How to Solve Integrals with a Linear Denominator?

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Homework Help Overview

The original poster presents an integral problem involving the expression ∫ x/(4-x) dx, seeking assistance with the approach to solve it. The context is calculus, specifically focusing on integration techniques with linear denominators.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the potential to manipulate the integral by adjusting the numerator, with one suggesting the addition of a term to facilitate integration. Another participant explores the idea of breaking the integral into simpler components.

Discussion Status

The discussion is active, with participants sharing hints and confirming ideas. There is a collaborative exploration of different approaches to the integral, though no consensus or final method has been established yet.

Contextual Notes

Participants are navigating the problem with the understanding that full workings or detailed steps are not to be provided, adhering to the forum's guidelines on homework help.

briton
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quite simple but need some help:

∫ x/(4-x) dx.


when there's ∫f'(x)/f(x) you can use natural log but what about this


full workings or some tips anyone?


Thanks.
 
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Hint: Add to the numerator 0=4-4
 
erm so you get
∫ 4/(4-x) dx - ∫1 dx ?
 
That was the idea, yes.
 
cheers!






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