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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

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.