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Question
` ∫ cot^3 x "cosec"^2 x dx `
Solution
` ∫ cot^3 x "cosec"^2 x dx `
\[Let, \cot x = t\]
\[ \Rightarrow - {cosec}^2 x = \frac{dt}{dx}\]
\[ \Rightarrow {cosec}^2\text{ x dx} = - dt\]
\[Now, \int \cot^3 \text{x }{cosec}^2\text{ x dx}\]
\[ = \int t^3 \left( - dt \right)\]
\[ = \frac{- t^4}{4} + C\]
\[ = \frac{- \cot^4 x}{4} + C\]
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