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Ex 7.6, 5 - Integrate x log 2x - Chapter 7 Class 12 - Ex 7.6

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.6, 5 ๐‘ฅ logโก2๐‘ฅ Integrating the function ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ โˆซ1โ–’ใ€–๐‘ฅ logโก2๐‘ฅ ใ€— ๐‘‘๐‘ฅ Hence, we take First function :- ๐‘“(๐‘ฅ)=logโก(2๐‘ฅ) Second function :- g(๐‘ฅ)=๐‘ฅ โˆซ1โ–’ใ€–๐‘ฅ logโก๐‘ฅ ใ€— ๐‘‘๐‘ฅ=โˆซ1โ–’(logโก๐‘ฅ )๐‘ฅ ๐‘‘๐‘ฅ =logโก(2๐‘ฅ) โˆซ1โ–’๐‘ฅ ๐‘‘๐‘ฅโˆ’โˆซ1โ–’(๐‘‘(logโก2๐‘ฅ )/๐‘‘๐‘ฅ โˆซ1โ–’ใ€–๐‘ฅ.๐‘‘๐‘ฅใ€—)๐‘‘๐‘ฅ =logโก(2๐‘ฅ) (๐‘ฅ^2/2)โˆ’โˆซ1โ–’ใ€–1/2๐‘ฅ . 2 .๐‘ฅ^2/2. ๐‘‘๐‘ฅใ€— =ใ€–๐‘ฅ^2/2 logใ€—โก(2๐‘ฅ)โˆ’โˆซ1โ–’ใ€–๐‘ฅ/2. ๐‘‘๐‘ฅใ€— =ใ€–๐‘ฅ^2/2 logใ€—โก(2๐‘ฅ)โˆ’1/2 โˆซ1โ–’ใ€–๐‘ฅ ๐‘‘๐‘ฅใ€— =ใ€–๐‘ฅ^2/2 logใ€—โก(๐‘ฅ)โˆ’ 1/2 (๐‘ฅ^2/2)+๐ถ =ใ€–๐‘ฅ^2/2 logใ€—โก(2๐‘ฅ)โˆ’ ๐‘ฅ^2/4 +๐ถ

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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