Question 8 (Or 1st) - CBSE Class 12 Sample Paper for 2019 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at March 23, 2023 by Teachoo

Question 8 (OR 1 st question)

Find: ∫ e ^x (x - 3) / (x - 1) ³ dx

Find integral e^x (x - 3) / (x - 1)^3 dx - Teachoo - CBSE Class 12 Sam

Question 8 (Or 1st) - CBSE Class 12 Sample Paper for 2019 Boards - Part 2

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Question 8 (OR 1st question) Find: ∫1▒(𝑒^𝑥 (𝑥 − 3))/(𝑥 − 1)^3 dx ∫1▒(𝑒^𝑥 (𝑥 − 3))/(𝑥 − 1)^3 dx = ∫1▒(𝑒^𝑥 (𝑥 − 1 − 2))/(𝑥 − 1)^3 dx = ∫1▒(𝑒^𝑥 [(𝑥 − 1)− 2])/(𝑥 − 1)^3 dx = ∫1▒〖𝑒^𝑥 [((𝑥 − 1) − 2)/(𝑥 − 1)^3 ] 〗 dx = ∫1▒〖𝑒^𝑥 [((𝑥 − 1))/(𝑥 − 1)^3 +((−2)/(𝑥 − 1)^3 )] 〗 dx = ∫1▒〖𝑒^𝑥 [1/(𝑥 − 1)^2 +((−2)/(𝑥 − 1)^3 )] 〗 dx It is of form ∫1▒〖𝑒^𝑥 (𝑓(𝑥)+𝑓^′ (𝑥)) 〗 𝑑𝑥=𝑒^𝑥 𝑓(𝑥)+𝐶 Putting, 𝑓(𝑥)=1/(𝑥 − 1)^2 " " ∴ 𝑓^′ (𝑥)= (−2)/(𝑥 − 1)^3 ∫1▒〖𝑒^𝑥 [1/(𝑥 − 1)^2 +((−2)/(𝑥 − 1)^3 )] 〗 dx =𝒆^𝒙/(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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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