Is ln(x-2) the Correct Integration of 1/4(x-2)?

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Homework Statement

Homework Equations

The Attempt at a Solution


i got ln(x-2) but not sure what to do with the 4[/B]
 
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truffle42 said:

Homework Statement

Homework Equations

The Attempt at a Solution


i got ln(x-2) but not sure what to do with the 4[/B]
Use ##\int kf(x)~dx = k\int f(x)~dx##. And don't forget the constant of integration.
 
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@truffle42, as written, your problem is ambiguous -- "integration of 1/4(x - 2)"

Due to the order of operations, what you wrote is ##\frac 1 4 (x - 2)##, surely not what you meant.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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