let f(a) =∫_(−∞) ^(+∞) (dx/((x^2 +1)(a +e^(ix) ))) with a>0
1)find a explicit form of f(a)
2) determine also g(a)=∫_(−∞) ^(+∞) (dx/((x^2 +1)(a+e^(ix) )^2 ))
3)let I =Re(∫_(−∞) ^(+∞) (dx/((x^2 +1)(2+e^(ix) )))) and J=Im(∫_(−∞) ^(+∞) (dx/((x^2 +1)(2+e^x ))))
determine I and J and its values.