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Last updated at Sept. 27, 2018 by Teachoo

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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

Integration by specific formulaes - Formula 3

Chapter 7 Class 12 Integrals

Concept wise

- Using Formulaes
- Using Trignometric Formulaes
- Integration by substitution - x^n
- Integration by substitution - lnx
- Integration by substitution - e^x
- Integration by substitution - Trignometric - Normal
- Integration by substitution - Trignometric - Inverse
- Integration using trigo identities - sin^2,cos^2 etc formulae
- Integration using trigo identities - a-b formulae
- Integration using trigo identities - 2x formulae
- Integration using trigo identities - 3x formulae
- Integration using trigo identities - CD and CD inv formulae
- Integration using trigo identities - Inv Trigo formulae
- Integration by parts
- Integration by parts - e^x integration
- Integration by specific formulaes - Formula 1
- Integration by specific formulaes - Formula 2
- Integration by specific formulaes - Formula 3
- Integration by specific formulaes - Formula 4
- Integration by specific formulaes - Formula 5
- Integration by specific formulaes - Formula 6
- Integration by specific formulaes - Formula 7
- Integration by specific formulaes - Formula 8
- Integration by specific formulaes - Method 9
- Integration by specific formulaes - Method 10
- Integration by partial fraction - Type 1
- Integration by partial fraction - Type 2
- Integration by partial fraction - Type 3
- Integration by partial fraction - Type 4
- Integration by partial fraction - Type 5
- Definite Integral as a limit of a sum
- Definite Integration - By Formulae
- Definite Integration - By Partial Fraction
- Definite Integration - By e formula
- Definite Integration - By Substitution
- Definite Integration by properties - P2
- Definite Integration by properties - P3
- Definite Integration by properties - P4
- Definite Integration by properties - P6
- Definite Integration by properties - P7

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.