Integrals: Euler's constant differences

[C.Ret]

Bonjour tout le monde

At first, I thought that evaluating all these expressions in the HOME mode is the really good way to obtain and compare the numerical values for this constant. Also to see which methods are the fastest and most accurate.

Reading Albert Chan's remark, I tried in CAS mode. I am sure that this mode is generally much more informative, but however, I did not find any way to get the value of this constant. I have a confirmation that it is Euler's y constant !
But not the slightest idea of ​​its numerical value (even approximate) in this mode!



EDIT: Oops! Sorry, I forgot to press the SHIFT-ENTER to get the approximations ! I am bad.