Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
Related questions
Question
![Evaluate the indefinite integral.
dx
1 + x10
Step 1
x4
We must decide what to choose for u. If u = f(x), then du = f '(x) dx, and so it is helpful to look for some expression in
dx for which the derivative is also present, though perhaps missing a
1 + x10
constant factor.
Finding u in this integral is a little trickier than in some others.
We see that 1 + x10 is part of this integral, but the derivative of 1 + x10 is 10x
which is not present in the integrand.
109
4
However, notice that the x4 in the numerator is close to the derivative of x, which is 5x
5,4
Step 2
If we choose u = x5, thenx10
4.
and du = 5x
|dx.
574
=
x4
x4
1
If u = x is substituted into
dx, then we have
dx =
dx).
1 + x10
1 + x10
1 + u²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F435327ce-ad1d-47b0-9d05-42b05e19b7ae%2F1698b18d-17ce-4179-b1b7-2800687cc8f0%2Ftb4u8n5_processed.png&w=3840&q=75)
Transcribed Image Text:Evaluate the indefinite integral.
dx
1 + x10
Step 1
x4
We must decide what to choose for u. If u = f(x), then du = f '(x) dx, and so it is helpful to look for some expression in
dx for which the derivative is also present, though perhaps missing a
1 + x10
constant factor.
Finding u in this integral is a little trickier than in some others.
We see that 1 + x10 is part of this integral, but the derivative of 1 + x10 is 10x
which is not present in the integrand.
109
4
However, notice that the x4 in the numerator is close to the derivative of x, which is 5x
5,4
Step 2
If we choose u = x5, thenx10
4.
and du = 5x
|dx.
574
=
x4
x4
1
If u = x is substituted into
dx, then we have
dx =
dx).
1 + x10
1 + x10
1 + u²
![Step 3
We must also convert x4 dx into an expression involving u.
1
Using du = 5x4 dx, then we get xª dx =
1
du.
Step 4
x4
1
1
1
Now, if u = x5, then
dx =
du
du.
1 + u?
1 + x10
1 + u
12
5
1
1
This evaluates as
+ C.
du =
1 + u2
Submit
Skip (you cannot come back)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F435327ce-ad1d-47b0-9d05-42b05e19b7ae%2F1698b18d-17ce-4179-b1b7-2800687cc8f0%2Fsm9ytze_processed.png&w=3840&q=75)
Transcribed Image Text:Step 3
We must also convert x4 dx into an expression involving u.
1
Using du = 5x4 dx, then we get xª dx =
1
du.
Step 4
x4
1
1
1
Now, if u = x5, then
dx =
du
du.
1 + u?
1 + x10
1 + u
12
5
1
1
This evaluates as
+ C.
du =
1 + u2
Submit
Skip (you cannot come back)
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Functions and Change: A Modeling Approach to Coll…](https://www.bartleby.com/isbn_cover_images/9781337111348/9781337111348_smallCoverImage.gif)
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781337282291/9781337282291_smallCoverImage.gif)
![Functions and Change: A Modeling Approach to Coll…](https://www.bartleby.com/isbn_cover_images/9781337111348/9781337111348_smallCoverImage.gif)
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781337282291/9781337282291_smallCoverImage.gif)