# Example 9 (i) - Chapter 7 Class 12 Integrals

Last updated at Sept. 25, 2018 by Teachoo

Last updated at Sept. 25, 2018 by Teachoo

Transcript

Example 9 Find the following integrals: (i) ∫1▒𝑑𝑥/(𝑥^2− 6𝑥 + 13) ∫1▒𝑑𝑥/(𝑥^2− 6𝑥 + 13) =∫1▒𝑑𝑥/(𝑥^2− 2 × 3 × 𝑥 + 13) = ∫1▒𝑑𝑥/((𝑥^2 − 2 . 3 𝑥 + 3^2 ) + 13 − 3^2 )("Adding and subtracting " (3)^2 ) = ∫1▒𝑑𝑥/((𝑥 − 3)^2 + 13 − 9)("Using " 𝑎^2−2𝑎𝑏+𝑏^2=(𝑎−𝑏)^2 ) = ∫1▒𝑑𝑥/((𝑥 − 3)^2 + 4) = ∫1▒𝑑𝑥/((𝑥 − 3)^2 + 2^2 ) It is of form 𝑑𝑥/(𝑥^2 + 𝑎^2 )=1/𝑎 〖𝑡𝑎𝑛〗^(−1)〖𝑥/𝑎〗+𝐶 Replacing 𝑥 with (𝑥−3) and 𝑎 with 2 =𝟏/𝟐 〖𝒕𝒂𝒏〗^(−𝟏)〖(𝒙 − 𝟑)/𝟐〗 +𝑪

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
- Definate Integral as a limit of a sum
- Definate Integration - By Formulae
- Definate Integration - By Partial Fraction
- Definate Integration - By e formula
- Definate Integration - By Substitution
- Definate Integration by properties - P2
- Definate Integration by properties - P3
- Definate Integration by properties - P4
- Definate Integration by properties - P6
- Definate 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 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.