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the values of ln for negative x are not the values of the anti-derivative of 1/x for negative x<br />

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the values of ln for negative x are not the values of the anti-derivative of 1/x for negative x


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Hi Zenoture.<br />
<br />
Im sure you will find the following link interesting.<br />
<br />
<a href="http://en.wikipedia.org/wiki/Integration_by_parts" rel="ugc">http://en.wikipedia.org/wiki/Integration_by_parts</a>
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Hi Zenoture.

Im sure you will find the following link interesting.

http://en.wikipedia.org/wiki/Integration_by_parts [http://en.wikipedia.org/wiki/Integration_by_parts]

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deighton gave the key to the answer to your question when he said<br />
&nbsp;&quot;in the real numbers ln(x) is not defined for x&lt;0&quot;<br />
He then went on to give a nice illustration of what the situation is if one considers complex numbers.
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deighton gave the key to the answer to your question when he said
 "in the real numbers ln(x) is not defined for x<0"
He then went on to give a nice illustration of what the situation is if one considers complex numbers.

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Sorry, forgot to award points.
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So I know derivative of ln(x) = 1/x, but the anti-derivative of 1/x = ln(|x|), why the absolute value? It is possible to have negative values for x in ln, so why isn't it just x?
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So I know derivative of ln(x) = 1/x, but the anti-derivative of 1/x = ln(|x|), why the absolute value? It is possible to have negative values for x in ln, so why isn't it just x?

derivates and anti-derivatives of ln x and 1/x (respectively)

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