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I'm interested in finding the value of

  1. the integral of $\left\{\frac{1}{x}\right\}\cdot x$ (the fractional part of $\dfrac{1}{x}$ multiplied by $x$) on the interval $(a,b), a\ge 0$
  2. 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

  • 4
    It would be helpful if you clarified your question. When you say "the fractional part of 1/x multiplied by x", do you mean $(\frac{1}{x} - \lfloor{\frac{1}{x}}\rfloor)x$? Also, can you tell us how you've attempted this or where the problem cropped up?2011-04-13
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    it is well know formula for integral of fract(1/x) on (0,1), given by Euler-mascheroni constant. I'm arriving to a integral on (0,a) with 'a' depending on a parameter, its value is < 1. Moreover, I'm arriving to find an expression/calculate a similar integral from xfract(1/x) on (0,a), with no idea how to do it.2011-04-13

2 Answers 2