Mathematics

Solve $$\int\cot x \log \sin xdx$$


SOLUTION
 $$\int\cot x \log \sin xdx$$
Put, $$ \log \sin x  = t $$

$$\implies \dfrac{1}{\sin x} \cos x dx = dt$$

$$\implies \cot x dx = dt $$

Now, $$\int \cot x \log \sin xdx = \int t dt$$

$$ = \dfrac{t^2}{2} + c$$

$$ = \dfrac{(\log \sin x)^2 }{2}+ c$$

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Subjective Medium Published on 17th 09, 2020
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