Another problem of the week has been long overdue. Here’s one that may appeal to those who liked POW-5 (maybe we should have an integration problem every fifth time?):

Evaluate \displaystyle \int_{0}^{\pi/2} \frac{x}{\tan x} dx.

Please submit solutions to topological[dot]musings[At]gmail[dot]com by Friday, October 10, 11:59 pm (UTC); do not submit solutions in Comments. Everyone with a correct solution will be inducted into our Hall of Fame! We look forward to your response.