How to Solve Integrals with a Linear Denominator?

Thread starter briton
Start date Feb 15, 2005
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Dx Integral

AI Thread Summary

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.

Feb 15, 2005

briton

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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Feb 15, 2005

arildno

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Hint: Add to the numerator 0=4-4

Feb 15, 2005

briton

erm so you get
∫ 4/(4-x) dx - ∫1 dx ?

Feb 15, 2005

arildno

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That was the idea, yes.

Feb 15, 2005

briton

cheers!

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