I'm interested in finding the value of
- the integral of $\left\{\frac{1}{x}\right\}\cdot x$ (the fractional part of $\dfrac{1}{x}$ multiplied by $x$) on the interval $(a,b), a\ge 0$
- the integral of $\left\{\frac{1}{x}\right\}$ (fractional part of $\dfrac{1}{x}$) on the interval $(a,b), a\ge 0$
NOTE: $\left\{x \right\}= x-\left\lfloor x \right\rfloor $
Thanks