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]. $\int$ $\frac{1}{a^{2} – x^{2}}$ $\mathrm{d} x$ $=$ $\frac{1}{2a}$ $\ln \Big| \frac{a+x}{a-x} \Big|$[B]. $\int$ $\frac{1}{a^{2} – x^{2}}$ $\mathrm{d} x$ $=$ $\frac{1}{2a}$ $\ln \Big| \frac{a+x}{a-x} \Big|$ $+$ $C$
[C]. $\int$ $\frac{1}{a^{2} – x^{2}}$ $\mathrm{d} x$ $=$ $\frac{1}{2a}$ $\ln \Big| \frac{a-x}{a+x} \Big|$ $+$ $C$
[D]. $\int$ $\frac{1}{a^{2} – x^{2}}$ $\mathrm{d} x$ $=$ $\frac{1}{2a}$ $\ln \Big| \frac{a+x}{a+x} \Big|$ $+$ $C$
$$\int \textcolor{Red}{\frac{1}{a^{2} – x^{2}}} \mathrm{d} x =$$ $$\textcolor{Red}{\frac{1}{2a}} \textcolor{Green}{\times} \textcolor{Red}{\ln \Big| \frac{a+x}{a-x} \Big|} + \textcolor{Yellow}{C}.$$其中，$a$ 为常数且 $a$ $\neq$ $0$.