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

1 Answer
Dec 1, 2016

#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#