Tìm nguyên hàm \(I = \int {\frac{1}{{4 - {x^2}}}dx} .\)

Tìm nguyên hàm \(I = \int {\frac{1}{{4 - {x^2}}}dx} .\)
A. \(I = \frac{1}{2}\ln \left| {\frac{{x + 2}}{{x - 2}}} \right| + C\)
B. \(I = \frac{1}{2}\ln \left| {\frac{{x - 2}}{{x + 2}}} \right| + C\)
C. \(I = \frac{1}{4}\ln \left| {\frac{{x - 2}}{{x+2}}} \right| + C\)
D. \(I = \frac{1}{4}\ln \left| {\frac{{x + 2}}{{x - 2}}} \right| + C\)

\(\begin{array}{l} \int {\frac{1}{{4 - {x^2}}}dx} = \int {\frac{1}{{\left( {2 - x} \right)\left( {2 + x} \right)}}dx} \\ = \frac{1}{4}\int {\left( { - \frac{1}{{x - 2}} + \frac{1}{{2 + x}}} \right)dx} = \frac{1}{4}\ln \left| {\frac{{x + 2}}{{x - 1}}} \right| + C \end{array}\)