Problem

Evaluate the integral. $ \displaystyle \int \f…

03:15

Question

Answered step-by-step

Problem 20 Medium Difficulty

Evaluate the integral.

$ \displaystyle \int x \tan^2 x dx $

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Wen Zheng

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 1

Integration by Parts

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

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

Video Transcript

The problem is evaluated the integral x times standard x, squared dx, for this problem. First, we can write that this integral is equal to integral x m. O n in the x squared is equal to second x squared minus 1 point. This is equal to integral of x times second x, squared dx minus the integral of x. Now we compute this integral to the integral of x times second x, squared dx, for this integral, we will use method of integration by powers. The formula is integral of u times. Prime dx is equal to: u times, v minus integral of? U prime, for this problem we can write. U is equal to x and the prime is equal to second x square. Then prime is equal to 1 and v is equal to tan, and now this integral is equal to u times b. So this is x times tan ant x, minus the integral you prim times v. So this is tangent x, dx minus the tenor x d x is 1 half x square and the integral of tenant x x. This is the integral of sine x over cosine x. We can use? U substitution that? U is equal to cosine, x and d? U is equal to negative sine x x, so this is equal to the integral of negative. 1 number? U d! U s! This is negative n have absolute value of u so this is absolute value of cosine x. So this is equal to x, tangent, x, minus minus negative point. So this is as an absolute value of cosine x, minus 1, half x square and plus constant number c.

Get More Help with this Textbook

James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups

Study with other students and unlock Numerade solutions for free.

Problem

Evaluate the integral. $ \displaystyle \int \f…

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 2 / BC Educators

Heather Zimmers

Caleb Elmore

Samuel Hannah

Michael Jacobsen

Calculus 2 / BC Courses

Recommended Videos

Watch More Solved Questions in Chapter 7

Video Transcript

James Stewart

Calculus: Early Transcendentals

Heather Zimmers

Caleb Elmore

Samuel Hannah

Michael Jacobsen

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus: Early Transcendentals

Heather Zimmers

Caleb Elmore

Samuel Hannah

Michael Jacobsen

James StewartCalculus: Early Transcendentals

Heather Zimmers

Caleb Elmore

Samuel Hannah

Michael Jacobsen

James Stewart

Calculus: Early Transcendentals