- Thread starter
- #1
Krizalid
Active member
- Feb 9, 2012
- 118
Here's an integral I love:
For each integer $\alpha>1,$ compute $\displaystyle \int_0^\infty {\left\lfloor {{{\log }_\alpha }\left\lfloor {\frac{{\left\lceil x \right\rceil }}{x}} \right\rfloor } \right\rfloor \,dx} .$
For each integer $\alpha>1,$ compute $\displaystyle \int_0^\infty {\left\lfloor {{{\log }_\alpha }\left\lfloor {\frac{{\left\lceil x \right\rceil }}{x}} \right\rfloor } \right\rfloor \,dx} .$