# Example 9 (ii)

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Example 9 Find the following integrals: (ii) 𝑑𝑥 3𝑥2−13𝑥 + 10 𝑑𝑥 3𝑥2 − 13𝑥 + 10 Solving denominator 3𝑥2+13𝑥−10 =3 𝑥2+ 133𝑥 − 103 =3 𝑥2+2. 𝑥× 136 − 103 Adding and subtracting 1362 =3 𝑥2+2. 𝑥× 136+ 1362− 103− 1362 =3 𝑥+ 1362− 103− 16936 =3 𝑥+ 1362− 103 + 16936 =3 𝑥+ 1362− 120 + 6936 =3 𝑥+ 1362− 18936 =3 𝑥+ 1362− 1762 Hence, our equation becomes 𝑑𝑥 3𝑥2−13𝑥 + 10 = 13 𝑑𝑥 𝑥 + 1362− 1762 = 13 × 12 176 × log 𝑥 + 136 − 176𝑥+ 136 + 176 + C = 13 × 62 17 × log 6𝑥 + 13 − 176 6𝑥 +13 + 176 + C = 117 log 6𝑥 − 46𝑥 + 30 + C = 117 log 2(3𝑥 − 2)6(𝑥 + 5)+ C = 117 log 2(3𝑥 − 2)6(𝑥 + 5)+ C = 117 log (3𝑥 − 2)3(𝑥 + 5)+ C = 117 log (3𝑥 − 2)(𝑥 + 5)− 117 log3 + C = 𝟏𝟏𝟕 𝒍𝒐𝒈 (𝟑𝒙 − 𝟐)(𝒙 + 𝟓)+ C1

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

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.