The value of the complex integral...

(1)

... is given by...

(2)

... where and is the red path represented in figure...

All that is true only if the socalled 'Jordan's lemma' is verified, just as in this case. For the 'second Cauchy integral formula' is...

(3)

... where is the residue relative at each pole of inside and it is given by...

(4)

In our case the only pole of inside is so that is...

(5)

... and finally...

(6)

Kind regards