Chapter 7 Class 12 Integrals
Concept wise

Ex 7.6, 5 - Integrate x log 2x - Chapter 7 Class 12 - Integration by parts

Ex 7.6, 5 - Chapter 7 Class 12 Integrals - Part 2


Ex 7.6, 5 𝑥 log⁡2𝑥 Integrating the function 𝑤.𝑟.𝑡.𝑥 ∫1▒〖𝑥 log⁡2𝑥 〗 𝑑𝑥 Hence, we take First function :- 𝑓(𝑥)=log⁡(2𝑥) Second function :- g(𝑥)=𝑥 ∫1▒〖𝑥 log⁡𝑥 〗 𝑑𝑥=∫1▒(log⁡𝑥 )𝑥 𝑑𝑥 =log⁡(2𝑥) ∫1▒𝑥 𝑑𝑥−∫1▒(𝑑(log⁡2𝑥 )/𝑑𝑥 ∫1▒〖𝑥.𝑑𝑥〗)𝑑𝑥 =log⁡(2𝑥) (𝑥^2/2)−∫1▒〖1/2𝑥 . 2 .𝑥^2/2. 𝑑𝑥〗 =〖𝑥^2/2 log〗⁡(2𝑥)−∫1▒〖𝑥/2. 𝑑𝑥〗 =〖𝑥^2/2 log〗⁡(2𝑥)−1/2 ∫1▒〖𝑥 𝑑𝑥〗 =〖𝑥^2/2 log〗⁡(𝑥)− 1/2 (𝑥^2/2)+𝐶 =〖𝑥^2/2 log〗⁡(2𝑥)− 𝑥^2/4 +𝐶

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.