Time for our next problem in the POW series! Earlier, Todd and I deliberated for a bit on whether we should pose a “hard” Ramanujan identity (involving an integral and Gamma function) as the next POW, but decided against doing it. Perhaps, we may do so some time in the future.

Okay, the following integral was brought to our attention by Carl Lira, and for the time being I won’t reveal the actual source of the problem.

Compute $\displaystyle \int \frac{x^2 - 1}{(x^2 + 1) \sqrt{x^4 + 1}} \, dx$.

It is “hard” or “easy” depending on how you look at it!

Please send your solutions to topological[dot]musings[At]gmail[dot]com by Wednesday, June 26, 11:59pm (UTC); do not submit solutions in Comments. Everyone with a correct solution gets entered in our Hall of Fame! We look forward to your response.