∫e^πzdz 0->2+i/2,C:z=x+ix/4,x=0->2
=(1+i/4)∫e^π(x+ix/4)dx
=(1/π)e^π(1+i/4)x|0->2
=(1/π)(ie^2π-1)
C=C1+C2
C1:z=x=0->2
C2:z=2+iy,y=0->1/2
∫C1e^πxdx=(1/π)(e^2π-1)
∫C2e^π(2+iy)idy
=ie^2π(-i/π)e^πiy,y=0->1/2
=(1/π)e^2π(i-1)
∫C1+C2e^πzdz=(1/π)(ie^2π-1)