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

问题

[$\textcolor{Orange}{\int \frac{1}{\sqrt{x^{2} \pm a^{2}}} \mathrm{d} x}$] 的积分该怎么计算?

选项

[A].   $\int$ $\frac{1}{\sqrt{x^{2} \pm a^{2}}}$ $\mathrm{d} x$ $=$ $\ln \Big| x + \sqrt{x^{2} \mp a^{2}} \Big|$ $+$ $C$

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

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

[D].   $\int$ $\frac{1}{\sqrt{x^{2} \pm a^{2}}}$ $\mathrm{d} x$ $=$ $\ln \Big| x \pm \sqrt{x^{2} \pm a^{2}} \Big|$ $+$ $C$



显示答案

$$\int \textcolor{Red}{\frac{1}{\sqrt{x^{2} \pm a^{2}}}} \mathrm{d} x =$$ $$\textcolor{Red}{\ln \Big| x + \sqrt{x^{2} \pm a^{2}} \Big|} + \textcolor{Yellow}{C}.$$

基本积分公式: