Ex 7.2, 29 - Integrate cot x log sin x - Chapter 7 NCERT - Integration by substitution - Trignometric - Normal

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  1. Chapter 7 Class 12 Integrals
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Ex 7.2, 29 cot⁡𝑥 log⁡sin⁡𝑥 Step 1: Let log⁡sin⁡𝑥=𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 1﷮ sin﷮𝑥﷯﷯ . 𝑑﷮𝑑𝑥﷯ sin 𝑥﷯= 𝑑𝑡﷮𝑑𝑥﷯ 1﷮ sin﷮𝑥﷯﷯ . co𝑠﷮𝑥﷯= 𝑑𝑡﷮𝑑𝑥﷯ cot﷮𝑥﷯= 𝑑𝑡﷮𝑑𝑥﷯ 𝑑𝑥= 𝑑𝑡﷮ cot﷮𝑥﷯﷯ Step 2: Integrating the function ﷮﷮ cot⁡𝑥 log⁡sin⁡𝑥﷯. 𝑑𝑥 putting 𝑙𝑜𝑔﷮ 𝑠𝑖𝑛﷮𝑥﷯﷯=𝑡 & 𝑑𝑥= 𝑑𝑡﷮ cot﷮𝑥﷯﷯ = ﷮﷮ cot﷮𝑥﷯﷯. 𝑡 . 𝑑𝑡﷮ cot﷮𝑥﷯﷯ = ﷮﷮ 𝑡﷯. 𝑑𝑡 = 𝑡﷮1 + 1﷯﷮1 + 1﷯ +𝐶 = 𝑡﷮2﷯﷮2﷯ +𝐶 = 𝟏﷮𝟐﷯ 𝐥𝐨𝐠﷮ 𝐬𝐢𝐧﷮𝒙﷯﷯﷯﷮𝟐﷯+𝑪

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