evaluate the triple integral $z/( x^2 + z^2)$ 
i set this up in the order $dxdzdy$ and i tried factoring out the z, but I'm not sure how to integrate the denominator. I tried raising it to the -1 power and putting it to the top, and using u substitution, but there is no extra x. Can someone show me detailed steps on how to do this triple integral?

$$\begin{aligned}\int_1^4\int_1^z\int_0^z \frac{z}{x^2+z^2}\,dx\,dy\,dz &= \int_1^4\int_1^z \left[\arctan(x/z)\right]_0^z \,dy\,dz\\\
&=\int_1^4\int_1^z \frac{\pi}{4}\,dy\,dz\\
&=\int_1^4 \frac{\pi}{4}(z-1)\,dz\\
&=\frac{\pi}{4}\left[\frac{z^2}{2}-z\right]_1^4\\
&=\frac{9\pi}{8}
\end{aligned}$$
