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

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

Question
Integrals
asked 2021-02-22
Evaluate the following integrals. Include absolute values only when needed.
\(\int 3^{-2x}dx\)

Answers (1)

2021-02-23
\(\text{We have to solve the integral }I=\int 3^{-2x}dx\)
\(I=\int3^{-2x}dx\)
\(let\ -2x=t\)
\(-2dx=dt\)
\(dx=\frac{dt}{-2}\)
\(I=\frac{-1}{2}\int 3^tdt\)
\(I=\frac{-1}{2}(\frac{3^t}{\ln|3|})+C\)
\(I=\frac{-1}{2}(\frac{3^{-2x}}{\ln3})+C\)
\(I=\frac{-1}{2(\ln3.3^{2x})}+C\)
0

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