ok I see a double substitution yields the solution
when I input for the integral arising from the calculation of the E field a distance z above the center of a spherical surface with radius R I get this solution ? this integral can be done by partial fractions, I don't see it quickly in Stewart's table of integrals
Integrate [(z-R*u)/(R^2+z^2-2*z*R*u)^(3/2),{u,-1,1}]
ConditionalExpression[(-R+z)/( z^{2)+/(z2 (R+z)),((Im[R] Re[R]+Im[z] Re[z])/(Im[z] Re[R]+Im[R] Re[z])1||Im[z] Re[R]+Im[R] Re[z]0||(Im[z] Re[R]+Im[R] Re[z]0&&((Im[R]+Im[z]) (Re[R]+Re[z])0||Im[R]3 Re[z]+Im[z] Re[R] (Im[z]2-Re[R]2+Re[z]2)Im[R] (Im[R] Im[z] Re[R]+Re[z] (Im[z]2-Re[R]2+Re[z]2))))||(Im[z] Re[R]+Im[R] Re[z]0&&((Im[R]+Im[z]) (Re[R]+Re[z])0||Im[R]3 Re[z]+Im[z] Re[R] (Im[z]2-Re[R]2+Re[z]2)Im[R] (Im[R] Im[z] Re[R]+Re[z] (Im[z]2-Re[R]2+Re[z]2)))))&&(R/z+z/RReals||Re[R/z+z/R]2||Re[R/z+z/R]-2)]}