<img height="1" width="1" style="display:none" src="https://www.facebook.com/tr?id=539359806247306&ev=PageView&noscript=1"/>

Ex 7.6, 6 - Integrate x2 log x - Chapter 7 Class 12 - Integration by parts

Slide10.JPG


Transcript

Ex7.6, 6 𝑥2 log﷮𝑥﷯ ﷮﷮ 𝑥﷮2﷯ log﷮𝑥﷯﷯ 𝑑𝑥 Hence, by ILATE First function :- 𝑓 𝑥﷯= log﷮𝑥﷯ Second function :- g 𝑥﷯= 𝑥﷮2﷯ ﷮﷮ 𝑥﷮2﷯ log﷮ 𝑥﷯﷯﷯ 𝑑𝑥 = ﷮﷮ log﷮𝑥﷯﷯ 𝑥﷮2﷯﷯𝑑𝑥 = log﷮𝑥﷯ ﷮﷮ 𝑥﷮2﷯﷯𝑑𝑥− ﷮﷮ 𝑑 log﷮𝑥﷯﷯﷮𝑑𝑥﷯ ﷮﷮ 𝑥﷮2﷯.𝑑𝑥﷯﷯𝑑𝑥﷯ = log﷮𝑥﷯ 𝑥﷮3﷯﷮3﷯− ﷮﷮ 1﷮𝑥﷯ . 𝑥﷮3﷯﷮3﷯. 𝑑𝑥﷯ = 𝑥﷮3﷯﷮3﷯ log﷮𝑥﷯− ﷮﷮ 𝑥﷮2﷯﷮3﷯ 𝑑𝑥﷯ = 𝑥﷮3﷯﷮3﷯ log﷮𝑥﷯− 1﷮3﷯ ﷮﷮ 𝑥﷮2﷯ 𝑑𝑥﷯ = 𝑥﷮3﷯﷮3﷯ log﷮𝑥﷯− 1﷮3﷯ 𝑥﷮3﷯﷮3﷯﷯+𝐶 = 𝒙﷮𝟑﷯﷮𝟑﷯ 𝒍𝒐𝒈﷮𝒙﷯− 𝒙﷮𝟑﷯﷮𝟗﷯ +𝑪

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can contact him here.
Jail