Misc 13 - Chapter 7 Class 12 Integrals

Last updated at April 16, 2024 by

Misc 13 - Integrate ex / (1 + ex) (2 + ex) - Miscellaneous

Misc 13 - Chapter 7 Class 12 Integrals - Part 2
Misc 13 - Chapter 7 Class 12 Integrals - Part 3

Transcript

Misc 13 Integrate the function ^ /((1 + ^ )(2+ ^ ) ) 1 ^ /((1 + ^ )(2+ ^ ) ) Let t = ^ / = ^ dt = ^ Substituting 1 ^ /((1 + ^ )(2+ ^ ) ) = 1 /((1 + ) (2 + )) We can write, 1/((1 + )(2 + ))=A/(1 + )+B/(2 + ) 1/(( + 1) ( + 2))=(A(t + 2) + B(t + 1))/(( + 1) ( + 2)) Cancelling denominators 1 = (t + 2)A + (t + 1)B Putting in (1) 1 1/((1 + )(2 + )) = 1 1/( + 1) 1/( + 2) = log |1+ | |2+ |+ C = log |(1 + )/(2 + )|+ C Putting t = ^ = log (( + ^ )/( + ^ ))+ C

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.