\[\int_{0}^{\pi /4}{\frac{{{\sec }^{2}}x}{(1+\tan x)(2+\tan x)}}\,dx=\

1.	\[\int_{0}^{\pi /4}{\frac{{{\sec }^{2}}x}{(1+\tan x)(2+\tan x)}}\,dx=\]
A.	\[{{\log }_{e}}\left( \frac{2}{3} \right)\]
B.	\[{{\log }_{e}}3\]
C.	\[\frac{1}{2}{{\log }_{e}}\left( \frac{4}{3} \right)\]
D.	\[{{\log }_{e}}\left( \frac{4}{3} \right)\]
Answer» E.

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\[\int_{0}^{\pi /4}{\frac{{{\sec }^{2}}x}{(1+\tan x)(2+\tan x)}}\,dx=\]

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