Given the function
$$f(x)= \cases{ x\sin\Big(\frac{1}{x}\Big) & if $x\neq 0$ \\ 0 & if $x=0$} $$
Find $$\int\limits_{-\infty}^\infty \frac{1}{f(x)} dx $$
Given the function
$$f(x)= \cases{ x\sin\Big(\frac{1}{x}\Big) & if $x\neq 0$ \\ 0 & if $x=0$} $$
Find $$\int\limits_{-\infty}^\infty \frac{1}{f(x)} dx $$