Re: Why Mathematica *always* fails at quite simple integrals Maple cracks? (10 examples)

"G. A. Edgar" <edgar@xxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
In article <20080202220804.734$iP@xxxxxxxxxxxxxx>, David W. Cantrell
<DWCantrell@xxxxxxxxxxx> wrote:

Here's a nice little challenge for anyone who might be interested:
Evaluate precisely

Integrate[Floor[Log[10, x]], {x, 0, 100}]

I'll post the answer in about 24 hours if nobody has posted it.

800/9

Correct. Thanks to all who responded, and congratulations to Oleksandr,
quasi and Gerald.

For those who might be interested, I had gotten my answer using a general
result. Letting the floor function be denoted by square brackets, for real
x, c and d, with x and c nonzero,

the integral of [c log|t| + d] from t = 0 to x

is

x [c log|x| + d] + sign(x) e^(([c log|x| + d] + 1 - d)/c)/(1 - e^(1/c))

Of course, to answer the challenge question, we may simply substitute,
resp., 1/log(10), 0 and 100 for c, d and x in the general result.

Finally, note that, if x or c is zero, the integral can be evaluated
trivially.

David W. Cantrell
.

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