Complex line integral - where the length of the complex number is given I'm trying to study ahead of class so I alleviate some upcoming stress in the semester. I have currently read the chapters on line integrals of complex numbers and am currently trying to deepen the content with some problems given in the workbook.

a)$$\oint_{|z|=1}\frac{dz}{z(z+2)}$$
b) $$\oint_{|z|=3}\frac{dz}{z(z+2)}$$

My general approach on this was to first use partial fraction decomposition to make it a bit easier on the integral.
Meaning that $\frac{1}{z(z+2)}$ becomes $\frac{1}{2z}-\frac{1}{2(z+2)}$ if I didn't make any mistake. The integral would then be $\frac{1}{2}(\ln (2z)-\ln(2(z+2))$. But how do I evaluate that?

Do you understand that, in the complex plane (real part on the x-axis, imaginary part on the y-axis) the set of points such that |z|= 3 is the circle with center at (0, 0) and radius 3?  Further, you can write $z= 3e^{i\theta}$ or, equivalently $x= 3 cos(\theta)$, $y= 3sin(\theta)$ on that circle and do the integration with those parametric equations.
