Contour Integral for Triangle with Non-Analytic Integrands

[squaremeplz]

Homework Statement

let t be the triangle with vertices at the points -3, 2i, and 3, oriented counterclockwise. compute$$\int \frac {z+1}{z^2 + 1} dz$$

Homework Equations

$$f(z) = \frac {1}{2 \pi i} * \int \frac {f(z)}{z - z_o} dz$$

The Attempt at a Solution

the integrand fails to be analytic at z^2 = +/- i , but only the point i is inside the triangle t so I rewrote the equation as:

$$\int \frac {\frac {z+1}{z+i}}{z-i} dz$$

= $$2 \pi i * f(i)$$

= $$2 \pi i * \frac {i+1}{2i}$$

is this correct? thanks!

 

[n!kofeyn]

Good job! It looks good to me, but be sure to simplify your answer. Also, there was just a small typo in the relevant equations as the f(z) to the left of the equals sign should be f(z₀), but this was obviously just a typo.