Originally Posted by

**platinumpimp68plus1** I'm stuck... its been awhile since I've done integrals.

So the integral is $\displaystyle \int\frac{dz}{z}$ along the straight line segment from 1 to i. I parameterized the curve as $\displaystyle \gamma:[0,1]\rightarrow C$, defined as $\displaystyle \gamma(t)=(-t+1)+it$ and then used the property that dividing 1 by z is the equivalent of $\displaystyle z^{-1}$. So I have:

$\displaystyle \int(\frac{-t+1}{(-t+1)^2+t^2})-i\frac{t}{(-t+1)^2+t^2}dt\\=\int(\frac{-t+1}{(-t+1)^2+t^2})dt-i\int\frac{t}{(-t+1)^2+t^2}dt$

I have no clue how to integrate these... is there some trick I'm forgetting? any help?