How to integrate int x/(x^2+1)dx

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Homework Help Overview

The discussion revolves around the integration of the function x/(x^2 + 1) with respect to x, a topic within calculus focusing on integration techniques.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster inquires about how to start the integration process, noting familiarity with a related integral. Some participants suggest using substitution, specifically u = x^2 + 1, and question the implications of this approach.

Discussion Status

Participants have explored the substitution method, with one confirming a potential solution. There is a note regarding the necessity of absolute values in the final expression, indicating a productive exchange of ideas.

Contextual Notes

There is a discussion about the conditions under which the function x^2 + 1 is always positive, which may influence the use of absolute values in the solution.

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[tex]\int{\left(\frac{x}{x^2 + 1}\right)\,dx}[/tex]

how to integrate?
i know [tex]\int{\left(\frac{1}{x^2 + 1}\right)\,dx}[/tex]
is tan^-1 x + C

how am i going to start answering this question
 
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try substituting u=x2+1, du=?
 


rock.freak667 said:
try substituting u=x2+1, du=?

meaning.. i should u integration by substitution?
 


Yes, try the u substitution.
 


got it..
1/2 ln |x^2 + 1| + C

correct?
 


That's right. One thing though: since x2 + 1 is always greater than 0, no absolute values are needed.
 

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