The value of ∫ ln ⁡ c o t x sin ⁡ 2 x d x is equal to (where, C is the constant of integration)

Question

The value of ∫ ln ⁡ c o t x sin ⁡ 2 x d x is equal to (where, C is the constant of integration), ln ⁡ cot ⁡ x 2 2 + C, ln ⁡ cot ⁡ x 2 4 + C, ln ⁡ cot ⁡ x 2 6 + C, - 1 4 ln ⁡ cot ⁡ x 2 + C

MARKS App · Accepted Answer

∫ ln ⁡ cot ⁡ x 2 sin ⁡ x cos ⁡ x d x = Ι (let) Put ln ⁡ cot ⁡ x = t ⇒ 1 cot ⁡ x × cosec 2 ⁡ x d x = - d t ⇒ d x cos ⁡ x sin ⁡ x = - d t So, Ι = 1 2 ∫ - t d t = - 1 2 t 2 2 + C = - 1 4 ln ⁡ cot ⁡ x 2 + C

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