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∫ Cot 3 X C O S E C 2 X D X - Mathematics

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प्रश्न

 ` ∫       cot^3   x  "cosec"^2   x   dx `

बेरीज
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उत्तर

 ` ∫       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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पाठ 19: Indefinite Integrals - Exercise 19.09 [पृष्ठ ५७]

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आरडी शर्मा Mathematics [English] Class 12
पाठ 19 Indefinite Integrals
Exercise 19.09 | Q 7 | पृष्ठ ५७

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