Integral of x/x^2 + 2x+2: Solving Tips

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Homework Help Overview

The discussion revolves around the integral of the expression x/(x^2 + 2x + 2). Participants are exploring different methods to approach the problem, including completing the square and substitution techniques.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss completing the square and substituting variables, questioning the presence of x in the numerator after substitution. There is also a suggestion to consider trigonometric substitution.

Discussion Status

The discussion is ongoing, with participants sharing their attempts and questioning the correctness of their approaches. Some guidance has been offered regarding the use of trigonometric substitution, and there are multiple interpretations of the problem being explored.

Contextual Notes

There is a noted correction regarding the expression being integrated, as one participant clarifies the correct form of the integral. This indicates a potential misunderstanding of the problem setup among participants.

apiwowar
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integral of x/x2 +2x+2

so the first thing i did was complete the square which gave me

integral of x/(x-1)2+1

then i tried substituting by w=x-1 and dw = dx but that leaves the x on the top.

what am i not seeing?
 
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apiwowar said:
integral of x/x2 +2x+2

so the first thing i did was complete the square which gave me

integral of x/(x-1)2+1

then i tried substituting by w=x-1 and dw = dx but that leaves the x on the top.

what am i not seeing?

[tex]\frac{x}{x^2} + 2x +2 = \frac{1}{x} +2x +2[/tex]

Just do each of those separately.
 
my bad its x/(x2+2x+2)

not x/x2+2x+2
 
Try trigonometric substitution after completing the square. You completing the square is wrong btw, it should be a +.
 

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