How to Integrate Fractions with Substitution?

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Homework Help Overview

The discussion revolves around integrating a fraction involving a polynomial in the numerator and a power of x in the denominator. The subject area is calculus, specifically focusing on integration techniques.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts substitution with u=5x-6 but questions the setup. There are suggestions to expand the numerator and separate the terms to simplify the integration process.

Discussion Status

Participants are exploring different methods to approach the integration problem. Some have offered guidance on expanding the numerator, while the original poster expresses uncertainty about the best path forward.

Contextual Notes

The original poster indicates a lack of clarity in their approach and is considering whether factoring might complicate the problem further.

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Homework Statement


Integrate: (5x-6)2/x1/2


Homework Equations





The Attempt at a Solution


I tried substitution, letting u=5x-6 and then plugging that in but realized that I didn't have the proper set up for that. I'm unsure how to go about this; should I factor out the numerator or would that only make things more difficult?
 
Last edited:
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Multiply (5x-6)^2 out and separate the equation into three terms.
 
Expand the numerator and then it should be easy.
 
It was very easy indeed. thanks.
 

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