How do you find the antiderivative of $e^{- 2 x}$ $e^(-2x)$ ?

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Answer 1 · 2015-03-02T01:38:23

Starting from the integral:
$\int e^{- 2 x} d x =$ $inte^(-2x)dx=$

By substitution, you set $- 2 x = t$ $-2x=t$
so: $x = - \frac{t}{2}$ $x=-t/2$
and $d x = - \frac{1}{2} d t$ $dx=-1/2dt$

The integral becomes:

$\int e^{t} (- \frac{1}{2}) d t = - \frac{e^{t}}{2} + c$ $inte^t(-1/2)dt=-e^t/2+c$

going back to $x$ $x$ :
$= - \frac{e^{- 2 x}}{2} + c$ $=-e^(-2x)/2+c$

How do you find the antiderivative of e−2xe^(-2x)?