okay the problem at first glance it's hard, but i don't want to give any hint yet, so i'll wait a couple of days and i'll post a solution.
Posting in thread so I remember about it. I think it has to do with...
Then find an expression for arctan(x)/x maybe and use integration by parts. I'll look at it later.
Will just post any working as I go along...
I make use of (again) 'magic differentiation' to solve this problem .
Sub. , it becomes
sub .... After a few steps , we can obtain
Magic Differentiation !
The answer to the problem is
okay, my solution uses the fact that
as a double one.
sorry for the late answer, actually, it holds for a better way.
try to find it, my time is bounded by now.