$\: f(z)=3z+z^3-1\: \Longrightarrow\: f^3(\frac{-1}{2})=6\: \: \Longrightarrow\int\: \frac{3z+z^3-1}{(2z+1)^4}dz\: :\: \: \: 2\pi i\: \ast\: \frac{f^3(\frac{-1}{2})}{3!}=2\pi i\ast\frac{6}{6}=2\pi i$