Did you want
\int \left(\frac{2+\sin x}{1+\cos x}\right) \ e^{\frac{x}{2}} \ dx
expand and use integration by parts....i dnt knw a better method....
Did you want
\int \left(\frac{2+\sin x}{1+\cos x}\right) \ e^{\frac{x}{2}} \ dx
@saikat: write 1+sinx as [sin(x/2) + cos(x/2)]2 and cosx + 1 as 2cos2(x/2)...
now try....