Line Integral of a complex function

[mateomy]

I'm trying to solve this integral as x-> Infinity
$$\int \frac{dz}{8i + z^2}$$

...on the y=x line, but I have no idea what I'm doing. The book I'm using is less than helpful in this regard. I'm not supposed to use any complex analysis tools (Cauchy, etc), but just solve it as a line integral. I'm not looking for an easy answer I would rather receive a hint. I've thought about expanding the function of $z^2$ and after doing so I'm still at a loss. Any advice would be great, thanks.

 

[jackmell]

I'm trying to solve this integral as x-> Infinity
$$\int \frac{dz}{8i + z^2}$$

...on the y=x line, but I have no idea what I'm doing. The book I'm using is less than helpful in this regard. I'm not supposed to use any complex analysis tools (Cauchy, etc), but just solve it as a line integral. I'm not looking for an easy answer I would rather receive a hint. I've thought about expanding the function of $z^2$ and after doing so I'm still at a loss. Any advice would be great, thanks.

You can parameterize the line y=x. Isn't that just $z=re^{\pi i/4}$. Ok, turn the crank now.