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Re: Troubles with Integrating certain functions in 5.0

On 1 Jul 2004, at 18:26, Matt Hancher wrote:

> Hi all,
> I'm running on OS X, and Integrate is misbehaving.  Below I 
> show
> the results of performing the same definite integral two times.  The 
> only
> difference is that I pulled out the constant factor Sqrt[E] in the 
> second
> case.  Only the second case is correct; the Struve function shouldn't 
> be
> there in the first case.
> I'm pretty sure I'm not just being dumb.  Anybody have any thoughts?
> I'd be curious to know how this plays out with other versions and on
> other platforms....
> In: Integrate[Exp[-Sin[x]^2]*Sqrt[E], {x, 0, Pi}]
> Out: Pi ( BesselI[0, 1/2] - StruveL[0, 1/2] )
> Versus:
> In: Integrate[Exp[-Sin[x]^2], {x, 0, Pi}]*Sqrt[E]
> Out: Pi BesselI[0,1/2]
> Thanks for any thoughts,
> Matt
> Matt Hancher
> NASA Ames Research Center
> Official: mdh at
> Personal: mdh at
Version 4.2 gives the right answer:

Integrate[E^(-Sin[x]^2), {x, 0, Pi}]

(Pi*BesselI[0, 1/2])/Sqrt[E]

This is on Mac OS X but I am pretty sure that the behaviour of both 
version 4.2 and 5.0 is the same in this respect on both platforms. I do 
not have 5.01 so I am not sure if this problem is still present.

Mathematica 5.0 introduced some pretty radical changes in the way 
Integrate works. Many bugs have been fixed (though naturally one rarely 
hears of this). Partly as a result of these fixes and partly due the 
more ambitious approach in version 5, a substantial number of new bugs 
have also been created. At the moment it seems to me that the best 
thing to do is to use use both versions (it is possible to line two 
Kernels to the same front end) and also check the answer with 
NIntegrate, which is very reliable.

Andrzej Kozlowski
Chiba, Japan

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