Integration by Partial Fractions

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Homework Help Overview

The discussion revolves around the integration of the function 4x/(x^3+x^2+x+1) with respect to x. Participants are exploring methods to approach this integral, particularly focusing on the denominator's structure.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants express uncertainty about how to begin solving the integral, noting that the degree of the numerator is less than that of the denominator. There are suggestions to consider the denominator as a geometric sum and to explore partial fractions. Additionally, one participant mentions the possibility of factoring the denominator and refers to the rational root theorem.

Discussion Status

The discussion includes various attempts to identify a starting point for the integration problem. Some guidance has been offered regarding the geometric interpretation of the denominator and factoring possibilities. However, there is no explicit consensus on a single method or approach at this stage.

Contextual Notes

Participants are operating under the constraint of not needing a complete solution, but rather assistance in getting started with the problem. There is an emphasis on exploring different interpretations and methods without resolving the integral itself.

KTiaam
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Homework Statement



∫ 4x/(x^3+x^2+x+1) dx

The Attempt at a Solution



I really don't know where to start, you can't complete the square, the degree of the numerator is less than the denominator so you can't use long division to simplify it.

I can't really simplify the denominator as well, so I am stuck.

Help is greatly appreciated.!

Edit: I don't need you to work out the whole problem, i just need help getting started.
 
Last edited:
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If you will look hard at the denominator you will see that it is a geometric sum. You can replace that long expression with something simpler, which is the sum of the terms. Not sure what that would be? Look up geometric sum.

At that point maybe partial fractions will help.
 
KTiaam said:

Homework Statement



∫ 4x/(x^3+x^2+x+1) dx


The Attempt at a Solution



I really don't know where to start, you can't complete the square, the degree of the numerator is less than the denominator so you can't use long division to simplify it.

I can't really simplify the denominator as well, so I am stuck.

Help is greatly appreciated.!

Edit: I don't need you to work out the whole problem, i just need help getting started.

Try factoring the denominator. The rational root theorem says that there are only two possibilities for rational roots - and one of them does work.
 
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Solved. Thank you Mark
 

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