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Integrate each of the given functions.$$\int\left(2 \cos ^{2} 4 x-1\right) d x$$

$\frac{1}{8} \sin 8 x+C$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 4

Basic Trigonometric Forms

Integrals

Missouri State University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

05:53

In mathematics, an indefin…

40:35

In mathematics, integratio…

00:54

Find each integral.$$\…

01:11

Evaluate the following int…

03:53

01:19

Evaluate the indicated int…

02:23

Evaluate the integrals.

01:38

Evaluate the integrals…

01:21

Evaluate the integral.…

02:06

02:08

01:05

01:23

00:55

03:43

01:07

03:37

01:14

00:49

Now evaluate the following…

03:24

we want to evaluate the given integral which is the indefinite into groups of two. Cosine squared for x minus one dx. This question is testing our knowledge of methods of integration. We've already learned about the power roll log rule and exponential rules in this problem we're being tested on our ability to use trig and metric integral. Remember the chicken metric integral? Are one through 10 listed here. When you define which one matches the form of are given function. So because we have to consent square four x minus one. We're actually gonna have to separate integral. Is the first one? Is this two co squared export X for this? We're going to be using our coastline integral. So that means we're gonna be using rules three here. The reason we're using the C can't squared integral rather than the coast an integral I just mentioned is because co sign here is squared. We have no integral from one through 10 that does cosine squared. So we have to do one over cosine squared, which is you cant square. Therefore we use, well, three for U equals four X d u equals 40 X. Thus we can plug in and solve our integral ass. Israel's Tuesday can't square four X minus one dx is one half 10, 4 x minus X plus C.

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