$\int$ $\frac{1}{a^{2} – x^{2}}$ $\mathrm{d} x$ 的积分公式(B006)

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].   $\int$ $\frac{1}{a^{2} – x^{2}}$ $\mathrm{d} x$ $=$ $\frac{1}{2a}$ $\ln \Big| \frac{a+x}{a-x} \Big|$ $+$ $C$

[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].   $\int$ $\frac{1}{a^{2} – x^{2}}$ $\mathrm{d} x$ $=$ $\frac{1}{2a}$ $\ln \Big| \frac{a+x}{a-x} \Big|$


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

基本积分公式: