coexpennan

2021-02-22

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

Bentley Leach

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

$-2dx=dt$
$dx=\frac{dt}{-2}$
$I=\frac{-1}{2}\int {3}^{t}dt$
$I=\frac{-1}{2}\left(\frac{{3}^{t}}{\mathrm{ln}|3|}\right)+C$
$I=\frac{-1}{2}\left(\frac{{3}^{-2x}}{\mathrm{ln}3}\right)+C$
$I=\frac{-1}{2\left(\mathrm{ln}{3.3}^{2x}\right)}+C$

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