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

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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