问题
[$\textcolor{Orange}{\int \frac{1}{\sqrt{a^{2} – x^{2}}} \mathrm{d} x}$] 的积分该怎么计算？选项
[A]. $\int$ $\frac{1}{\sqrt{a^{2} – x^{2}}}$ $\mathrm{d} x$ $=$ $\arcsin \frac{x}{a}$ $+$ $C$[B]. $\int$ $\frac{1}{\sqrt{a^{2} – x^{2}}}$ $\mathrm{d} x$ $=$ $\sin \frac{x}{a}$ $+$ $C$
[C]. $\int$ $\frac{1}{\sqrt{a^{2} – x^{2}}}$ $\mathrm{d} x$ $=$ $- \arcsin \frac{a}{x}$ $+$ $C$
[D]. $\int$ $\frac{1}{\sqrt{a^{2} – x^{2}}}$ $\mathrm{d} x$ $=$ $\arcsin \frac{x}{a}$
$$\int \textcolor{Red}{\frac{1}{\sqrt{a^{2} – x^{2}}}} \mathrm{d} x =$$ $$\textcolor{Red}{\arcsin \frac{x}{a}} + \textcolor{Yellow}{C}.$$
相关公式：当 $a$ $=$ $1$ 时，$\int$ $\frac{1}{\sqrt{a^{2} – x^{2}}}$ $\mathrm{d} x$ 的积分公式可以简化为 $\int$ $\frac{1}{\sqrt{1 – x^{2}}}$ $\mathrm{d} x$ 的积分公式.