If ∫ f x log ⁡ sin ⁡ x d x = log ⁡ [ log ⁡ sin ⁡ x ] + c , then f x =

Step-by-step solution

Given ∫ f x log ⁡ sin ⁡ x d x = log ⁡ [ log ⁡ sin ⁡ x ] + C By using anti differentiation method, we will get d d x log ⁡ log ⁡ sin ⁡ x + c = 1 log ⁡ sin ⁡ x ⋅ 1 sin ⁡ x ⋅ cos ⁡ x = cot ⁡ x log ⁡ sin ⁡ x ∴ f x = cot ⁡ x