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

1 Answer
Sep 8, 2015

Answer:

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#

Explanation:

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#