Integrate ∫ 4e^x dx

Step by step

The question

Question: find the integral of 4eˣ.

1 The rules

First, e to the x.

Its derivative is eˣ itself: its slope equals its height.

So its integral is eˣ + C too.

2 Integrate

e to the x stays e to the x.

The 4 waits in front.

Add C: the slope cannot tell us a number added on the end.

So the answer is 4eˣ + C.

3 Check

Let's check: take the derivative of our answer.

The numbers cancel, and we get 4eˣ: the question again.

Right!

Let's look back.

First: the rules.

Then: integrate.

Last: check.