Integral Help: 1/((4x^2)+(4x)+5)

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Homework Help Overview

The discussion revolves around the integration of the function 1/((4x^2)+(4x)+5), focusing on the challenges presented by the denominator's structure and the nature of the integral.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the difficulty of factoring the denominator and the implications of a complex discriminant. There is a suggestion to complete the square and a mention of a potential u-substitution leading to a form resembling an arctangent integral.

Discussion Status

Some participants have offered guidance on completing the square and have identified a possible substitution. There is an acknowledgment of the need for careful selection of substitution, but no consensus has been reached on the final approach.

Contextual Notes

Participants note that the original problem lacks certain details, particularly in the setup of the attempt at a solution. The discussion reflects a collaborative effort to clarify the problem and explore various methods without arriving at a definitive solution.

tmclary
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Homework Statement



Integrate the indefinite integral of 1/((4x^2)+(4x)+5)

Homework Equations





The Attempt at a Solution

 
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tmclary said:

Homework Statement



Integrate the indefinite integral of 1/((4x^2)+(4x)+5)
I assume you mean find the indefinite integral. You also forgot to fill in the following two sections, in particular the final one:
tmclary said:

The Attempt at a Solution

 
Sorry, I have no clue how to get started. The denominator won't factor (at least to linear factors w/ integral coefficients) and the discriminant is complex anyway. So if it's a partial fraction type solution, how do you get started? Thanks.
 
Try completing the square of the denominator.
 
So 1/(4x^2)+4x+5 =1/((2x+1)^2)+4 and I make a u-sub. Looks like tan^-1 type integral. Correct?
 
tmclary said:
So 1/(4x^2)+4x+5 =1/((2x+1)^2)+4 and I make a u-sub. Looks like tan^-1 type integral. Correct?
Looks good to me :approve:. Choose your substitution carefully.
 
Thanks for your help, Def & Hoot!
 
tmclary said:
Thanks for your help, Def & Hoot!
A pleasure :smile:
 
http://www.4nw.net/s_thumbnailer-6-2008/hb6z6g1g.JPG
 
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