Question

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

Answer 1

`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`