# Ex 7.4, 3 - Chapter 7 Class 12 Integrals

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 7.4, 3 1/โ((2 โ ๐ฅ)^2 + 1) Let 2โ๐ฅ=๐ก Diff both sides w.r.t. x 0โ1=๐๐ก/๐๐ฅ ๐๐ฅ=โ๐๐ก Integrating the function ๐ค.๐.๐ก.๐ฅ โซ1โ1/โ((2 โ ๐ฅ)^2 + 1) ๐๐ฅ Put the Values of 2โ๐ฅ=๐ก and ๐๐ฅ=โ๐๐ก =โซ1โ(โ๐๐ก)/โ(๐ก^2 + 1) =โโซ1โ๐๐ก/โ(๐ก^2 +(1)^2 ) =โlogโก|๐ก+โ(๐ก^2+1) |+๐ถ =logโกใ|๐ก+โ(๐ก^2+1) |^(โ1) ใ+๐ถ =logโกใ1/|๐ก + โ(๐ก^2 + 1) | ใ +๐ถ =logโกใ1/|2 โ ๐ฅ + โ((2 โ ๐ฅ)^2 + 1) | ใ +๐ถ =logโกใ1/|2 โ ๐ฅ + โ(ใ4 + ๐ฅใ^2 โ 4๐ฅ + 1) | ใ +๐ถ =๐๐๐โกใ๐/|๐ โ ๐ + โ(๐^๐ โ ๐๐ + ๐) | ใ +๐ช

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

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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.