Primitives of two rational functions on the exterior of a disk

Let \(U=\{z\in\mathbb C:|z|>4\}\).

1. Show that there is a holomorphic function on \(U\) whose derivative is \[ \frac{z}{(z-1)(z-2)(z-3)}. \]
2. Is there a holomorphic function on \(U\) whose derivative is \[ \frac{z^2}{(z-1)(z-2)(z-3)}? \]