How Do You Solve Integration Using Partial Fractions?

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Homework Help Overview

The discussion revolves around the integration of the rational function (4x^2 + 3x + 6)/(x^2(x+2)) using partial fractions. Participants are exploring the setup and execution of the partial fraction decomposition method.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the decomposition of the rational function into partial fractions, with one suggesting the form A/x + B/x^2 + C/(x+2). There are attempts to equate coefficients from the resulting equation to solve for A, B, and C. Some participants question the clarity of the original poster's setup and suggest alternative methods, including obtaining the numerator as a derivative of the denominator.

Discussion Status

The discussion is active, with participants providing feedback on the original poster's approach and suggesting different perspectives on the problem. There is recognition of potential confusion in the method used, and some participants are encouraging further exploration of the problem.

Contextual Notes

There is a lack of provided equations or specific methods from the original poster, which may affect the clarity of the discussion. The original poster expresses uncertainty about their solution, indicating a need for clarification and guidance.

noobie!
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Homework Statement


integrate (4x^2 + 3x + 6)/x^2 (x+2) dx


Homework Equations


don't have sorry..


The Attempt at a Solution


firstly = A/x + B/x^2 + C /x+2 , = A(x^2)(x+2) + B(x)(x+2) + C(x)(x^2) equating with the 4x^2 + 3x + 6,then i integrate it,but my ans turn out to be wrong..so could you please rectify my mistakes..thanks
 
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Hi noobie! :smile:
noobie! said:
(4x^2 + 3x + 6)/x^2 (x+2) dx

= A/x + B/x^2 + C /x+2 , = A(x^2)(x+2) + B(x)(x+2) + C(x)(x^2) equating with the 4x^2 + 3x + 6

Nooo … too many x's! :wink:

get some sleep :zzz:

then try again! :smile:
 
Try to obtain the numerator as a derivative of the denominator. And then the extra term which you get try to break it in simple parts.
 
Hi Noobie,

noobie! said:

Homework Statement


integrate (4x^2 + 3x + 6)/([/color]x^2 (x+2))[/color] dx


Homework Equations


don't have sorry..


The Attempt at a Solution


firstly = A/x + B/x^2 + C /x+2 , = A(x^2)(x+2) + B(x)(x+2) + C(x)(x^2) equating with the 4x^2 + 3x + 6,then i integrate it,but my ans turn out to be wrong..so could you please rectify my mistakes..thanks
If you have

\frac{4x^2+3x+6}{x^2(x+2)} = \frac{A}{x} + \frac{B}{x^2} + \frac{C}{x+2}

then multiplying through gives

4x^2 + 3x + 6 = Ax(x+2) + B(x+2) + Cx^2.

Now you can equate coefficients as you intended to.
 
Unco the method which you did is the same which noobie has presented. It contains too many x's. There is an another nice way of doing it.
 
FedEx said:
Try to obtain the numerator as a derivative of the denominator. And then the extra term which you get try to break it in simple parts.

ok,i understand..thanks a lot..
 
noobie! said:
ok,i understand..thanks a lot..

Understood! What did you do with the remaining term?
 

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