Mathematics

$$\displaystyle \int cosec^{n}x\cdot cotxdx,(n\neq 0)=$$


ANSWER

$$ -\displaystyle \dfrac{cosec^{n}x}{n}+c$$


SOLUTION
$$\int cosec^{n}x.cot x.dx$$
 
$$\int \dfrac{cos x}{sin^{n+1}x}dx$$

$$d sin x = cos x.dx$$

$$\int \dfrac{d sin x}{sin^{n+1}x}   sin x=t$$

$$\int \dfrac{dt}{t^{n+1}}=\dfrac{t^{-n}}{-n}+c$$

$$=\dfrac{-1}{n}cosec^{n}x+c$$

$$\int cosec^{n}x.cotx dx. =-\dfrac{cosec^{n}x}{n}+c$$
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Single Correct Medium Published on 17th 09, 2020
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