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 ourproblematicpoint 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 byG. 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:

and

Question:

Why we need the both substitutions,?or

Thank you.

To be continued...