问题
[$\textcolor{Orange}{\int \frac{1}{a^{2} + x^{2}} \mathrm{d} x}$] 的积分该怎么计算？选项
[A]. $\int$ $\frac{1}{a^{2} + x^{2}}$ $\mathrm{d} x$ $=$ $\frac{x}{a}$ $\arctan \frac{1}{a}$ $+$ $C$[B]. $\int$ $\frac{1}{a^{2} + x^{2}}$ $\mathrm{d} x$ $=$ $\frac{1}{a}$ $\arctan x$ $+$ $C$
[C]. $\int$ $\frac{1}{a^{2} + x^{2}}$ $\mathrm{d} x$ $=$ $\frac{1}{a}$ $\arctan \frac{x}{a}$
[D]. $\int$ $\frac{1}{a^{2} + x^{2}}$ $\mathrm{d} x$ $=$ $\frac{1}{a}$ $\arctan \frac{x}{a}$ $+$ $C$
$$\int \textcolor{Red}{\frac{1}{a^{2} + x^{2}}} \mathrm{d} x =$$ $$\textcolor{Red}{\frac{1}{a}} \textcolor{Green}{\times} \textcolor{Red}{\arctan (\frac{x}{a})} + \textcolor{Yellow}{C}.$$其中，$a$ 为常数且 $a$ $\neq$ $0$.
当 $a$ $=$ $1$ 时，$\int$ $\frac{1}{a^{2} + x^{2}}$ $\mathrm{d} x$ 的积分公式就是：$\int$ $\frac{1}{1 + x^{2}}$ $\mathrm{d} x$ 的积分公式.