Problem

Evaluate the indefinite integral as an infinite s…

02:37

Problem 54 Hard Difficulty

Evaluate the indefinite integral as an infinite series.

$$ \int x^2 \sin (x^2) dx $$

Answer

$\sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{(2 n-1) !} \cdot \frac{x^{4 n+1}}{(4 n+1)}$

Topics

Sequences

Series

Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 10

Taylor and Maclaurin Series

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

Watch More Solved Questions in Chapter 11

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

Problem 85

Problem 86

Video Transcript

So you value this indefinite Negro as an infant. A serious. All right. So I because too squirm terms the experience of this part. So it's gonna be in from one too, if any. Next square to the power two minus one over two minutes. One times months went off on months one. So this is Thies takes Baron sign t and we said ticks and swear, Yes. So this is our This is too much for Taro, actually. And here have the X. It is really correct. And a close too, which in the order of indigo and some So it becomes who actually pour for in minus two plus two is power foreign over two minutes with tutorial and natural wants apartment minus one the X and this is just equal to and from one to infinity that you want north and minus one over two minutes with pictorial And what isthe the integral of four x four Foreign. The excess Libby Extra car for us. One over Foreign press one. And this is over. Result it ISS and their finance. Siri's

Yiming Z.

University of Illinois at Urbana-Champaign