I have been working on these integral for 4 weeks... haven't been able to get anything yet. I am preparing for a competition and came across these bad boys.
Try using this page. Wolfram Mathematica Online Integrator
I ve done for you the first one. Doesnt seem to have any sense but maybe I made a typing mistake.
http://integrals.wolfram.com/index.jsp?expr=(x*sin(x))%2F(1+%2B+cos(x)^2)&rando m=false