Experiment with integrals - f(x) dx, f(x) = [(x - 1 )(x -

Experiment with integrals ∫^∞ _-∞ f(x) dx, f(x) = [(x - α₁)(x - α₂) · · · (x - α_k)]^-1, α_j real and all different, k > 1. Conjecture that the principal value of these integrals is 0. Try to prove this for a special k, say, k = 3. For general k.