Mathematics

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

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

##### 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
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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