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Integration homework problem help

  • Thread starter alexis36
  • Start date
8
0
1. Homework Statement
I have this equation:
integrate: dN/(4-2N)


2. Homework Equations



3. The Attempt at a Solution
I am understanding that the dN part just goes away and comes one on the top of the fraction. Then on the bottom, I am still left with 4-2N. I am simply saying that it is equal to ln|4-2N| .. however, I am told that it should be -1/2 ln(|4-2N|) . The -1/2 in front, is that coming from performing a chain rule? And if so, how do you get a chain rule out of this?
 

rock.freak667

Homework Helper
6,230
31
[tex]\int \frac{1}{4-2N} dN[/tex]

Let u=4-2N (*) ;[itex]\frac{du}{dN}=-2 \Rightarrow dN=\frac{du}{-2}[/itex]


[tex]\int \frac{1}{4-2N} dN \equiv \int \frac{-1}{2} \frac{1}{u} du[/tex]

[tex]\frac{-1}{2}\int \frac{1}{u} du = \frac{-1}{2}lnu + Constant[/tex]


and *
 

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