Hi there,

integrate() seems to have a bug which leads to wrong answers for
rational trigonometric functions. E.g.

In [7]: integrate(1/(cos(x)+2),(x,0,2*pi))
Out[7]: 0

It's obvious that the answer is wrong: the function is strictly
positive everywhere, so integral cannot be 0.

It seems (I didn't check it) that SymPy uses trigonometric
substitution like u=tan x/2 and then incorrectly substitute 0 and 2*pi
as limits. (There are singular points in the interval (0,2*pi) for tan
x/2, so it does not work.)

See an issue on the tracker: 
http://code.google.com/p/sympy/issues/detail?id=3179

Thanks!

--
Sincerely yours,
Ilya V. Schurov.

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