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∫ C O S E C X C O S E C X − Cot X D X - Mathematics

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प्रश्न

` ∫  {cosec x} / {"cosec x "- cot x} ` dx      

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उत्तर

` ∫ ( {"cosec "x} / {"cosec x "- cot x} )` dx 
\[ = \int\frac{\text{cosec x}\left( \text{cosec x }+ \cot x \right)}{\left(\text{ cosec x} - \cot x \right) \left( \text{cosec x }+ \cot x \right)}dx\]
\[ = \int\frac{\text{cosec x} \left( \text{cosec x }+ \cot x \right)}{\left( {\text{cosec}}^2 x - \cot^2 x \right)}dx\]
\[ = \int\left( {\text{cosec}}^2 x + \text{cosec x } \cot x \right)dx\]
\[ = - \cot x - \text{cosec x }+ C\]

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अध्याय 19: Indefinite Integrals - Exercise 19.02 [पृष्ठ १५]

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आरडी शर्मा Mathematics [English] Class 12
अध्याय 19 Indefinite Integrals
Exercise 19.02 | Q 32 | पृष्ठ १५

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