integrals involving floor(x)

[nob...@nowhere.invalid]

Maple and Sage (per GIAC, I assume) get certain integrals involving
FLOOR(x) wrong, whereas Derive 6.10 does not:

INT(FLOOR(x)^2, x) = - 2*FLOOR(x)^3/3 + (x - 1/2)*FLOOR(x)^2 +
FLOOR(x)/6

INT(2*FLOOR(x), x) = (2*x - 1)*FLOOR(x) - FLOOR(x)^2

The integrands are from a complaint on sage-devel at Google Groups.

Martin.

[nob...@nowhere.invalid]

"clicl...@freenet.de" schrieb:

Oops, the second integral should have been:

INT(2^FLOOR(x), x) = 2^FLOOR(x)*(x + 1) - 2^FLOOR(x)*FLOOR(x)

Martin.

[Albert Rich]

Mathematica 13 returns Integrate[Floor[x], x] unevaluated, even when assuming x is real.

Derive 6.10 is 20 years old and its mathematical engine was implemented by two people. Wonder how many people worked on Maple and Mathematica over the past 20 years.

Albert