Integrate with PrincipalValue->True

*To*: mathgroup at smc.vnet.net*Subject*: [mg79924] Integrate with PrincipalValue->True*From*: chuck009 <dmilioto at comcast.com>*Date*: Thu, 9 Aug 2007 05:12:09 -0400 (EDT)

Can someone explain to me how Integrate calculates the following improper integral? In[42]:= $Version Integrate[Sqrt[x]/(1 - x^2), {x, 0, a}, PrincipalValue -> True, Assumptions -> a > 1] Out[42]= "6.0 for Microsoft Windows (32-bit) (June 19, 2007)" Out[43]= ArcCoth[Sqrt[a]] - ArcTan[Sqrt[a]] Thanks, Charles