Fixed in 11.3

I have the following issue, trying to evaluate an integral. Mathematica tells me

Integrate[x^2 (1 + x^2)^(1/2) + y + z, {x, y, z} ∈ Sphere[{0, 0, 0}, 1]]

(* 1/2 π (3 Sqrt[2] - Log[2 (2 + Sqrt[2])]) *)

By the way, it also gives me

Integrate[x^2 (1 + x^2)^(1/2), {x, y, z} ∈ Sphere[{0, 0, 0}, 1]]

(* 1/4 π (6 Sqrt[2] + Log[3 - 2 Sqrt[2]]) *)

And, of course,

Integrate[y + z, {x, y, z} ∈ Sphere[{0, 0, 0}, 1]]

(* 0 *)

You can check that the two results are not equal (they differ by $\frac{3\pi}{8}\log 2$); therefore the linearity of the integral is not respected. How can I explain this fact?

Thank you in advance! This is really puzzling me up.

  • 3
    $\begingroup$ Same behavior here on Mathematica 11.0.1 on macos 10.12.6. I would classify that as a bug. Note that this does not happen with NIntegrate which has some other issues instead. $\endgroup$ Commented Nov 25, 2017 at 15:52
  • $\begingroup$ Thank you for quick answer. By the way, do you know what is the bug caused by? So that one can at least try to avoid it. $\endgroup$ Commented Nov 25, 2017 at 15:56
  • 2
    $\begingroup$ I have absolutely no idea. Personally, I mostly avoid everything provided by Mathematica related to two dimensional MeshRegions; mostly for the reason that many features haven't been implemented yet. But this issue is really striking. Would you please be so kind and send a bug report to Wolfram Research? $\endgroup$ Commented Nov 25, 2017 at 16:47
  • $\begingroup$ Same behavior for 11.2 on Windows 10. Bug. $\endgroup$
    – bbgodfrey
    Commented Nov 25, 2017 at 21:44
  • 1
    $\begingroup$ confirm it is fixed in 11.3 !Mathematica graphics $\endgroup$
    – Nasser
    Commented Mar 10, 2018 at 21:31

1 Answer 1


This is a bug introduced in 10.4.0 and persisting through 11.2.0. It is already fixed in our internal development build, so it should be fixed in our next release.

I haven't tracked down the cause, but based on the different answers over various versions, it is probably either a simplification bug, or a branch cut issue.

  • $\begingroup$ Upvoting for saving me the time tracking down the actual cause... $\endgroup$ Commented Nov 27, 2017 at 20:36

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