\[\int_{0}^{\pi /4}{\frac{\sec x}{1+2{{\sin }^{2}}x}}\] is equal to [MNR 1994]

\[\frac{1}{3}\left[ \log (\sqrt{2}+1)-\frac{\pi }{2\sqrt{2}} \right]\]

\[\frac{1}{3}\left[ \log (\sqrt{2}+1)+\frac{\pi }{2\sqrt{2}} \right]\]

\[3\left[ \log (\sqrt{2}+1)-\frac{\pi }{2\sqrt{2}} \right]\]

\[3\left[ \log (\sqrt{2}+1)+\frac{\pi }{2\sqrt{2}} \right]\]

\[\int_{0}^{\pi /4}{\frac{\sec x}{1+2{{\sin }^{2}}x}}\] is equal to [

1.	\[\int_{0}^{\pi /4}{\frac{\sec x}{1+2{{\sin }^{2}}x}}\] is equal to [MNR 1994]
A.	\[\frac{1}{3}\left[ \log (\sqrt{2}+1)+\frac{\pi }{2\sqrt{2}} \right]\]
B.	\[\frac{1}{3}\left[ \log (\sqrt{2}+1)-\frac{\pi }{2\sqrt{2}} \right]\]
C.	\[3\left[ \log (\sqrt{2}+1)-\frac{\pi }{2\sqrt{2}} \right]\]
D.	\[3\left[ \log (\sqrt{2}+1)+\frac{\pi }{2\sqrt{2}} \right]\]
Answer» B. \[\frac{1}{3}\left[ \log (\sqrt{2}+1)-\frac{\pi }{2\sqrt{2}} \right]\]