Calculer
1
\(\displaystyle \int_0^{2\pi}{dt\over a+\cos t}\) (\(a>1\)) ;
2
\(\displaystyle \int_0^{2\pi}{dt\over (a+b\cos t)^2}\) (\(a>b>0\)) ;
3
\(\displaystyle \int_0^{2\pi}{\cos^3{3t}\over 1-2a\cos t+a^2}\ dt\) (\(a\in\C\setminus \{\pm 1\}\)) ;
4
\(\displaystyle \int_0^{2\pi}\exp{(\cos t)}\cos{(nt-\sin t)}\ dt\) (\(n\in {\Zz}\)).