Graph $x\sin(x)$
I am having problem with the period section of the graph. I can see that the function is even, and that as $x \rightarrow \pm\infty$, the amplitude $\rightarrow \infty$.
I am used to dividing $2\pi$ by the coefficient of the angle inside the $\sin$ term; however, I have notes saying that the function is not periodic. Why can't I say that the function is periodic with period $\frac{2\pi}{1} = 2\pi$? Is it the $x$ term attached? How does this term affect things and how do I solve these types of problems generally?