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How does Limit in mma work?


I was trying to understand how mma deals with the improper integral

   Integrate[Sqrt[(x + 1)/(1 - x )], {x,-1,1}]

It seems to get stuck while evaluating the limit:

In[22]:= Integrate[Sqrt[(x + 1)/(1 - x )], {x,-1,b}]

                                                       Sqrt[1 - b]
Out[22]= Pi - Sqrt[2 - (1 - b)] Sqrt[1 - b] - 2 ArcSin[-----------]
                                                         Sqrt[2]

In[23]:= Limit[%, b->1]


Can anyone explain to me why it has trouble?

Ken






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