Partial fractions integral

  • #1
462chevelle
Gold Member
305
9

Homework Statement


integral(0>1) of (x^2+x)/(x^2+x+1)dx

Homework Equations


Factor denominator, and set numerator with A,B,C, etc. multiply both sides by the common denominator.

The Attempt at a Solution


Since the denominator won't factor at all I don't really know where to start, I could rewrite it into 2 fractions or factor the numerator. Both useless though, I can't find an example in my book for this type of problem.

Any hints on the first step?
Thanks.
 

Answers and Replies

  • #2
PeroK
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
16,112
8,131
It's not partial fractions. The numerator and denominator are similar. Can you make use of that?
 
  • #3
462chevelle
Gold Member
305
9
Almost, as far as I can tell, if I take the denominator to be u I get du/(2x+1)=dx then I can factor a x out of the numerator and i get x(x-1)/(u(2x+1)). Unless I'm missing or forgetting something.
 
  • #4
462chevelle
Gold Member
305
9
Sorry, I'm bad at latex so I'm posting a picture of my work. I can't remember if that is allowed or not.
 

Attachments

  • #5
PeroK
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
16,112
8,131
How would you make the numerator the same as the denominator? Something very simple.
 
  • #6
462chevelle
Gold Member
305
9
You could add 2x+1 and that would be the derivative of the denominator. Then I would have to do that to the denominator. I'll see what I can figure out and post my work.
 
  • #7
PeroK
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
16,112
8,131
You're missing the obvious thing and going for more complicated things. What is the difference between the top and bottom?
 
  • #8
462chevelle
Gold Member
305
9
A constant and a sign.
 
  • #9
PeroK
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
16,112
8,131
Do you mean 1?
 
  • #10
462chevelle
Gold Member
305
9
Well, yes the constant would be 1. I just realized I made a typo on the first post, sorry. Its (x^2-x)/(x^2+x+1) the problem is correct in the picture I posted.
 
  • #11
PeroK
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
16,112
8,131
That makes the solution a lot easier you'll be glad to know!

Let me do the original one and see if that helps:

##\frac{x^2 + x}{x^2+x+1} = 1 - \frac{1}{x^2+x+1}##
 
  • #12
HallsofIvy
Science Advisor
Homework Helper
41,833
961
Since numerator and denominator have the same degree, first do the division to get a polynomial plus a fraction with numerator of lower degree than the denominator. Then complete the square in the denominator.
 
  • #13
462chevelle
Gold Member
305
9
HMM, this seems to make it easy. I would have never thought of that otherwise.
 

Attachments

  • #14
462chevelle
Gold Member
305
9
I think I got it, thanks. I would have been beating my head against the wall all day otherwise.
 

Attachments

  • #15
34,667
6,379
@462chevelle, since we saved you a whole day of beating your head against the wall, maybe you could devote some of that saved time to learning a bit of LaTeX? It's really not very hard. We have a brief summary here: https://www.physicsforums.com/help/latexhelp/

Here are a few of the things you could have used in your problem. Note that I have omitted the # # pairs (without the space) at the beginning and end in my examples below. I did that so that the LaTeX script remains visible.

Exponents:
x^2
e^{x + 1}

Fractions:
\frac{x^2 + x}{x^2 + x + 1}

Integrals:
\int 3x^2 dx

\int_0^3 e^{x + 1} dx
 

Related Threads on Partial fractions integral

  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
5
Views
3K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
4
Views
113
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
10
Views
5K
Top