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

Ex 7.2, 2 - Chapter 7 Class 12 Integrals - Part 2


Transcript

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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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.