\[\int_{0}^{\pi /4}{\frac{\sec x}{1+2{{\sin }^{2}}x}}\] 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. \[\frac{1}{3}\left[ \log (\sqrt{2}+1)-\frac{\pi }{2\sqrt{2}} \right]\]

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

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