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Integrate bug and workaround
*To*: mathgroup at christensen.cybernetics.net
*Subject*: [mg1050] Integrate bug and workaround
*From*: Steven Trainoff <steve at borglet.ucsb.edu>
*Date*: Wed, 10 May 1995 09:05:38 -0400
Hello all,
I am constantly amazed at how fickle MMA's integrator is. Perhaps
this example is well known, but it sure surprised me. Can anyone
explain this behaviour, or is it a simple bug? I am running MMA
version "NeXT 2.0 (November 14, 1991)"
(* It can't do this... *)
In[1]:= Integrate[x E^(Sqrt[z^2]*x), x ]
2
x Sqrt[z ]
Out[1]= Integrate[E x, x]
(* Replace Sqrt with an arbitrary unknown function and it works
fine... *)
In[2]:= Integrate[x E^(f[z^2]*x), x ]
2
x f[z ] 2 -2 x
Out[2]= E (-f[z ] + -----)
2
f[z ]
(* Here is a brute force workaround *)
In[3]:= Unprotect[Integrate]
Out[3]= {Integrate}
In[4]:= Integrate[x_ E^(a_ x_), x] := E^(a*x)*(-a^(-2) + x/a) /;
FreeQ[a,x]
In[5]:= Protect[Integrate]
Out[5]= {Integrate}
(* Now it can do the original integral *)
In[6]:= %1
2
x Sqrt[z ] -2 x
Out[6]= E (-z + --------)
2
Sqrt[z ]
...STeve
------------------------------------
Insert pithy maxim here...
steve at tweedledee.ucsb.edu (NeXT mail)
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