# Evaluate the following integrals. Include absolute values only when needed. ∫3−2xdx

coexpennan

## Answered question

2021-02-22

Evaluate the following integrals. Include absolute values only when needed.

$\int {3}^{-2x}dx$

### Answer & Explanation

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

$I=\int {3}^{-2x}dx$

$let\text{}-2x=t$

$-2dx=dt$

$dx=\frac{dt}{-2}$

$I=\frac{-1}{2}\int {3}^{t}dt$

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

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

$I=\frac{-1}{2(\mathrm{ln}{3.3}^{2x})}+C$

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