# Ex 7.6, 20 - Chapter 7 Class 12 Integrals

Last updated at April 16, 2024 by Teachoo

Ex 7.6

Ex 7.6, 1

Ex 7.6, 2 Important

Ex 7.6, 3

Ex 7.6, 4

Ex 7.6, 5 Important

Ex 7.6, 6

Ex 7.6, 7 Important

Ex 7.6, 8

Ex 7.6, 9

Ex 7.6, 10 Important

Ex 7.6, 11

Ex 7.6, 12

Ex 7.6, 13 Important

Ex 7.6, 14 Important

Ex 7.6, 15

Ex 7.6, 16

Ex 7.6, 17

Ex 7.6, 18 Important

Ex 7.6, 19

Ex 7.6, 20 Important You are here

Ex 7.6, 21

Ex 7.6, 22 Important

Ex 7.6, 23 (MCQ)

Ex 7.6, 24 (MCQ) Important

Last updated at April 16, 2024 by Teachoo

Ex 7.6, 20 Integrate the function (𝑥 − 3)𝑒𝑥/(𝑥 − 1)3 ∫1▒〖((𝑥 − 3))/(𝑥 −1)3 .𝑒𝑥" " 𝑑𝑥〗 = ∫1▒〖(𝑥 − 1 − 2)/(𝑥 −1)^3 .𝑒𝑥" " 𝑑𝑥〗 = ∫1▒〖𝑒𝑥 ((𝑥 − 1)/(𝑥 −1)^3 − 2/(𝑥 −1)^3 )𝑑𝑥〗 = ∫1▒〖𝑒𝑥 (1/(𝑥 −1)^2 − 2/(𝑥 −1)^3 )𝑑𝑥〗 It is of the form ∫1▒〖𝑒^𝑥 [𝑓(𝑥)+𝑓^′ (𝑥)] 〗 𝑑𝑥=𝑒^𝑥 𝑓(𝑥)+𝐶 Where 𝑓(𝑥)=" " 1/(𝑥 −1)^2 ∴ 𝑓^′ (𝑥)= (− 2)/(𝑥 − 1)^3 So, our equation becomes ∫1▒〖𝑒𝑥 (1/(𝑥 − 1)^2 − 2/(𝑥 − 1)^3 )𝑑𝑥〗 = 𝒆𝒙/(𝒙 − 𝟏)𝟐 +𝑪