What is the antiderivative of $e^(-3x)$ ?

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Answer 1 · 2015-09-08T15:40:37

The general antiderivative is $-1/3 e^(-3x)+C$ . We can also write the answer as $int e^(-3x)\ dx=-1/3 e^(-3x)+C$

This is just a matter of reversing the fact that, by the Chain Rule, $d/dx(e^(kx))=k*e^(kx)$ and also using "linearity".

Alternatively, you can use the substitution $u=-3x$ , $du=-3\ dx$ to write $int e^(-3x)\ dx=-1/3 int e^(u)\ du=-1/3 e^(u)+C=-1/3 e^(-3x)+C$

What is the antiderivative of e^(-3x)e^(-3x)?