How to Solve Integrals with a Linear Denominator?

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To solve the integral ∫ x/(4-x) dx, a useful technique involves manipulating the numerator by adding and subtracting a constant, specifically 0=4-4. This leads to the expression ∫ 4/(4-x) dx - ∫ 1 dx, which simplifies the integration process. The first part can be integrated using the natural logarithm, while the second part is straightforward. This method effectively breaks down the integral into manageable components. Understanding these techniques can enhance skills in solving integrals with linear denominators.
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 waht 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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