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Why should there not be an absolute value-sign instead of () when I find the primitive of $r/(1+r^2)$? Maybe it should only be there when I derive?

http://www.wolframalpha.com/input/?i=primitive+r%2F%281%2Br%5E2%29

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    $\begingroup$ In principle there shoud be, but since $r^2+1> 0$, for all $r\in \mathbb R$, you can remove them. In any case, if I recall correctly, WA never includes $\text{abs}$ even when it's necessary. $\endgroup$
    – Git Gud
    Apr 16, 2014 at 10:54
  • $\begingroup$ Ok. Question solved then. $\endgroup$
    – jacob
    Apr 16, 2014 at 11:14
  • $\begingroup$ Feel free to answer it below, so the question doesn't come up as unanswered. $\endgroup$
    – Git Gud
    Apr 16, 2014 at 11:15
  • $\begingroup$ By default Mathematica and W|A work with complex functions. Now, $\log(z)$ is differentiable on the complex plane, except on the negative real axis where it has a branch cut. $\log(|z|)$, by contrast is nowhere differentiable as a complex plane. So, to assert that $\int(1/z)dz=\log(z)$ in this context is simply incorrect. $\endgroup$ Apr 16, 2014 at 15:10

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In principle there shoud be, but since r2+1>0, for all r∈ℝ, you can remove them. In any case, if I recall correctly, WA never includes abs even when it's necessary. -- Git Gud Apr 16 at 10:54

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  • $\begingroup$ You should really learn to cite the people you copy stuff from. See also math.stackexchange.com/q/955806. $\endgroup$
    – Did
    Oct 3, 2014 at 6:13
  • $\begingroup$ There is nothing to cite here. It's a short question and a link to wolfram alpha. $\endgroup$
    – jacob
    Oct 3, 2014 at 14:09
  • $\begingroup$ Yes there is (in boldface or not): you posted as an answer a comment from user Git Gud, which you copied without attribution. $\endgroup$
    – Did
    Oct 3, 2014 at 16:22

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