Updates:
Status: Valid
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Comment #1 on issue 3700 by asmeu...@gmail.com: integration of
cos(n*(x-phi))*cos(n*x) from x=-pi..pi does not work
http://code.google.com/p/sympy/issues/detail?id=3700
The relevant part of the code is sympy/integrals/trigonometry.py. You
would need to implement the indefinite integral (the definite integral is
handled automatically by the fundamental theorem of calculus).
You could do this either by extending the match patterns and integrators to
handle shifts, or by intelligently calling expand_trig() (intelligently
meaning not to the point that it makes integrals that already work come out
worse).
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