# Ex 7.5, 1 - Chapter 7 Class 12 Integrals (Term 2)

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 7.5, 1 ๐ฅ/((๐ฅ + 1) (๐ฅ + 2) ) Solving integrand ๐ฅ/((๐ฅ + 1) (๐ฅ + 2) ) We can write it as ๐ฅ/((๐ฅ + 1) (๐ฅ + 2) ) " " = ๐ด/((๐ฅ + 1) ) + ๐ต/((๐ฅ + 2) ) ๐ฅ/((๐ฅ + 1) (๐ฅ + 2) ) " " = (๐ด(๐ฅ + 2) + ๐ต (๐ฅ + 1))/((๐ฅ + 1) (๐ฅ + 2) ) Cancelling denominator ๐ฅ = ๐ด(๐ฅ+2) + ๐ต(๐ฅ+1) Putting x=โ1 in (1) โ1=๐ด(โ1+2) + ๐ต(โ1+1) โ1=๐ดร1+ ๐ตร0 โ1=๐ด ๐ด=โ1 Similarly Putting y=โ2 in (1) โ2 = ๐ด(โ2+2) + ๐ต(โ2+1) โ2 = ๐ดร0+ ๐ตร(โ1) โ2 = โ ๐ต ๐ต = 2 Hence we can write it as ๐ฅ/((๐ฅ + 1) (๐ฅ + 2) ) = (โ1)/((๐ฅ + 1) ) + 2/((๐ฅ + 2) ) Therefore โซ1โ๐ฅ/((๐ฅ + 1) (๐ฅ + 2) ) ๐๐ฅ = โซ1โ(โ1)/((๐ฅ + 1) ) ๐๐ฅ + โซ1โ2/((๐ฅ + 2) ) ๐๐ฅ = โ1โซ1โ1/((๐ฅ + 1) ) ๐๐ฅ + 2โซ1โ1/((๐ฅ + 2) ) ๐๐ฅ = โใlog ใโก|๐ฅ+1|+2 ใlog ใโก|๐ฅ+2|+๐ถ = โใlog ใโก|๐ฅ+1|+ใlog ใโกใ|๐ฅ+2|^2 ใ+๐ถ = ใlog ใโก|(๐ฅ + 2)^2/(๐ฅ + 1)|+๐ถ = ใ๐ฅ๐จ๐ ใโกใ(๐ + ๐)^๐/|๐ + ๐| ใ +๐ช

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.