a definite integral

*To*: mathgroup at smc.vnet.net*Subject*: [mg83806] a definite integral*From*: "Arnold Knopfmacher" <Arnold.Knopfmacher at wits.ac.za>*Date*: Sat, 1 Dec 2007 05:40:11 -0500 (EST)

Given the function f=(1 - z - u*z - Sqrt[-4*z + (1 + z - u*z)^2])/ (2*u*z*Sqrt[-4*z + (1 + z - u*z)^2]) I wish to compute g[z]=Integrate[f,{u,0,1}] (Here z and u are independent variables, that are real and positive and the function inside of Sqrt[ ] is nonnegative.) Mathematica 5.2 can only evaluate this if I ask for the indefinite integral but this then gives errors when u=0 or u=1 is substituted. I believe it is because Mathematica is choosing the wrong branches of the square root or of the Log function when it computes the indefinite integral.=0D The function f is integrable, as can be obseved by first finding say Series[f,{z,0,10}] and then integrating term by term to find the (correct) initial power series terms of g[z]. Thanks Arnold Knopfmacher