A) \[\frac{1}{2\sqrt{7}}\,\log \,\left| \frac{\sqrt{7+x}}{\sqrt{7-x}} \right|+C\]
B) \[{{\sin }^{-1}}\,\left( \frac{x}{\sqrt{7}} \right)+C\]
C) \[\log |x+\sqrt{{{x}^{2}}-7}|+C\]
D) \[\frac{1}{2\sqrt{7}}\log \,\left| \frac{x-\sqrt{7}}{x+\sqrt{7}} \right|+C\]
Correct Answer: B
Solution :
\[\int{\frac{1}{\sqrt{7-{{x}^{2}}}}\,\,dx=\int{\frac{1}{\sqrt{{{(\sqrt{7})}^{2}}-{{x}^{2}}}}\,dx}}\] \[={{\sin }^{-1}}\left( \frac{x}{\sqrt{7}} \right)+C\]
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