\[\int{\frac{dx}{{{a}^{2}}-{{x}^{2}}}}\] is equal to[EAMCET 2002]

• A. \[\frac{1}{a}{{\tan }^{-1}}\left( \frac{x}{a} \right)\]
• B. \[\frac{1}{2a}{{\sin }^{-1}}\left( \frac{a-x}{a+x} \right)\]
• C. \[\frac{1}{2a}\log \,\left( \frac{a+x}{a-x} \right)\]
• D. \[\frac{1}{2a}\log \,\left( \frac{a-x}{a+x} \right)\]