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Ex 7.6, 4 - Finding integration x log x - CBSE NCERT - Integration by parts

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.6, 4 ๐‘ฅ logโก๐‘ฅ โˆซ1โ–’ใ€–๐‘ฅ logโก๐‘ฅ ใ€— ๐‘‘๐‘ฅ โˆซ1โ–’ใ€–๐‘ฅ logโก๐‘ฅ ใ€— ๐‘‘๐‘ฅ=โˆซ1โ–’(logโก๐‘ฅ )๐‘ฅ ๐‘‘๐‘ฅ =logโก๐‘ฅ โˆซ1โ–’๐‘ฅ ๐‘‘๐‘ฅโˆ’โˆซ1โ–’(๐‘‘(logโก๐‘ฅ )/๐‘‘๐‘ฅ โˆซ1โ–’ใ€–๐‘ฅ.๐‘‘๐‘ฅใ€—)๐‘‘๐‘ฅ =logโก๐‘ฅ (๐‘ฅ^2/2)โˆ’โˆซ1โ–’ใ€–1/๐‘ฅ . ๐‘ฅ^2/2. ๐‘‘๐‘ฅใ€— =ใ€–๐‘ฅ^2/2 logใ€—โกใ€– ๐‘ฅใ€—โˆ’1/2 โˆซ1โ–’ใ€–๐‘ฅ. ๐‘‘๐‘ฅใ€— =ใ€–๐‘ฅ^2/2 logใ€—โก๐‘ฅโˆ’1/2 . ๐‘ฅ^2/2 +๐ถ =ใ€–๐’™^๐Ÿ/๐Ÿ ๐’๐’๐’ˆใ€—โกใ€– ๐’™ใ€—โˆ’ ๐’™^๐Ÿ/๐Ÿ’ +๐‘ช " "

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