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Misc 8 - Integrate e5 log x - e4 log x / e3 log x - e2 log x

Misc 8 - Chapter 7 Class 12 Integrals - Part 2


Transcript

Misc 8 Integrate the function (๐‘’^(5 logโก๐‘ฅ ) โˆ’ ๐‘’^(4 logโก๐‘ฅ ))/(๐‘’^(3 logโก๐‘ฅ ) โˆ’ ๐‘’^(2 logโก๐‘ฅ ) ) โˆซ1โ–’(๐‘’^(5 logโก๐‘ฅ ) โˆ’ ๐‘’^(4 logโก๐‘ฅ ))/(๐‘’^(3 logโก๐‘ฅ ) โˆ’ ๐‘’^(2 logโก๐‘ฅ ) ) ๐‘‘๐‘ฅ = โˆซ1โ–’((ใ€–๐‘’ ใ€—^logโกใ€–๐‘ฅ^5 ใ€— โˆ’ ๐‘’^( logโกใ€–๐‘ฅ^4 ใ€— ))/(๐‘’^( logโกใ€–๐‘ฅ^3 ใ€— ) โˆ’ ๐‘’^( logโกใ€–๐‘ฅ^2 ใ€— ) )) ๐‘‘๐‘ฅ = โˆซ1โ–’(๐‘ฅ^5 โˆ’ ๐‘ฅ^4)/(๐‘ฅ^3 โˆ’ ๐‘ฅ^2 ) ๐‘‘๐‘ฅ = โˆซ1โ–’(๐‘ฅ^4 (๐‘ฅ โˆ’ 1))/(๐‘ฅ^2 (๐‘ฅ โˆ’ 1) ) ๐‘‘๐‘ฅ = โˆซ1โ–’๐‘ฅ^2 ๐‘‘๐‘ฅ =๐’™^๐Ÿ‘/๐Ÿ‘ +๐‘ช (Using ๐‘Ž logโก ๐‘ = logโก๐‘^๐‘Ž) (Using ๐‘’^(log ๐‘Ž)=๐‘Ž) =๐’™^๐Ÿ‘/๐Ÿ‘ +๐‘ช

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Davneet Singh

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.