Mathematics

# $\displaystyle \int \frac{cosec x}{\log \tan \left ( x/2 \right )}dx$

$\displaystyle \log \left [ \log \tan \left ( x/2 \right ) \right ].$

##### SOLUTION
Let $\displaystyle I=\int \frac{cosec x}{\log \tan \left ( x/2 \right )}dx$
Put $\displaystyle \log \tan \left( x/2 \right) =t\Rightarrow \cos \sec xdx=dt$
Therefore
$\displaystyle I=\int { \frac { dt }{ t } } =\log { t } =\log \left[ \log \tan \left( x/2 \right) \right]$
Hence, option 'A' is correct.

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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The average value of a function f(x) over the interval, [a,b] is the number $\displaystyle \mu =\frac{1}{b-a}\int_{a}^{b}f\left ( x \right )dx$
The square root $\displaystyle \left \{ \frac{1}{b-a}\int_{a}^{b}\left [ f\left ( x \right ) \right ]^{2}dx \right \}^{1/2}$ is called the root mean square of f on [a, b]. The average value of $\displaystyle \mu$ is attained id f is continuous on [a, b].