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

Last updated at Dec. 16, 2024 by

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

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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 and Computer Science at Teachoo