Using a partial fraction decomposition, show that if z lies in the right half plane and C is the line segment from 0 to z, then
∫C dz/(z2+1) = i/2 Log(z+i) - i/2 Log(z-i) + π/2
Log(z) = ln(z) + i Arg(z) (maybe relevant?????)
The Attempt at a Solution
∫C dz/(z2+1) = -1/2 ∫C dz/(z+1) + 1/2 ∫C dz/(z-1) = -1/2 Log(z+1) + 1/2 Log(z+1) .......... This isn't looking promising. Suggestions?