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differentiate/integrate a function

• To: mathgroup at smc.vnet.net
• Subject: [mg92496] differentiate/integrate a function
• From: RG <gobithaasan at gmail.com>
• Date: Wed, 1 Oct 2008 18:35:13 -0400 (EDT)

Hi, i have been trying to differentiate to following term:
Blince[u_]=\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(t\)]\(
FractionBox[\(\((S - u)\) \[Kappa]0 + \((1 + r)\) u\ \[Kappa]1\), \(r\
u\  + \ S\)] \[DifferentialD]u\)\)

M6 seem to give inappropriate answers...When i do the following:

x[s_] = x0 + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(s\)]\(Cos[
\*FractionBox[\(r\ t\ \((\(-\[Kappa]0\) + \[Kappa]1 + r\ \[Kappa]1)\)
+ \((1 + r)\)\ S\ \((\[Kappa]0 - \[Kappa]1)\)\ \((\(-Log[S]\) + Log[S
+ r\ t])\)\),
SuperscriptBox[\(r\), \(2\)]]] \[DifferentialD]t\)\)

The answer seemed very complex not readable... pls help. i also need
to find the first derivative to x[s] or x'[s]


thank you in advance