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Integrate each of the functions.$$\int \frac{\left(1+3 e^{-2 x}\right)^{4} d x}{6 e^{2 x}}$$

$-\frac{1}{180}\left(1+3 e^{-2 x}\right)^{5}+C$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 1

The General Power Formula

Integrals

Missouri State University

Harvey Mudd College

Idaho State University

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

03:13

Evaluate each integral. $$…

01:53

Evaluate each definite int…

01:18

01:04

Evaluate each integral.

02:15

02:34

03:40

Use substitution to find e…

01:15

04:45

$$\text {Evaluate the foll…

04:50

Yeah. We want to evaluate the following the integral from one plus three E. The negative to actually four D. X. Divided by six. Each of the two X. This question is challenging our understanding of methods of integration. In particular. It's challenging our understanding of our recently learned method called the power Rule for integration. The powerful states that the integral of U. To the N. D. U. Is U. To the endless one over endless ones. Let's see. So if we can identify you, do you And and in this problem we can solve since one plus three equals negative two X. To the fourth is in parentheses raising power four and it has derivative negative 62 X. Or rather than negative two X. We must have you as one plus three. Either negative two X. Do you as negative six negative two X. The X and n equals four. In this integral we have an extra factor of negative 36. So we must have that are integral is negative 1/36 times 1/5 plus one times one plus three negative two X plus C. Or negative one over 100 and 81 plus three E. To the negative two extra 50 plus C.

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