Example 9 (i) - Example 9Find the following integrals dx / x2 - x6 - Chapter 7 Class 12 CBSE NCERT Math - Integration by specific formulaes - Formula 3

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  1. Chapter 7 Class 12 Integrals
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Example 9 Find the following integrals: (i) โˆซ1โ–’๐‘‘๐‘ฅ/(๐‘ฅ^2โˆ’ 6๐‘ฅ + 13) โˆซ1โ–’๐‘‘๐‘ฅ/(๐‘ฅ^2โˆ’ 6๐‘ฅ + 13) =โˆซ1โ–’๐‘‘๐‘ฅ/(๐‘ฅ^2โˆ’ 2 ร— 3 ร— ๐‘ฅ + 13) = โˆซ1โ–’๐‘‘๐‘ฅ/((๐‘ฅ^2 โˆ’ 2 . 3 ๐‘ฅ + 3^2 ) + 13 โˆ’ 3^2 )("Adding and subtracting " (3)^2 ) = โˆซ1โ–’๐‘‘๐‘ฅ/((๐‘ฅ โˆ’ 3)^2 + 13 โˆ’ 9)("Using " ๐‘Ž^2โˆ’2๐‘Ž๐‘+๐‘^2=(๐‘Žโˆ’๐‘)^2 ) = โˆซ1โ–’๐‘‘๐‘ฅ/((๐‘ฅ โˆ’ 3)^2 + 4) = โˆซ1โ–’๐‘‘๐‘ฅ/((๐‘ฅ โˆ’ 3)^2 + 2^2 ) It is of form ๐‘‘๐‘ฅ/(๐‘ฅ^2 + ๐‘Ž^2 )=1/๐‘Ž ใ€–๐‘ก๐‘Ž๐‘›ใ€—^(โˆ’1)โกใ€–๐‘ฅ/๐‘Žใ€—+๐ถ Replacing ๐‘ฅ with (๐‘ฅโˆ’3) and ๐‘Ž with 2 =๐Ÿ/๐Ÿ ใ€–๐’•๐’‚๐’ใ€—^(โˆ’๐Ÿ)โกใ€–(๐’™ โˆ’ ๐Ÿ‘)/๐Ÿใ€— +๐‘ช

Chapter 7 Class 12 Integrals
Concept wise

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