# Ex 7.5, 11 - Chapter 7 Class 12 Integrals

Last updated at July 11, 2018 by Teachoo

Last updated at July 11, 2018 by Teachoo

Transcript

Ex 7.5, 11 5𝑥 𝑥 + 1 𝑥2− 4 We can write the integrand as 5𝑥 𝑥 + 1 𝑥2− 4 = 5𝑥 𝑥 + 1 𝑥 − 2 𝑥 + 2 5𝑥 𝑥 + 1 𝑥2− 4 = 𝐴 𝑥 + 1 + 𝐵 𝑥 − 2 + 𝐶 𝑥 + 2 5𝑥 𝑥 + 1 𝑥2− 4 = 𝐴 𝑥 − 2 𝑥 + 2 + 𝐵 𝑥 + 1 𝑥 + 2 + 𝐶 𝑥 +1 𝑥 − 2 𝑥 + 1 𝑥 − 2 𝑥 + 2 By cancelling denominator 5𝑥 = 𝐴 𝑥−2 𝑥+2+𝐵 𝑥+1 𝑥+2+𝐶 𝑥+1 𝑥−2 Putting x = −1, in (1) 5 × −1 = 𝐴 −1−2 −1+2+𝐵 −1+1 −1+2+𝐶 −1+1 −1−2 −5 = 𝐴 −3 1+𝐵×0+𝐶×0 −5 = −3𝐴 𝐴 = − 5− 3 = 53 Similarly Putting x = 2, in (1) 5(2) = 𝐴 2−2 2+2+𝐵 2+1 2+2+𝐶 2+1 2−2 10 = 𝐴×0+𝐵 3 4+𝐶×0 10 = 12𝐵 𝐵 = 1012= 56 Similarly Putting x = −2 , in (1) 5(−2) = 𝐴 −2−2 −2+2+𝐵 −2+1 −2+2+𝐶 −2+1 −2−2 −10 = 𝐴×0+𝐵×0+𝐶 −1 −4 −10 = 4𝐶 𝐶 = −104 𝐶 = −52 Therefore 5𝑥 𝑥 + 1 𝑥2− 4= 𝐴𝑥 + 1+ 𝐵𝑥 − 2+ 𝐶𝑥 + 2𝑑𝑥 = 53 𝑑𝑥𝑥 + 1 𝑑𝑥+ 56 𝑑𝑥𝑥 − 2 𝑑𝑥− 52 𝑑𝑥 𝑥 + 2 = 𝟓𝟑 𝒍𝒐𝒈 𝒙+𝟏− 𝟓𝟐 𝐥𝐨𝐠 𝒙+𝟐+ 𝟓𝟔 𝐥𝐨𝐠 𝒙−𝟐+𝑪

Ex 7.5, 1

Ex 7.5, 2

Ex 7.5, 3

Ex 7.5, 4

Ex 7.5, 5

Ex 7.5, 6

Ex 7.5, 7

Ex 7.5, 8

Ex 7.5, 9 Important

Ex 7.5, 10

Ex 7.5, 11 Important You are here

Ex 7.5, 12

Ex 7.5, 13

Ex 7.5, 14

Ex 7.5, 15

Ex 7.5, 16

Ex 7.5, 17 Important

Ex 7.5, 18 Important

Ex 7.5, 19

Ex 7.5, 20

Ex 7.5, 21 Important

Ex 7.5, 22

Ex 7.5, 23

About the Author

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.