Hello,

I have been working on complex integration in my own time and have managed to solve a few, but these three seriously have me stumped. I was wondering if anyone would be willing to help me understand these problems.

a) $\displaystyle \int_{\gamma } \frac{z}{(z+2)(z-1)}dz$ where $\displaystyle \gamma$ is the circle of radius 4 about the origin, traversed twice in the clockwise direction.

b) $\displaystyle \int_{\gamma } \frac{2z^{2}-z+1}{(z-1)^2(z+1)}dz$ where $\displaystyle \gamma$ proceeds around the boundary of the figure eight formed by two circles of radius 1 with centres 1 and −1 by starting at 0, going once counterclockwise around the right circle followed by going once counterclockwise around the left circle.

c) $\displaystyle \int_{\gamma } \frac{5z-2}{z(z-1)(z-3)}dz$ where $\displaystyle \gamma$ is the circle of radius 2 about the origin.

I thank you all in advance! Your help is very much appreciated.