Problem

Evaluate the integral. $ \displaystyle \int x …

02:33

Problem 78 Medium Difficulty

Evaluate the integral.

$ \displaystyle \int \frac{1 + \sin x}{1 - \sin x}\ dx $

Name: evaluate the integral displaystyle int frac1 sin x1 sin x dx
Uploaded: 2018-02-11
Duration: 2 min 39 s
Channel: Numerade
Description: Evaluate the integral. $ \displaystyle \int \frac{1 + \sin x}{1 - \sin x}\ dx $

Answer

$\int \frac{1+\sin x}{1-\sin x} d x=2 \tan x+2 \sec x-x+C$

Topics

Integration Techniques

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 5

Strategy for Integration

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

Grace H.

Heather Z.

Oregon State University

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University

Watch More Solved Questions in Chapter 7

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Problem 73

Problem 74

Problem 75

Problem 76

Problem 77

Problem 78

Problem 79

Problem 80

Problem 81

Problem 82

Problem 83

Problem 84

Video Transcript

Let's just start off by rewriting. That's right. This is two plus and then sine minus one. And then let's rewrite this. So we have one, say two and then one minus sign and then we have, unless free right, This's negative. One minus sign. No hearing. Good. Cancel. So for this one, let's multiply. It's happened, but and then for the second one, this is just in general. Negative one. So for the first but one plus sign and then here that equals one minus signs clear, which is co sign square. So let's put that in. And then here, that should have been a plus from this both pluses. And then this integral x minus x ten plus e. Now we could rewrite this. So all I did here it just break this into two fractions and then rewrite these as these two terms respectively. And then we could integrate this two ten to see can't and then our minus X and plus E. And that's our answer

J H.

Topics

Integration Techniques

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 5

Strategy for Integration

Problem

Evaluate the integral. $ \displaystyle \int x …

Problem 78 Medium Difficulty

Evaluate the integral.

$ \displaystyle \int \frac{1 + \sin x}{1 - \sin x}\ dx $

Answer

$\int \frac{1+\sin x}{1-\sin x} d x=2 \tan x+2 \sec x-x+C$

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 2 / BC Educators

Grace H.

Heather Z.

Kayleah T.

Caleb E.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Watch More Solved Questions in Chapter 7

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 2 / BC Educators

Grace H.

Heather Z.

Kayleah T.

Caleb E.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos