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Integrate each of the given functions.$$\int \sqrt{\tan ^{2} 2 x+1} d x$$

$\frac{1}{2} \ln |\sec 2 x+\tan 2 x|+C$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 4

Basic Trigonometric Forms

Integrals

Missouri State University

Oregon State University

Harvey Mudd College

University of Nottingham

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

01:12

Evaluate the integrals.

03:31

$$\text { Integration by p…

03:11

Evaluate each of the follo…

00:59

Evaluate the integrals usi…

00:58

Evaluate the indicated int…

00:30

02:19

Evaluate the integral.…

03:47

Calculate the integral.

00:41

Evaluate the following int…

Uh huh. We want to integrate the following expression. The integral or rather the indefinite integral of the square root of can square. To expose one DX as I'd be written on the right by tricking metric identity. Town square to expose one is equal to see Camp square two X. So are integral is the square root of C. Can't square two X. Dx or C can't two X dx. We're going to have to rely on methods of integration to solve particularly we're going to use the method known as trigger metric integral. So you should geometric intercultural properly we have to identify which of the 10 integral Justin here has the same form as are integral. Then we can plug into the given solution to solve so for integral where she can't square two X. Dx. We are looking for the form of C. Can you do you? So this corresponds to do equation nine. Listen here. Thus for U equals two X two U equals two dx. Our initial integral is missing a factor of two, which we carry over the solution as follows. So integral has solution one half Ln absolute values. You can't do expose 10 2 X plus C the concept of integration.

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