Check sibling questions

CBSE Class 12 Sample Paper for 2019 Boards

CBSE Class 12 Sample Paper for 2018 Boards →
Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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 May 29, 2023 by

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

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Book a free demo

Transcript

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

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

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.