Problem

Evaluate the integral. $ \displaystyle \int_0^…

01:31

Problem 36 Medium Difficulty

Evaluate the integral.

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

Answer

$-\cot x-\ln |\cot x+\csc x|+\csc x-\ln |\sin x|+C$

Topics

Integration Techniques

Book Cover for Calculus: Early Tra…

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.

Catherine R.

Missouri State University

Anna Marie V.

Campbell University

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

for this integral, luscious Tara. I re ready and then multiplying the numerator and denominator both. Bye, Let's do one minus co site. What So schools and simplify that. So multiply out numerator and the nominees are separately on the bottom one. Minus co sign squared Attack one minus cosa. Next, Plus I kn minus sign times Co sign running out of room here times Cosette Nix. And here we can rewrite. This is Science Square. That's one of your dragon identities. So it's good and split this into foreigner rules. What? So the first Herman over sine squared, then co sign science weird on the bottom for all these terms, then here we have sine X over science. Where do you see that? You could cancel one of those signs and then finally, our last term side Times co sign science Weird again. Cancel one of those signs here is Well, oh, so let's go to the next page and then simplify each of these fractions. That's the first thing, and we're off to re writing it. Second integral, you can go ahead and do a use of there if you want to, or you could just rewrite it as co tangent times because he can. Then the next one. This was the one over sign cause he can't minus. And then we have co sign over, Sign attention. And we know the answer to each of these these air just tricking the rules. So here, for the first one, we know it's negative. Attention X, then hear this week, plus course he can. And then over here we get a minus ln plus coach engine. And then over here we'LL have a minus natural log of sign. Let's add that constancy and and there's a final answer.

JH

J H.

Topics

Integration Techniques

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 5

Strategy for Integration

Top Calculus 2 / BC Educators

Grace H.

Numerade Educator

Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Caleb E.

Baylor University