Integrating Along C: Solving ∫ tan(z/2)/(z+π/2)(z-π/2)² dz

[jiho.j]

Homework Statement

∫\frac{tan(\frac{z}{2})}{(z+\frac{\pi}{2})(z-\frac{\pi}{2})^{2}} dz

integration along C: abs(z) = 4

(along the circle of radius is 4)

Homework Equations

Cauchy Integral Formula

The Attempt at a Solution

I tried to set g(z) that is analytic inside C but I cannt set it.

Do I have to use Laurent seires or residue or something?

 

[CAF123]

I tried to set g(z) that is analytic inside C but I cannt set it.

Do I have to use Laurent seires or residue or something?

Yes, nothing comes to mind quickly for you to use the Cauchy Integral formula. It should be fine using residues though.