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MathGroup Archive 1995

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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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