Mathematics

$$Evalute\;\int {\dfrac{{\cot x}}{{\sqrt {\sin x} }}} dx.$$


SOLUTION
Solution :-

$$ \displaystyle I = \int \frac{cotx}{\sqrt{sinx}}dx$$

$$ \displaystyle = \int \frac{cosx}{sinx \sqrt{sinx}}dx$$

Let $$ sinx = t$$

$$ \therefore cosx\, dx = dt$$
$$ \displaystyle \therefore I = \int \frac{dt}{t^{3/2}}$$

$$ =- 2t^{-1/2}+C$$

$$ = -\dfrac{2}{\sqrt{t}}+c$$

$$ = \dfrac{-2}{\sqrt{sinx}}+c$$
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Subjective Medium Published on 17th 09, 2020
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