Please refer to : http://math.stackexchange.com/quest...x-arctan-frac1x-mathrm-dx-fra/1069065#1069065
The answer by @venus.
What is the procedure in converting that single integral, dividing it into parts, and making it a double integral?
And also, how Venus took $\sin(x)$ and brought it inside the first integral, and interchanging the integrals?
What is the criterion?
I am very interested in this.
Any **links** advice or comment is very helpful.
The Attempt at a Solution
I am looking for a general method, thats all.