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speeding up intergration of sum


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


  



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