Question

(1 point) The form of the partial fraction decomposition of a rational function is given below. \frac{x^2 + 4x + 12}{(x + 2)(x^2 + 4)} = \frac{A}{x + 2} + \frac{Bx + C}{x^2 + 4} A = B = C = Now evaluate the indefinite integral $\int \frac{x^2 + 4x + 12}{(x + 2)(x^2 + 4)} dx = $

          (1 point) The form of the partial fraction decomposition of a rational function is given below.
\frac{x^2 + 4x + 12}{(x + 2)(x^2 + 4)} = \frac{A}{x + 2} + \frac{Bx + C}{x^2 + 4}
A = 
B = 
C = 
Now evaluate the indefinite integral
$\int \frac{x^2 + 4x + 12}{(x + 2)(x^2 + 4)} dx = $
        
Show more…
(1 point) The form of the partial fraction decomposition of a rational function is given below.
(x^2 + 4x + 12)/((x + 2)(x^2 + 4)) = (A)/(x + 2) + (Bx + C)/(x^2 + 4)
A = 
B = 
C = 
Now evaluate the indefinite integral
∫(x^2 + 4x + 12)/((x + 2)(x^2 + 4)) dx =

Added by Agust-N S.

Close

Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
1 pointThe form of the partial fraction decomposition of a rational function is given below +4x+12 A Bx+C +2x2+4 2 2+4 A B a Now evaluate the indefinite integral +4x+12 dr +2x2+4
Close icon
Play audio
Feedback
Powered by NumerAI
David Collins Kathleen Carty
Danielle Fairburn verified

Bryan Lynn and 51 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

*

Key Concepts

-
Key Concept
Premium Feature
Explore the core concept behind this problem.
Play button
Key Concept
Premium Feature
Explore the core concept behind this problem.
Your browser does not support the video tag.

*

Recommended Videos

-
in-exercises-1-4-find-the-values-of-a-and-b-that-complete-the-partial-fraction-decomposition-fracx-1

In Exercises $1-4,$ find the values of $A$ and $B$ that complete the partial fraction decomposition. $$\frac{x-12}{x^{2}-4 x}=\frac{A}{x}+\frac{B}{x-4}$$

Calculus: Graphical, Numerical, Algebraic

Differential Equations and Mathematical Modeling

Logistic Growth

partial-fraction-decomposition-in-exercises-1-4-write-the-form-of-the-partial-fraction-decompositi-4

Partial Fraction Decomposition In Exercises $1-4,$ write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants. $$ \frac{2 x-1}{x\left(x^{2}+1\right)^{2}} $$

Calculus of a Single Variable

Integration Techniques, L'Hopital's Rule, and Improper Integrals

Partial Fractions

the-form-of-the-partial-fraction-decomposition-of-a-rational-function-is-given-below-2x25x4x5x24ax5bxcx242x25x4x5x24ax5bxcx24-aa-bb-cc-now-evaluate-the-indefinite-integral-2x25x4x5x24dx-93496

The form of the partial fraction decomposition of a rational function is given below. 2x^2+5x+4(x+5)(x^2+4)=A/(x+5)+(Bx+C)/(x^2+4) A= B= C= Now evaluate the indefinite integral. ∫(2x^2+5x+4)/((x+5)(x^2+4))dx=

Abdul W.


*

Recommended Textbooks

-
Calculus: Early Transcendentals

Calculus: Early Transcendentals

James Stewart 8th Edition
achievement 1,988 solutions
Calculus: Early Transcendentals

Calculus: Early Transcendentals

William Briggs, Lyle Cochran, Bernard Gillet 3rd Edition
achievement 1,303 solutions
Thomas Calculus

Thomas Calculus

George B. Thomas Jr. 14th Edition
achievement 1,955 solutions

*

Transcript

-
00:01 Okay, so for this problem, we are given that x minus 12 over x squared minus 4x is going to be equal to a over x over x minus 4.
00:18 Plus, b over x minus 4.
00:25 And so in order for us to add these two fractions together, they would have to share a denominator, right? so we can do that by multiplying a over x by x minus 4 over x minus 4, right? because that's essentially equal to 1, so we're not changing it.
00:49 And we can multiply b over x minus 4 by x over x over x, which is also equal to 1.
00:59 So it's not being changed.
01:01 And so this would give us ax minus 4 times a.
01:06 Over x squared minus 4x plus b x over x squared minus 4x okay so this tells us that a plus b times x must minus 4a over x squared minus 4x must be equivalent to x squared or so x minus 12 over x squared over x squared minus 4x so we're only really interested in the numerator here...
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Join the community

18,000,000+

Students on Numerade


Trusted by students at 8,000+ universities

Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever