Calcul de integrala 5

ins- · Post by **ins-** » Sat Feb 09, 2008 2:02 pm

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.

aleph · Post by **aleph** » Sun Feb 10, 2008 2:24 pm

The antiderivative cannot be expressed in closed form using only elementary functions. If you are curious to see the result in terms of some special functions, go to the site

http://integrals.wolfram.com/

and plug your function there.

ins- · Post by **ins-** » Sun Feb 10, 2008 3:15 pm

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?

aleph · Post by **aleph** » Sun Feb 10, 2008 4:01 pm

ins- wrote:How we can understand without using programs if some integral may be expressed in elementary functions?

This is a rather deep mathematical subject. It is beyond of a high school student.
Some keywords to look for in www are:
differential fields, Liouville principle, Risch algorithm.

ins- · Post by **ins-** » Sun Feb 10, 2008 5:30 pm

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