Re: [Axiom-developer] One more integral to add to the tests, if not already there

[William Sit]

On Tue, 17 Oct 2006 17:18:37 -0700 (PDT)
 C Y <address@hidden> wrote:
> integrate(%e^cos(x)*cos(x-sin(x)),x = 0..2*%pi)
>
> Apparently this can be solved by Mathematica in it's 
> upcoming version. 
> We currently get "failed."
>
> Cheers,
> CY

Apparently, Mathematica got this wrong in Version 5.2:
In[1]:=
Integrate[Exp[Cos[x]] Cos[x-Sin[x]], {x,0,2 Pi}]

Out[1]=
0

But a look at the graph of the integrand shows this is 
clearly wrong. Indeed,
In[3]:=
NIntegrate[Exp[Cos[x]] Cos[x-Sin[x]], {x,0,2 Pi}]

Out[3]=
6.28319

which looks like the exact answer is 2 Pi.

William