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Decimal expansion of the number u such that the arclength on y = e^x from (0,1) to (u, e^u) is 1.
1

%I #4 Jul 08 2020 08:08:21

%S 5,8,9,7,5,5,2,1,5,8,4,0,2,9,0,1,5,7,5,3,5,9,6,1,7,5,9,6,8,0,1,9,4,6,

%T 2,8,3,0,3,2,4,4,5,6,4,0,4,1,1,5,9,6,8,4,6,5,6,7,6,0,3,2,6,6,5,4,6,0,

%U 4,3,0,2,3,1,3,0,5,6,7,3,4,9,9,3,3,0

%N Decimal expansion of the number u such that the arclength on y = e^x from (0,1) to (u, e^u) is 1.

%e u = 0.5897552158402901575359617596...

%t u = u /. FindRoot[-Sqrt[2] + Sqrt[1 + E^(2 u)] + ArcTanh[Sqrt[2]] -

%t ArcTanh[Sqrt[1 + E^(2 u)]] - 1, {u, 0}, WorkingPrecision -> 100]

%t RealDigits[u][[1]]

%Y Cf. A336002.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Jul 06 2020