Is the function y = xcosx bounded in (negative infinity, positive infinity) and infinite when x approaches positive infinity?

Is the function y = xcosx bounded in (negative infinity, positive infinity) and infinite when x approaches positive infinity?

Boundless is not infinite
When x = 2K π and K →∞, y →∞, so it is unbounded;
When x = 2K π + (π / 2) and K →∞, y = 0, not infinite