As reported,

var('r')
assume(r>0)
integrate(r * sqrt( (2*r*cos(x)/sqrt(3))^2 + ( 2/3 + 4*r*sin(x)/3 )^2 ), x)

gives

-1/12*(2*r*x - r*sin(2*x))*r

which is indeed incorrect. Is the root cause known?


---------- Forwarded message ----------
Dear Mr Andrey Novoseltsev,



I am writing you to report a problem that I have encountered  while
computing a one variable integral with Sage. I attach a document with
the result that Sage produces for the indefinite integral. This
happens to be wrong, as can easily be proved by comparing the
derivative of the result with the function to be integrated (the
difference is not constant).



Sorry, I cannot provide any hint on how to fix this. It is not an
important issue for me anymore, since I have worked around my problem
and have solved it an a different way. I am reporting it for your
records, in case you find it interesting to know.

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Attachment: Indefinite_integral.pdf
Description: Adobe PDF document

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