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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: ∫1β–’(𝑒^π‘₯ (π‘₯ βˆ’ 3))/(π‘₯ βˆ’ 1)^3 dx ∫1β–’(𝑒^π‘₯ (π‘₯ βˆ’ 3))/(π‘₯ βˆ’ 1)^3 dx = ∫1β–’(𝑒^π‘₯ (π‘₯ βˆ’ 1 βˆ’ 2))/(π‘₯ βˆ’ 1)^3 dx = ∫1β–’(𝑒^π‘₯ [(π‘₯ βˆ’ 1)βˆ’ 2])/(π‘₯ βˆ’ 1)^3 dx = ∫1▒〖𝑒^π‘₯ [((π‘₯ βˆ’ 1) βˆ’ 2)/(π‘₯ βˆ’ 1)^3 ] γ€— dx = ∫1▒〖𝑒^π‘₯ [((π‘₯ βˆ’ 1))/(π‘₯ βˆ’ 1)^3 +((βˆ’2)/(π‘₯ βˆ’ 1)^3 )] γ€— dx = ∫1▒〖𝑒^π‘₯ [1/(π‘₯ βˆ’ 1)^2 +((βˆ’2)/(π‘₯ βˆ’ 1)^3 )] γ€— dx It is of form ∫1▒〖𝑒^π‘₯ (𝑓(π‘₯)+𝑓^β€² (π‘₯)) γ€— 𝑑π‘₯=𝑒^π‘₯ 𝑓(π‘₯)+𝐢 Putting, 𝑓(π‘₯)=1/(π‘₯ βˆ’ 1)^2 " " ∴ 𝑓^β€² (π‘₯)= (βˆ’2)/(π‘₯ βˆ’ 1)^3 ∫1▒〖𝑒^π‘₯ [1/(π‘₯ βˆ’ 1)^2 +((βˆ’2)/(π‘₯ βˆ’ 1)^3 )] γ€— dx =𝒆^𝒙/(𝒙 βˆ’ 𝟏)^𝟐 +π‘ͺ

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.