needed.
$$\int 3^{-2x}dx$$

2021-02-23
$$\text{We have to solve the integral }I=\int 3^{-2x}dx$$
$$I=\int3^{-2x}dx$$
$$let\ -2x=t$$
$$-2dx=dt$$
$$dx=\frac{dt}{-2}$$
$$I=\frac{-1}{2}\int 3^tdt$$
$$I=\frac{-1}{2}(\frac{3^t}{\ln|3|})+C$$
$$I=\frac{-1}{2}(\frac{3^{-2x}}{\ln3})+C$$
$$I=\frac{-1}{2(\ln3.3^{2x})}+C$$

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