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speeding up intergration of sum

• To: mathgroup at smc.vnet.net
• Subject: [mg126454] speeding up intergration of sum
• From: bar at ANTYSPAM.ap.krakow.pl
• Date: Sat, 12 May 2012 04:51:45 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Hello, 
I have a problem with Integrate[f[z]] where
f[z] is a sum of many parts, 

All those parts are very simple ( like a/(b+z) )

Sometimes Integrate[f[z],z] doesn't reach convergence

althouhg Integrate of the all of parts exists, 

The question is :
Is it possible to force the  Mathematica to calculate this sum

step by step (part by part) ??

The resylt should be a sum of the  a*Log[b+x]

greetings , Olaf