Let f(z) be a rational function with no poles on the positive real axis, and suppose that lim Pf(z) lim zf(z) = 0. - 2-0 Show that [x²-¹ f(x) dx = XP-1 0 ㅠ sin p ΣRes{(-2)²-¹(2)}, where the sum is over all the poles of f(z). [Hint. Consider the integral (-2)-1 f(z)dz = fre(p-1) ln(-2) f(z)dz, where I is a suitable contour.]

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