Example 9 (i) - Chapter 7 Class 12 Integrals
Last updated at April 16, 2024 by Teachoo
Integration by specific formulaes - Formula 3
Integration by specific formulaes - Formula 3
Last updated at April 16, 2024 by Teachoo
Example 9 Find the following integrals: (i) โซ1โ๐๐ฅ/(๐ฅ^2โ 6๐ฅ + 13) โซ1โ๐๐ฅ/(๐ฅ^2โ 6๐ฅ + 13) =โซ1โ๐๐ฅ/(๐ฅ^2โ 2 ร 3 ร ๐ฅ + 13) = โซ1โ๐๐ฅ/((๐ฅ^2 โ 2 . 3 ๐ฅ + 3^2 ) + 13 โ 3^2 )("Adding and subtracting " (3)^2 ) = โซ1โ๐๐ฅ/((๐ฅ โ 3)^2 + 13 โ 9)("Using " ๐^2โ2๐๐+๐^2=(๐โ๐)^2 ) = โซ1โ๐๐ฅ/((๐ฅ โ 3)^2 + 4) = โซ1โ๐๐ฅ/((๐ฅ โ 3)^2 + 2^2 ) It is of form ๐๐ฅ/(๐ฅ^2 + ๐^2 )=1/๐ ใ๐ก๐๐ใ^(โ1)โกใ๐ฅ/๐ใ+๐ถ Replacing ๐ฅ with (๐ฅโ3) and ๐ with 2 =๐/๐ ใ๐๐๐ใ^(โ๐)โกใ(๐ โ ๐)/๐ใ +๐ช