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Last updated at Dec. 20, 2019 by Teachoo

Transcript

Ex 7.4, 8 Integrate ๐ฅ^2/โ(๐ฅ^6 + ๐^6 ) Let ๐ฅ^3=๐ก Differentiating both sides w.r.t. x 3๐ฅ^2=๐๐ก/๐๐ฅ ๐๐ฅ=๐๐ก/(3๐ฅ^2 ) Integrating the function โซ1โ๐ฅ^2/โ(๐ฅ^6 + ๐^6 ) ๐๐ฅ=โซ1โ๐ฅ^2/โ((๐ฅ^3 )^2 + (๐^3 )^2 ) ๐๐ฅ Putting values of ๐ฅ^3=๐ก and ๐๐ฅ=๐๐ก/(3๐ฅ^2 ) , we get =โซ1โ๐ฅ^2/โ(๐ก^2 + (๐^3 )^2 ) ๐๐ฅ =โซ1โ๐ฅ^2/โ(๐ก^2 + (๐^3 )^2 ) . ๐๐ก/(3๐ฅ^2 ) =โซ1โ1/โ((๐ก^2 + (๐^3 )^2 ) ) . ๐๐ก/3 =1/3 โซ1โ๐๐ก/โ(๐ก^2 + (๐^3 )^2 ) =1/3 [logโก|๐ก+โ(๐ก^2 + (๐^3 )^2 )|+๐ถ1] It is of form โซ1โ๐๐ฅ/โ(๐ฅ^2 + ๐^2 ) =logโก|๐ฅ+โ(๐ฅ^2 + ๐^2 )|+๐ถ1 โด Replacing ๐ฅ by ๐ก and a by ๐^3, we get =1/3 logโก|๐ก+โ(๐ก^2 + ๐^6 ) |+๐ถ =1/3 logโก|๐ฅ^3+โ((๐ฅ^3 )^2 + ๐^6 ) |+๐ถ =๐/๐ ๐๐๐โก|๐^๐+โ(๐^๐+ ๐^๐ ) |+๐ช ("Using" ๐ก=๐ฅ^3 )

Integration by specific formulaes - Formula 6

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.