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Example 2 - Chapter 7 Class 12 Integrals - Part 4

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Example 2 Find the following integrals: (iii) โˆซโ–’(๐‘ฅ^(3/2)+2๐‘’^๐‘ฅโˆ’1/๐‘ฅ) ๐‘‘๐‘ฅ โˆซ1โ–’(๐‘ฅ^(3/2)+2๐‘’^๐‘ฅโˆ’1/๐‘ฅ) ๐‘‘๐‘ฅ =โˆซ1โ–’๐‘ฅ^(3/2) ๐‘‘๐‘ฅ+2โˆซ1โ–’๐‘’^๐‘ฅ ๐‘‘๐‘ฅโˆ’โˆซ1โ–’1/๐‘ฅ ๐‘‘๐‘ฅ = ๐‘ฅ^(3/2 + 1)/(3/2 + 1) +2๐‘’^๐‘ฅโˆ’logโกใ€– |๐‘ฅ|ใ€—+๐ถ = ๐‘ฅ^(5/2)/(5/2)+2๐‘’^๐‘ฅโˆ’ใ€–log ใ€—โก|๐‘ฅ|+๐ถ = ใ€–๐Ÿ๐’™ ใ€—^(๐Ÿ“/๐Ÿ)/๐Ÿ“+๐Ÿ๐’†^๐’™โˆ’ใ€–๐’๐’๐’ˆ ใ€—โก|๐’™|+๐‘ช As โˆซ1โ–’๐‘ฅ^๐‘› ๐‘‘๐‘ฅ=๐‘ฅ^(๐‘› + 1)/(๐‘› + 1) +๐ถ โˆซ1โ–’๐‘’^๐‘ฅ ๐‘‘๐‘ฅ=๐‘’^๐‘ฅ +๐ถ โˆซ1โ–’1/๐‘ฅ ๐‘‘๐‘ฅ=logโกใ€– |๐‘ฅ|ใ€— +๐ถ

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.