WEBVTT

1
00:00:00.000 --> 00:00:03.402
Here is the problem: integral of 2 to the power x.

2
00:00:03.852 --> 00:00:10.505
Find the indefinite integral (antiderivative) of 2 to the power x with respect to x.

3
00:00:11.304 --> 00:00:12.686
Start with the integral.

4
00:00:13.136 --> 00:00:20.032
Exponential rule: the integral of aᵘ du equals aᵘ/ln a.

5
00:00:20.482 --> 00:00:23.524
Simplify and add the constant of integration.

6
00:00:24.324 --> 00:00:28.631
So the answer is 2 to the power x / ln(2) plus C.

7
00:00:29.081 --> 00:00:39.936
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
00:00:40.736 --> 00:00:46.669
Differentiated the answer and compared it with the integrand at 8 sample points, which checks out.