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Ex 7.6, 6 - Chapter 7 Class 12 Integrals (Term 2)

Last updated at Dec. 8, 2016 by

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

Ex 7.6, 6 - Chapter 7 Class 12 Integrals - Part 2

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

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.