Solve ∫ int(t+z) wrt zdt/a^2+(z^2+t^2)

$$\int \int \frac { ( t + z ) d z d t } { a ^ { 2 } + ( z ^ { 2 } + t ^ { 2 } ) }$$

Evaluate

$$\left\{\begin{matrix}\frac{t\ln(z^{2}+a^{2}+t^{2})}{2}+\frac{z\ln(z^{2}+a^{2}+t^{2})}{2}+Сt+\arctan(\frac{t}{\sqrt{z^{2}+a^{2}}})\sqrt{z^{2}+a^{2}}+\arctan(\frac{z}{\sqrt{a^{2}+t^{2}}})\sqrt{a^{2}+t^{2}}-t+С_{1},&a\neq 0\text{ or }t\neq 0\\t\ln(|z|)+Сt+С_{1},&t=0\text{ and }a=0\end{matrix}\right.$$

Differentiate w.r.t. t

$$\left\{\begin{matrix}\frac{\ln(z^{2}+a^{2}+t^{2})}{2}+\frac{\arctan(\frac{z}{\sqrt{a^{2}+t^{2}}})t}{\sqrt{a^{2}+t^{2}}}+С,&a\neq 0\text{ or }t\neq 0\\\ln(|z|)+С,&t=0\text{ and }a=0\end{matrix}\right.$$