How do I find the antiderivative of $f(x)=e^(-5x)$ ?

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Answer 1 · 2018-04-07T19:05:29

$inte^(-5x)dx=-1/5e^(-5x)+C$

In general, the antiderivative of an exponential in the form

$inte^(ax)dx=1/ae^(ax)+C$ where $a$ is some non-zero constant.

This makes sense -- were we to differentiate $1/ae^(ax)+C,$ we'd get $a/ae^(ax)=e^(ax)$ , making this a suitable antiderivative.

Thus,

$inte^(-5x)dx=-1/5e^(-5x)+C$

How do I find the antiderivative of f(x)=e^(-5x)f(x)=e^(-5x)?