MathGroup Archive 2007

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Integrate using Assumptions


When I change an integrand in a way that shouldn't affect the result,
mathematica is no longer able to map the integral to the built-in
function. Is there any way I can help it correctly recognize the form
of the function in general and in this particular case?

In[1]:= Integrate[ E^Cos[theta], {theta, 0, 2Pi} ]

Out[1]= 2 Pi BesselI[0, 1]

but

In[2]:= Integrate[ E^Cos[theta - theta0], {theta, 0, 2Pi},
Assumptions-
>Element[theta0, Reals]]

                          Cos[theta - theta0]
Out[2]= Integrate[E                   , {theta, 0, 2 Pi},

>    Assumptions -> theta0 \[Element] Reals]

or even

In[4]:= Integrate[E^Cos[theta-0.],{theta,0,2Pi}]

                          Cos[0. + theta]
Out[4]= Integrate[E               , {theta, 0, 2 Pi}]



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