\[\int_{0}^{1}{{{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right)\,dx=}\] [Karnataka CET 1999]

\[\frac{\pi }{2}+2\log \sqrt{2}\]

\[\frac{\pi }{2}-2\log \sqrt{2}\]

\[\frac{\pi }{4}-\log \sqrt{2}\]

\[\frac{\pi }{4}+\log \sqrt{2}\]

\[\int_{0}^{1}{{{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right)\,dx

1.	\[\int_{0}^{1}{{{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right)\,dx=}\] [Karnataka CET 1999]
A.	\[\frac{\pi }{2}-2\log \sqrt{2}\]
B.	\[\frac{\pi }{2}+2\log \sqrt{2}\]
C.	\[\frac{\pi }{4}-\log \sqrt{2}\]
D.	\[\frac{\pi }{4}+\log \sqrt{2}\]
Answer» B. \[\frac{\pi }{2}+2\log \sqrt{2}\]