Evaluating integrals

• To: mathgroup at smc.vnet.net
• Subject: [mg66176] Evaluating integrals
• From: "masha" <mshunko at gmail.com>
• Date: Wed, 3 May 2006 02:44:42 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Hello,

I am new to Mathematica and am tryong to figure out how to work
efficently with integrals and run into the following issue. Let's say I
want to integrate a simple function like Exp[-r b c], where c is a
normal random variable. Doing this by hand, I can simply complete the
square and end up with a simple result: Exp[(r^2 b^2 sc^2 )/ 2].

However, if I run the following code in Mathematica:

g[c_] := PDF[NormalDistribution[µc, sc], c]
pi = Exp[-r b c]
FullSimplify[Integrate[pi g[c], c, Assumptions -> {c > 0, r > 0, b >
0}]]

I get:
\!\(1\/2\ \[ExponentialE]\^\(1\/2\ b\ r\ \((\(-2\)\ µc + b\ r\
sc\^2)\)\)\ \
Erf[\(c - µc + b\ r\ sc\^2\)\/\(\@2\ sc\)]\)

And Mathematica does not seem to be able to simplify this answer any
further. Is there a way to make it return the simple answer? Can it do
'tricks' like completing the square?

Thank you,
Masha

```

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