strange Integrate[] behavior

• To: mathgroup at smc.vnet.net
• Subject: [mg2089] strange Integrate[] behavior
• From: brianb at dendrite.cs.colorado.edu (Brian Bonnlander)
• Date: Fri, 29 Sep 1995 01:14:00 -0400
• Organization: University of Colorado, Boulder

```Integrate[] seems unable to split my integrand into two integrable pieces.
Am I simply doing something wrong?

In[23]:=  integrand

-(1/2) - x1 - x1 /2         -(1/2) + x1 - x1 /2
E                    x1     E                    x1
Out[23]= -(-----------------------) +  -----------------------
Sqrt[2 Pi]                   Sqrt[2 Pi]

In[24]:= Integrate[%, {x1, -1, 1}]

2                          2
-(1/2) - x1 - x1 /2        -(1/2) + x1 - x1 /2
E                    x1    E                    x1
Out[24]= Integrate[-(-----------------------) + -----------------------,
Sqrt[2 Pi]                 Sqrt[2 Pi]

>    {x1, -1, 1}]

There doesn't appear to be much search done by the Integrate[] function; it
returns within a second.  Yet I can integrate both terms individually:

In[25]:= InputForm[%]

Out[25]//InputForm= Integrate[-((E^(-1/2 - x1 - x1^2/2)*x1)/(2*Pi)^(1/2)) +
(E^(-1/2 + x1 - x1^2/2)*x1)/(2*Pi)^(1/2), {x1, -1, 1}]

In[26]:=  Integrate[-((E^(-1/2 - x1 - x1^2/2)*x1)/(2*Pi)^(1/2)), {x1, -1, 1}]

2             2                  1
2 Sqrt[Pi] - 2 E  Sqrt[Pi] + E  Sqrt[2 Pi] Gamma[-, 0, 2]
2
Out[26]= ---------------------------------------------------------
3/2  2
2    E  Pi

In[27]:= Integrate[(E^(-1/2 + x1 - x1^2/2)*x1)/(2*Pi)^(1/2), {x1, -1, 1}]

-2        Pi
-1 + E   + Sqrt[--] Erf[Sqrt[2]]
2
Out[27]= --------------------------------
Sqrt[2 Pi]

Why does the Integrate[] function seem unable to split the pieces?

Thanks for any help.

```

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