I was solving surface integral problems. I came across a solved problem. And I understood the concepts alright. But I got stuck at the penultimate step. It says $\displaystyle\int_{z=0}^{5}\int_{x=0}^{4}(\frac{xz}{\sqrt{16 - x^2}} + x)dxdz = \displaystyle\int_{z=0}^{5}(4z + 8)dz$
I have no idea how it came. Please show me the steps between these two steps.
I am in my first semester of Physics undergrad course.
Do the integration with respect to $x$: $$\int_{0}^{4}\left(\frac{xz}{\sqrt{16-x^2}}+x\right)\,dx=\left[-z\sqrt{16-x^2}+\frac{x^2}{2}\right]_{x=0}^{4} = 4z+8$$