Question

How do you integrate `\int e ^ { \frac { x } { 3} } d x`?

Answer 1

`inte^(x/3)dx=3e^(x/3)+C`

Explanation:

You need to remember that integration is the reverse of differentiation. So in this case we ask "what do we differentiate to get `" "e^(x/3)`?"

so what happens if we do `" "d/(dx)(e^(x/3))?`

using the chain rule we get

`" "d/(dx)(e^(x/3))?=1/3e^(x/3)`

so integration is simply adjust the constant.

`inte^(x/3)dx=3e^(x/3)+C`