Using Cauchy's integral formula to evaluate integrals

[Woolyabyss]

Homework Statement

Use Cauchy’s integral formula to evaluate the integral along γ(t) of (z/(z+9)^2)dz
where γ(t) = 2i + 4e^it , 0 ≤ t ≤ 2π.

Homework Equations

Cauchy's integral formula

The Attempt at a Solution

I was just wondering is the integral not just zero by Cauchy's theorem since (z/(z+9)^2) is holomorphic inside the circle defined by γ(t) ( the singularity at -9 is outside the circle ).

 

[Samy_A]

Homework Statement

Use Cauchy’s integral formula to evaluate the integral along γ(t) of (z/(z+9)^2)dz
where γ(t) = 2i + 4e^it , 0 ≤ t ≤ 2π.

Homework Equations

Cauchy's integral formula

The Attempt at a Solution

I was just wondering is the integral not just zero by Cauchy's theorem since (z/(z+9)^2) is holomorphic inside the circle defined by γ(t) ( the singularity at -9 is outside the circle ).

Yes, that seems to be the case.