Ex 7.6, 15 - Integrate (x2 + 1) log x - Chapter 7 NCERT - Integration by parts

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  1. Chapter 7 Class 12 Integrals
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Ex 7.6, 15 ( 𝑥﷮2﷯+1) log⁡𝑥 ﷮﷮( 𝑥﷮2﷯+1) log⁡𝑥 .𝑑𝑥﷯= ﷮﷮ log﷮𝑥﷯﷯ 𝑥﷮2﷯+1﷯ 𝑑𝑥﷯ ∴ ﷮﷮ log﷮𝑥﷯ 𝑥﷮2﷯+1﷯ 𝑑𝑥﷯ = log 𝑥﷮ ﷮﷮ 𝑥﷮2﷯+1﷯ 𝑑𝑥﷯﷯− ﷮﷮ 𝑑 log﷮𝑥﷯﷯﷮𝑑𝑥﷯ ﷮﷮ 𝑥﷮2﷯+1﷯ 𝑑𝑥﷯﷯ 𝑑𝑥﷯ = log 𝑥﷮ 𝑥﷮3﷯﷮3﷯ +𝑥﷯﷯− ﷮﷮ 1﷮𝑥﷯ 𝑥﷮3﷯﷮3﷯ +𝑥﷯ 𝑑𝑥﷯ = 𝑥﷮3﷯﷮3﷯ +𝑥﷯﷮log 𝑥﷯− ﷮﷮ 𝑥﷮2﷯﷮3﷯ +1﷯𝑑𝑥﷯ = 𝑥﷮3﷯﷮3﷯ +𝑥﷯﷮log 𝑥﷯− ﷮﷮ 𝑥﷮2﷯﷮3﷯𝑑𝑥﷯− ﷮﷮1 . 𝑑𝑥﷯ = 𝑥﷮3﷯﷮3﷯ +𝑥﷯﷮log 𝑥﷯− 𝑥﷮3﷯﷮3 . 3﷯ − 𝑥+𝐶 = 𝒙﷮𝟑﷯﷮𝟑﷯ +𝒙﷯﷮𝒍𝒐𝒈 𝒙﷯− 𝒙﷮𝟑﷯﷮𝟗﷯ − 𝒙+𝑪

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.