Mathematics

# $\displaystyle \int \frac{\cot x}{\log \sin x}dx.$

$\displaystyle\log \left ( \log \sin x \right )$

##### SOLUTION
Let $\displaystyle I=\int \frac { \cot x }{ \log \sin x } dx$
Put $\displaystyle \log \sin x=t\Rightarrow \cot xdx=dt$
$\displaystyle I=\int \frac { dt }{ t } =\log t=\log \left( \log \sin x \right)$

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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].