How do you find the antiderivative of $e^{- x}$ $e^-x$ ?

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How do you find the antiderivative of $e^{- x}$ $e^-x$ ?

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Answer 1 · 2016-11-16T05:55:44

$= - e^{- x} + C$ $= - e^(-x) + C$

Explanation:

Let
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$u (x) = e^{- x}$ $u(x) = e^(-x)$
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$d u (x) = - e^{- x} d x$ $du(x) = - e^(-x)dx$
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$\Rightarrow - d u (x) = e^{- x} d x$ $rArr - du(x) = e^(-x)dx$
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$\int e^{- x} d x$ $inte^(-x)dx$
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$= \int - d u (x)$ $= int-du(x)$
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$= - u (x) + C C$ $=-u(x) + C" " C$ is a constant
$" "$
$= - e^{- x} + C$ $= - e^(-x) + C$

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How do you find the antiderivative of $e^{- x}$ $e^-x$ ?

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How do you find the antiderivative of $e^{- x}$ $e^-x$ ?