Find ∫ (3 + 3 cos⁡x)/(x + sin⁡x ) dx

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  1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Transcript

Question 18 (OR 1st Question) Find ∫1 (3 + 3 cos⁡𝑥)/(𝑥 + sin⁡𝑥 ) dx ∫1 (3 + 3 cos⁡𝑥)/(𝑥 + sin⁡𝑥 ) dx = ∫1 (3(1 + cos⁡𝑥))/(𝑥 + sin⁡𝑥 ) dx Let t = x + sin x dt = (1 + cos x) dx Putting t and dt in equation = ∫1 3/𝑡 dt = 3 × ∫1▒1/𝑡 dt = 3 × log⁡〖|𝑡|〗 + C Putting back t = (x + sin x) = 3 × 𝒍𝒐𝒈⁡〖|(𝒙+𝐬𝐢𝐧⁡𝒙)|〗 + C

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.