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Problem

Find the most general antiderivative of the funct…

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Problem 14 Easy Difficulty

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

$ f(t) = \dfrac{3t^4 - t^3 + 6t^2}{t^4} $


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Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives

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Derivatives

Differentiation

Volume

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Watch More Solved Questions in Chapter 4

Problem 1
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Problem 5
Problem 6
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Problem 8
Problem 9
Problem 10
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Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
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Problem 22
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Problem 25
Problem 26
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Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
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Problem 45
Problem 46
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Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
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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
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Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79

Video Transcript

I saw something has to find the most general anti derivative of the function after t oo Street to the fourth managed thank you while sixty squared over teeth report. So this may look like a complicated function, but luckily we have a very simple denominator. And now this decision is just a fact of simple fraction and sometimes is overlooked. So you can actually hear you. We can ask you break this up so you can do three to thirteen, fourth over tea for minus Team Cube. You know that, uh, over teacher afford plus sixty squared over two meters a fourth and now we can begin the simplifies. A teaching fourth of it is the fourth wall that just cancel And I can just three, two Cuba teeth to fourth. We do you subtract it, Toby T minus one more shirt just the same as one over tea and then to square two, then discovers us six over t squared. And now we can take the We did the interval of this, but I'm going to rewrite it in terms of the exponents of three to the minus teas or minus one half. I mean to the minus one and plus six T minus two. And now it could take the interval of this D key. And this is a lot easier game compared to death. Well, I'm just bring it over. So I was going to give a three t and then teasing minus one is going to the natural log of absolute knowledge of tea and minus two plus one. Well, that's negative. One and then over negative one. Well, that's just gonna minus six, Uh, T to the minus one and then this pussy, and this is our answer.

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Related Topics

Derivatives

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Top Calculus 2 / BC Educators
Grace He

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Kristen Karbon

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Lectures

Video Thumbnail

04:35

Volume - Intro

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

Video Thumbnail

06:14

Review

A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

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