Physics brushup

[Gerson W. Barbosa]

The exact 10-digit result is 0.5772156649.
The integral result is 0.5572156635 (FIX 9), both on the HP emulator and on the JRPN simulator.
On the HP-15CE the result is 0.5572156619 (FIX 8), but it takes about four minutes and twenty seconds. Nice integral anyway.
14 steps, including LBN and RTN, but perhaps the limit hasn’t been reached yet.