Integrating Rational Functions: Is It Possible?

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Discussion Overview

The discussion revolves around the integration of the rational function \(\frac{x+1}{x-1}\). Participants explore whether it is possible to evaluate this integral and share their thoughts on the algebraic manipulation involved.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant asks if the integral \(\int \frac{x+1}{x-1} \, dx\) is possible, indicating a lack of clear answers found in their search.
  • Another participant provides an algebraic manipulation of the function, expressing it as \(1 + \frac{2}{x-1}\), suggesting a potential simplification for integration.
  • Several participants request further explanation and a complete solution to the integral, indicating confusion about the integration process.
  • One participant comments on the importance of basic algebra skills for tackling integration problems, implying that understanding the manipulation of functions is crucial.
  • Another participant expresses a desire to read ahead in their textbook, indicating a proactive approach to learning despite their current struggles with the material.

Areas of Agreement / Disagreement

There is no consensus on the integration of the function, as participants express varying levels of understanding and request further clarification. Some participants emphasize the need for foundational skills, while others focus on the specific integral at hand.

Contextual Notes

Participants exhibit uncertainty regarding the integration process and the necessary algebraic manipulations. There are unresolved questions about the anti-derivative of specific functions mentioned in the discussion.

Who May Find This Useful

This discussion may be useful for students learning about integration techniques, particularly those struggling with rational functions and the importance of algebra in calculus.

Oblivionator
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Evaluate the integral:

int ((x+1)/(x-1)) dx

is this possible?

i tried searching for this but there was no answer
 
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(x+1)/(x-1)=[(x-1)+2]/(x-1)=1+2/(x-1)

Have you ever seen a function g such that g'=f'/f
?
 
(x+1)/(x-1)=[(x-1)+2]/(x-1)=1+2/(x-1)

could you please explain this?

im having problems integrating ((x+1)/(x-1)) dx
 
no wait, could you please fully solve the problem?
 
Oblivionator said:
(x+1)/(x-1)=[(x-1)+2]/(x-1)=1+2/(x-1)

could you please explain this?

im having problems integrating ((x+1)/(x-1)) dx
If you cannot do basic algebra you are going to have great difficulty integrating any function. The above is just simple division. And you can see it is true just by adding the fractions on the right hand side.

Oblivionator said:
no wait, could you please fully solve the problem?
It would be much better for you to try yourself. Do you know the anti-derivative of 1/x?
 
no, not yet but thank you
 
Then why in the world are you trying to do this problem?
 
Sorry, I just like to read ahead in my textbook
 
Good! Just don't be upset if you are often puzzled!:smile:
 

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