6. (15 points) Let $c_R$ denote the semicircle, oriented in the counter-clockwise direction, $z = Re^{i\theta}$, where $0 \le \theta \le \pi$. Carefully show that \begin{equation*} \lim_{R \to \infty} \int_{c_R} \frac{(z - 3)dz}{(z^2 + 1)(2z^3 + 5)} = 0. \end{equation*}