I am in doubt about convergence of the folowing improper integration: +infinite / \ x * sin(kx) dx; (k is real) / 0 sorry about my sign of integration! I promisse that I will learn how to post correctly! I used the intuition: sin is periodic and bounded and x is unbounded. In my intuition this integration diverges. Bur I need rational answer, intuition in mathematics is something of nothing.