∫dx/x = log |(x)| is not possible when:  

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  1. x = 0
  2. x = 1
  3. x = -2
  4. x = -1

Answer (Detailed Solution Below)

Option 1 : x = 0
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Detailed Solution

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Explanation:

Consider the function \(f(x)=\frac{1}{x}\)

with the intention of examining the function's continuity for all real numbers, we will find that the function is discontinuous at x = 0, and hence the function is not integrable at x = 0.

However, if we review it within the region of all positive real numbers or all negative real numbers, then the function is continuous, and also integrable in this region.

This is the consolation we needed that the function is integrable for all positive real numbers (or negative numbers).

Moreover, the integration of the function \(\frac{1}{x}\) is ln|(x)|, which is not defined for x = 0.

So this further confirms the fact that \(\frac{1}{x}\) is not integrable only for x = 0 (since the integration of \(\frac{1}{x}\) is not defined for x = 0).

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