WEBVTT

1
00:00:00.000 --> 00:00:03.936
Here is the problem: integral e to the power x dx.

2
00:00:04.386 --> 00:00:10.551
Find the indefinite integral (antiderivative) of e to the power x with respect to x.

3
00:00:11.351 --> 00:00:12.837
Start with the integral.

4
00:00:13.287 --> 00:00:21.367
Exponential rule: the integral of eᵘ du equals eᵘ (divide by the inner slope).

5
00:00:21.817 --> 00:00:24.801
Simplify and add the constant of integration.

6
00:00:25.601 --> 00:00:28.376
So the answer is e to the power x plus C.

7
00:00:28.826 --> 00:00:39.890
An antiderivative F satisfies F prime of x equals f(x). Because the derivative of any constant is 0, every antiderivative differs by a constant C.

8
00:00:40.690 --> 00:00:46.402
Differentiated the answer and compared it with the integrand at 8 sample points, which checks out.