 Solution

ID: past-exam-of-the-probability-statistics-and-options-ii-course-of-the-university-of-oxford/2009/d/d3/ii/b/solution

For

x \geq 1

(1 + x)^{2} \leq 4 x^{2}

, so

x lo g x / (1 + x)^{2} \geq (lo g x) / (4 x) \geq 0

. The latter integral diverges because its primitive is

(lo g x)^{2} /8

. Thus the absolute integral diverges and the answer is

not integrable on (1, \infty)

 New to topics? Read the docs here!