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

问题

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

选项

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

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

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

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



显示答案

$$\int \textcolor{Red}{\frac{1}{1 – x^{2}}} \mathrm{d} x =$$ $$\textcolor{Red}{\frac{1}{2}} \textcolor{Green}{\times} \textcolor{Red}{\ln \Big| \frac{1+x}{1-x} \Big|} + \textcolor{Yellow}{C}.$$

基本积分公式: