If the above integral is too easy, also try to evaluate (though I personally wouldn't recommend it ).
With the substitution the integral becomes...
(1)
Now is...
(2)
... and remembering the general formula...
(3)
... You obtain...
(4)
To extablish if the sum of the series in (4) can be expressed as function of known constants it is necessary some more work...
Kind regards
If you make a slightly different substitution, you'll end up having to evaluate a much simpler series.
Now let
The first three integrals are straightforward, and the last one is equivalent to evaluating which is much easier to evaluate than .
The final answer is