Evaluate:
\[ \int_{|z|=1}\frac{\Log(z+e)}{z^2}\,dz; \]
\[ \int_{|z|=4}\left(\frac{\sin z}{z}\right)^{100}\,dz; \]
if \(\beta(t)=te^{it}\) for \(0\le t\le4\pi\) and \(\gamma\) is \(\beta\) followed by the segment from \(4\pi\) to \(0\), evaluate \[ \int_\gamma\frac{z^2+1}{(z+1)(z+4)}\,dz. \]