Okay, I'm trying to compute the following integral:
But first, I will try to prove that converge.
The integral (Dirichlet's test)
But what about ?
I know that is our problematic point and also I know that .
Can I say that because that limit exists the function is integrable?
Now to the the second part-computation.
It's from a book by G. M. Fikhtengoltz, The Fundamentals of Mathematical Analysis.
(I'm translating this from Russian into Hebrew and then into English.)
We will represent I in form of sum:
Putting or and the he says the following:
we substituting or , and we get:
Why we need the both substitutions, or ?
To be continued...