Mathematics

$$\displaystyle \int \frac{\sec x}{\log \left ( \sec x+\tan x \right )}dx$$


ANSWER

$$\displaystyle \log \left [ \log \left ( \sec x+\tan x \right ) \right ].$$


SOLUTION
Let $$ \displaystyle I=\int  \frac { \sec  x }{ \log  \left( \sec  x+\tan  x \right)  } dx$$
Put $$ \displaystyle \log  \left( \sec  x+\tan  x \right) =t\Rightarrow \sec  xdx=dt$$
Therefore 
$$ \displaystyle I=\int { \frac { dt }{ t }  } =\log { t } =\log  \left[ \log  \left( \sec  x+\tan  x \right)  \right] $$
Hence, option 'B' is correct.
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Single Correct Medium Published on 17th 09, 2020
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