Comment #3 on issue 3700 by t.hi...@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
With current git master, sympy is able to evaluate the integral. But this
only works if i expand the integrand first with integrand.expand(trig=True)
and then pass this expanded integrand to the integrate function. If I don't
do this then 0 is returned:
In : r/pi*integrate(cos(n*(x-phi))*cos(n*x), (x, -pi, pi))
Out:
⎛ n n ⎞
⎜(-1) ⋅85⋅cos(n⋅φ - π⋅n) (-1) ⋅85⋅cos(n⋅φ + π⋅n)⎟
r⋅⎜─────────────────────── - ───────────────────────⎟
⎝ n n ⎠
─────────────────────────────────────────────────────
π
which is 0 when I simplify it:
In : r/pi*integrate(cos(n*(x-phi))*cos(n*x), (x, -pi, pi)).simplify()
Out: 0
However, if I do this:
In : integrand = cos(n*(x-phi))*cos(n*x)
... r/pi * integrate(integrand.expand(trig=True), (x,-pi,pi))
Out: r⋅cos(n⋅φ)
'integrate' returns the expected result.
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