question_answer

\[\int{\frac{dx}{{{a}^{2}}-{{x}^{2}}}}\] 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)  \[\frac{1}{2a}\log \,\left( \frac{a-x}{a+x} \right)\]