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

1 Answer
Apr 7, 2018

Answer:

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

Explanation:

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#