Dxy：x² + y² ≤ 1
∫∫∫Ω 1/(x² + y² + z²) dV
= ∫∫Dxy dxdy [∫(r²→1) 1/(r² + z²) dz]
= ∫(0→2π) dθ ∫(0→1) rdr ∫(r²→1) 1/(r² + z²) dz
= 2π∫(0→1) rdr (1/r)arctan(z/r) |(r²→1)
= 2π∫(0→1) [arctan(1/r) - arctan(r)] dr
= 2π{[(1/2)ln(r² + 1) + rarctan(1/r)] - [rarctan(r) - (1/2)ln(r² + 1)]} |(0→1)
= 2π{[(1/2)ln(2) + π/4] - [π/4 - (1/2)ln(2)]}
= 2πl(wèi)n(2)