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bug in integration with version 5.0 ?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg46453] bug in integration with version 5.0 ?
*From*: "Florian Jaccard" <florian.jaccard at eiaj.ch>
*Date*: Thu, 19 Feb 2004 03:02:03 -0500 (EST)
*Reply-to*: <florian.jaccard at eiaj.ch>
*Sender*: owner-wri-mathgroup at wolfram.com
Hello Users !
I have the following problem :
If I integrate
1/(2x^2 + 8x + 20)
with version 4.1 , I obtain the same answer as by hand:
ArcTan[(2 + x)/Sqrt[6]]/(2*Sqrt[6])
Today, I was teaching with the version 5.0, and I obtained :
In[1]:=
expr = Integrate[1/(2*x^2 + 8*x + 20), x]
Out[1]=
(I*(Log[-2*I + Sqrt[6] - I*x] -
Log[2*I + Sqrt[6] + I*x]))/(4*Sqrt[6])
It is not as nice as with the version 4.1, but it is right too !
Let us check :
In[4]:=
Simplify[ComplexExpand[expr,TargetFunctions->{Re,Im}]]
Out[4]=
ArcTan[(2 + x)/Sqrt[6]]/(2*Sqrt[6])
One of my students suggested to load the RealOnly package. He hoped that the
answer would not have a complex form. I just wanted to show him that it
would not be better, and tried his suggestion :
In[5]:=
<< "Miscellaneous`RealOnly`"
In[6]:=
Integrate[1/(2*x^2 + 8*x + 20), x]
Out[6]=
x/(2*(x^2 + 4*x + 10))
This is completely wrong, for sure !
Curiosly, with version 4.1, with RealOnly loaded, Mathematica gives the
right answer... Is it a ugly bug of version 5 ?
Should I tell my students not to use RealOnly ?
Thanks in advance for your suggestions !
Meilleures salutations
Florian Jaccard
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