1. The problem statement, all variables and given/known data I am trying to directly calculate the electric field (using Coulomb) at some arbitrary point P(0,0,z). The charge is evenly distributed over the surface of a sphere (radius R, charge density σ). Here I use θ for the polar angle and p for the azimuthal angle. I will leave out the messy details, but I know by symmetry only projection onto z-axis is relevant. I also determined the angle ψ (that between separation vector π and the z-axis) in terms of z,R,θ, and π. 2. Relevant equations E(alongz) = (4∏ε0) ∫02∏∫0∏ [σR^2 sinθ (z - Rcosθ)] / (R^2 + z^2 - 2Rzcosθ)^(3/2) dθ dp 3. The attempt at a solution ∫dp → 2∏ removing 2∏R^2σ constants out from integrand ∫0∏ [(z - Rcosθ)sinθ] / (R^2 + z^2 - 2Rzcosθ)^(3/2) dθ using u-substitution: u = cosθ du= -sinθ dθ θ = 0 → u = 1 θ = ∏ → u =-1 and reversing the limits of integration gives (ignoring constants out front): ∫-11 (z - Ru) / (R^2 + z^2 - 2Rzu)^(3/2) du (#1) →according to solutions manual→ this works out to: z^-2 [(z-R) / |z-R| - (-z-R) / |z+R|] (#2) The manual says: Does anyone have any idea how you would use partial fractions to go from (1) to (2)??