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Integrate each of the given functions.$$\int_{1}^{3} 3 e^{2 x}\left(e^{-2 x}-1\right) d x$$

$6-\frac{3}{2}\left(e^{6}+e^{2}\right)$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 3

The Exponential Form

Integrals

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Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

03:40

Use substitution to find e…

01:15

01:04

Evaluate each integral.

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02:35

00:55

02:20

$$\text { Integration by p…

01:53

Evaluate each definite int…

01:18

02:34

mhm. We want to evaluate the integral given on the right as Andrew of 1233 Each of the two X times either of the two x minus one dx. Or as I've written to make simpler three times. Andrew grew from 1 to 3 of one minus either the two X. Ds. This question assessing our knowledge of methods of integration in particular is testing our knowledge of the newfound method that we recently learned calls exponential integration. As a formula here states exponential integration gives that the integral of either the U. D. U. Is each of you plus C. So if we can identify you and D. U. And are given integral we can go ahead and solve this formula. So are integral from 1 to 3 of 102 X is actually two integral. One of integral. 11 of integral negative two X. So for the negative each of the two X integral we have U equals two X. Do you equals two dx. Those were missing a factor of negative two and are negative two X integral. Which means that we can evaluate or in google S three X. From 1 to 3 minus three half integral. Either you do you or six minus three half. Even the two X. From 1 to 3 or six minus three half times even six minutes. E two or E squared.

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