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

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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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.