Integration Full Chapter Explained - https://you.tube/Integration-Class-12

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise

Transcript

Ex 7.6, 20 Integrate the function (๐‘ฅ โˆ’ 3)๐‘’๐‘ฅ/(๐‘ฅ โˆ’ 1)3 โˆซ1โ–’ใ€–((๐‘ฅ โˆ’ 3))/(๐‘ฅ โˆ’1)3 .๐‘’๐‘ฅ" " ๐‘‘๐‘ฅใ€— = โˆซ1โ–’ใ€–(๐‘ฅ โˆ’ 1 โˆ’ 2)/(๐‘ฅ โˆ’1)^3 .๐‘’๐‘ฅ" " ๐‘‘๐‘ฅใ€— = โˆซ1โ–’ใ€–๐‘’๐‘ฅ ((๐‘ฅ โˆ’ 1)/(๐‘ฅ โˆ’1)^3 โˆ’ 2/(๐‘ฅ โˆ’1)^3 )๐‘‘๐‘ฅใ€— = โˆซ1โ–’ใ€–๐‘’๐‘ฅ (1/(๐‘ฅ โˆ’1)^2 โˆ’ 2/(๐‘ฅ โˆ’1)^3 )๐‘‘๐‘ฅใ€— It is of the form โˆซ1โ–’ใ€–๐‘’^๐‘ฅ [๐‘“(๐‘ฅ)+๐‘“^โ€ฒ (๐‘ฅ)] ใ€— ๐‘‘๐‘ฅ=๐‘’^๐‘ฅ ๐‘“(๐‘ฅ)+๐ถ Where ๐‘“(๐‘ฅ)=" " 1/(๐‘ฅ โˆ’1)^2 โˆด ๐‘“^โ€ฒ (๐‘ฅ)= (โˆ’ 2)/(๐‘ฅ โˆ’ 1)^3 So, our equation becomes โˆซ1โ–’ใ€–๐‘’๐‘ฅ (1/(๐‘ฅ โˆ’ 1)^2 โˆ’ 2/(๐‘ฅ โˆ’ 1)^3 )๐‘‘๐‘ฅใ€— = ๐’†๐’™/(๐’™ โˆ’ ๐Ÿ)๐Ÿ +๐‘ช

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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.