Find ∫ (3 + 3 cos⁡x)/(x + sin⁡x ) dx
![Question 18 (OR 1st Question) - CBSE Class 12 Sample Paper for 2020 Boards - Part 2](https://d1avenlh0i1xmr.cloudfront.net/8171aa63-a8ce-4be4-bc4f-e408bd5a8267/slide46.jpg)
CBSE Class 12 Sample Paper for 2020 Boards
CBSE Class 12 Sample Paper for 2020 Boards
Last updated at April 16, 2024 by Teachoo
Question 18 (OR 1st Question) Find ∫1 (3 + 3 cos𝑥)/(𝑥 + sin𝑥 ) dx ∫1 (3 + 3 cos𝑥)/(𝑥 + sin𝑥 ) dx = ∫1 (3(1 + cos𝑥))/(𝑥 + sin𝑥 ) 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+𝐬𝐢𝐧𝒙)|〗 + C