Problem

Find the most general antiderivative of the funct…

02:06

Problem 13 Easy Difficulty

Find the most general antiderivative of the function.
(Check your answers by differentiation.)

$ f(x) = \dfrac{1}{5} - \dfrac{2}{x} $

Name: find the most general antiderivative of the function check your answers by differentiation fx dfrac1
Uploaded: 2021-06-03
Duration: 1 min 9 s
Channel: Numerade
Description: Find the most general antiderivative of the function. (Check your answers by differentiation.) $ f(x) = \dfrac{1}{5} - \dfrac{2}{x} $

Answer

$$\left\{\begin{array}{ll}
\frac{1}{5} x-2 \ln |x|+C_{1} & \text { if } x<0 \\
\frac{1}{5} x-2 \ln |x|+C_{2} & \text { if } x>0
\end{array}\right.$$

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

Grace H.

Heather Z.

Oregon State University

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University

Watch More Solved Questions in Chapter 4

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

Video Transcript

So for this problem, we want to produce the most general anti derivative of the function And the function that we're given is 1/5 -2 over X. So f of x. because 1 5th -2 over X. And we want to remember that one over X, the anti derivative of that is going to be the natural log of X. So what this is going to give us is 1/5 x minus two times the natural log of the absolute value of acts. All right. There is going to be our final answer, but we want to remember that there is going to be a constant classy. Um and we just know that X cannot equal zero. So it's this right here where X cannot equal zero is supposed to be our final function. If we took a crime of X and chose a different value of C, we see that this is the exact same graph given to us.

Carson M.

California Baptist University

Topics

Derivatives

Differentiation

Volume

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives

Problem