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

Transcript

Ex 7.2, 14 Integrate the function: 1/(๐‘ฅ(logโก๐‘ฅ )^๐‘š ) , ๐‘ฅ > 0 Step 1: Let logโก๐‘ฅ=๐‘ก Differentiating both sides ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ 1/๐‘ฅ= ๐‘‘๐‘ก/๐‘‘๐‘ฅ ๐‘‘๐‘ฅ=๐‘ฅ . ๐‘‘๐‘ก Step 2: Integrating the function โˆซ1โ–’ใ€–" " 1/(๐‘ฅ(logโก๐‘ฅ )^๐‘š )ใ€— . ๐‘‘๐‘ฅ Putting ๐‘™๐‘œ๐‘”โก๐‘ฅ=๐‘ก & ๐‘‘๐‘ฅ=๐‘ฅ . ๐‘‘๐‘ก = โˆซ1โ–’ใ€–" " 1/(๐‘ฅ . ๐‘ก^๐‘š )ใ€— . ๐‘ฅ ๐‘‘๐‘ก = โˆซ1โ–’ใ€–" " 1/๐‘ก^๐‘š ใ€— . ๐‘‘๐‘ก = โˆซ1โ–’ใ€–" " ๐‘ก^(โˆ’๐‘š) ใ€— . ๐‘‘๐‘ก = ๐‘ก^(โˆ’๐‘š + 1)/(โˆ’๐‘š +1) +๐ถ = ๐‘ก^(1 โˆ’ ๐‘š)/(1 โˆ’ ๐‘š) +๐ถ Putting back t = log x = (๐’๐’๐’ˆโก๐’™ )^(๐Ÿ โˆ’ ๐’Ž)/(๐Ÿ โˆ’ ๐’Ž) +๐‘ช (Using โˆซ1โ–’๐‘ฅ^๐‘› . ๐‘‘๐‘ฅ=๐‘ฅ^(๐‘›+1)/(๐‘› +1))

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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.