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This is an interesting problem in my opinion. I tried to solve it but without considerable success. A colleague of mine showed it few years ago. He said that the problem may have a practical application - for example for the spherical mirrors on the roads. I like this problem because it is combinati...

Just to be complete - it is the source of the integral:
http://www.mathlinks.ro/Forum/viewtopic.php?t=172825

Thank you for the good idea.
I have a question:
How we can understand without using programs if some integral may be expressed in elementary functions?

Ce se calculeze: \( \int \frac {1-x}{e^{x}+x^{2}e^{-x}}\ dx \).

Sa se calculeze:
\( \int \frac{x}{1+\cos^2x}dx \)

P.S. I think it is not an easy integral. It is not invented by me. It is posted in many forums but I still don't have a solution.