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integration of ((|x|)/([x]) from (1,9)..
throughout the range of x, mod(x)=x, I=∫(x/[x])dx from 1 to 9, =∫(x/[x])dx from 1 to 2...from 8 to 9
∑(((i+1)2-i2)/2)/i from i=1 to i=8
=3/2 + 5/4 +7/6 +9/8 = 121/24
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