ccae33e8-29eb-4ffa-ab72-2d17ffb8f736 9 6 9 decimal

&[DATE] &[TIME] - &[FILENAME]

a non sense reverse proof x ln x 0.0000169621190263 1 int 1 -

From educated knowledge, we know that

x ln x 01 int 1 - ≡

In Mathcad, adaptive/Romberg is coded 'on error' hyperfast at machine code level.

TOL 0.001 :

Smath typical adaptive integration f a b Singular app1 b a - (a b + 2 / f * : app2 b a - 6 / 2 a * b + 3 / f a 2 b * + 3 / f + (* : N 2 : app1 app2 - abs TOL ≥ app1 app2 : N 2 N * : app2 0 : h b a - N 1 + / : j 2 N range x0 a j 1 - (h * + : x1 x0 h + : app2 app2 h x0 f x1 f + 2 / (* + : 31 line for 51 line while app2 51 line :

x f x ln eval :

f 01 Singular 0.999352 -