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Question
\[\int \cot^n {cosec}^2 \text{ x dx } , n \neq - 1\]
Sum
Solution
∫ cotn x cosec2 x dx
Let cot x = t
⇒ –cosec2 x dx = dt
⇒ cosec2 x dx = –dt
\[Now, \int \cot^n \text{ x } {cosec}^2 \text { x dx }\]
\[ = - \int t^n dt \]
\[ = \frac{- t^{n + 1}}{n + 1} + C\]
\[ = - \frac{\cot^{n + 1} x}{n + 1} + C\]
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