What is the antiderivative of #e^(2x)#?
2 Answers
Antiderivative is another name for the Integral( if by some misfortune you didnt know)
So,
You can see that
that is
It follows :
NOTE: this is the same as letting
Generally,
It is
You can certainly use the technique of integration by substitution (reversing the chain rule) to find this, you can also reason as follows:
The antiderivative of
But we know some things about derivatives at this point of the course. Among other things, we know that the derivative of
So we know that the drivative of
We also know that constant factors just hang out in front when we take derivatives, so if we stick a
Note
An important consequence of the Mean Value Theorem is that a function whose derivative is
Therefore, any function that has derivative