1. The problem statement, all variables and given/known data 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. Thanks! 2. Relevant equations N/A 3. The attempt at a solution N/A I am looking for a general method, thats all.