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## Homework Statement

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!

## Homework Equations

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## The Attempt at a Solution

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I am looking for a general method, that's all.