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.