Integral of 1/x faulty?

Question

Just ran across what seems to be an error.

Then Integral of 1/x should be ln(|x|) but Mathcad sysmbolics (MC14_M030) forgets the absoulute value.

It seems to ignore the assumption of a variable range too. I remember having a similar effect with solve (trying to force the negative solution and Mathcad still serving a positive one). I'll try to find the file to post.

Another strange effect is that it refuses to plot a function which ist defined as the integral of a funcion, while it works fine with the derivation.

RMix

TomGutman · Answer

The use of ln(|x|) as the integral of 1/x is shown in some elementary texts. But it is actually wrong. It can be useful in some cases, with x sufficiently restricted, but it turns out that it provides correct answers in some cases only because of two canceling errors.

The indefinite integral is (by Mathcad definition) for symbolic evaluation only. It cannot be evaluated numerically, which is what the plot routine needs to do. Nor is it even properly a function. It is a family of functions, any two of which differ by a constant. No proper value can be assigned to the indefinite integral per se.
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� � � � Tom Gutman

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