How do I calculate the integral of $\lfloor1/x\rfloor$ from $x=\frac{1}{n+2}$ to $x=\frac{1}{n}$? How do I calculate integral : $$\int_{\frac{1}{n+2}}^{\frac{1}{n}}\lfloor1/x\rfloor dx$$ where $\lfloor t\rfloor$ means the integer part (I believe that's how it should be translated) or floor function of $t$.

I think this should be possible,to solve by decomposing the integrale from $1/(n+2)$ to $1/(n+1)$ and so on. On each of these Integrals, your function should be constant.
