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Ex 7.2, 2 - Integrate:  (log x)2 / x - Chapter 7 NCERT - Integration by substitution - x^n

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.2, 2 Integrate the function: (logโก๐‘ฅ )^2/๐‘ฅ Step 1: Let log ๐‘ฅ= ๐‘ก Differentiate ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ ๐‘‘๐‘ก/๐‘‘๐‘ฅ= 1/๐‘ฅ ๐‘‘๐‘ก.๐‘ฅ=๐‘‘๐‘ฅ ๐‘‘๐‘ฅ=๐‘‘๐‘ก.๐‘ฅ Step 2: Integrating function โˆซ1โ–’(logโก๐‘ฅ )^2/๐‘ฅ ๐‘‘๐‘ฅ Putting (๐‘™๐‘œ๐‘”โก๐‘ฅ )^2=๐‘ก=๐‘ฅ ๐‘‘๐‘ก = โˆซ1โ–’๐‘ก^2/๐‘ฅ ๐‘‘๐‘ก.๐‘ฅ = โˆซ1โ–’ใ€–๐‘ก^2 ๐‘‘๐‘กใ€— = ๐‘ก^(2+1)/(2+1)+๐ถ = ๐‘ก^3/3+๐ถ Putting ๐‘ก=logโก|๐‘ฅ| =๐Ÿ/๐Ÿ‘ (๐’๐’๐’ˆโก|๐’™| )^๐Ÿ‘+๐‘ช

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