Ex 7.6, 5 - Chapter 7 Class 12 Integrals

Last updated at May 29, 2018 by Teachoo

Integration Full Chapter Explained - Integration Class 12 - Everything you need

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

Transcript

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

Ex 7.6

Ex 7.6, 5 You are here

Ex 7.7 →

Chapter 7 Class 12 Integrals

Serial order wise

About the Author

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.