Integral of -: (v^2+2v-1)/(v^3+v^2+v+1)

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Discussion Overview

The discussion revolves around finding the integral of the function \(- (v^2 + 2v - 1) / (v^3 + v^2 + v + 1)\). Participants explore methods for solving this integral, including partial fractions decomposition.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant asks how to find the integral of the given function.
  • Another participant suggests using partial fractions decomposition and notes that the denominator is divisible by \((v+1)\), leading to a simpler expression.
  • A third participant reiterates the factorization of the denominator as \((v+1)(v^2+1)\) and emphasizes that using partial fractions will simplify the problem.
  • A later reply humorously claims to have provided the same insight first, indicating a friendly competition among participants.

Areas of Agreement / Disagreement

Participants generally agree on the approach of using partial fractions for the integral, but there is no explicit consensus on the complete solution or further steps.

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how to find the integral of -: (v^2+2v-1)/(v^3+v^2+v+1)

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Partial fractions decomposition.

Note that the denominator is divisible by (v+1):
[tex](v^{3}+v^{2}+v+1)/(v+1)=v^{2}+1[/tex]
 


Notice that [tex]v^3+v^2+v+1=(v+1)(v^2+1)[/tex]. Use the method of partial fractions, once it's done it's very easy.
 


losiu99 said:
Notice that [tex]v^3+v^2+v+1=(v+1)(v^2+1)[/tex]. Use the method of partial fractions, once it's done it's very easy.
HA! I beat you to it!
We oldies are still the best! :biggrin:
 


Yeah, soo true :approve: Maybe next time... :wink:
 

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