Ex 7.5

Chapter 7 Class 12 Integrals
Serial order wise

### Transcript

Ex 7.5, 1 ๐ฅ/((๐ฅ + 1) (๐ฅ + 2) ) Solving integrand ๐ฅ/((๐ฅ + 1) (๐ฅ + 2) ) We can write it as ๐/((๐ + ๐) (๐ + ๐) ) " " = ๐จ/((๐ + ๐) ) + ๐ฉ/((๐ + ๐) ) ๐ฅ/((๐ฅ + 1) (๐ฅ + 2) ) " " = (๐ด(๐ฅ + 2) + ๐ต (๐ฅ + 1))/((๐ฅ + 1) (๐ฅ + 2) ) Cancelling denominator ๐ = ๐จ(๐+๐) + ๐ฉ(๐+๐) Putting ๐=โ๐ in (1) โ1=๐ด(โ1+2) + ๐ต(โ1+1) โ1=๐ด ร 1+ ๐ต ร 0 โ1=๐ด ๐จ=โ๐ Putting ๐=โ๐ in (1) โ2 = ๐ด(โ2+2) + ๐ต(โ2+1) โ2 = ๐ด ร 0+ ๐ต ร (โ1) โ2 = โ ๐ต ๐ฉ = ๐ Hence we can write it as ๐/((๐ + ๐) (๐ + ๐) ) = (โ๐)/((๐ + ๐) ) + ๐/((๐ + ๐) ) Therefore โซ1โ๐/((๐ + ๐) (๐ + ๐) ) ๐๐ = โซ1โ(โ1)/((๐ฅ + 1) ) ๐๐ฅ + โซ1โ2/((๐ฅ + 2) ) ๐๐ฅ = โ1โซ1โ1/((๐ฅ + 1) ) ๐๐ฅ + 2โซ1โ1/((๐ฅ + 2) ) ๐๐ฅ = โใ๐ฅ๐จ๐  ใโก|๐+๐|+๐ ใ๐ฅ๐จ๐  ใโก|๐+๐|+๐ช = โใlog ใโก|๐ฅ+1|+ใlog ใโกใ|๐ฅ+2|^2 ใ+๐ถ = ใlog ใโก|(๐ฅ + 2)^2/(๐ฅ + 1)|+๐ถ = ใ๐ฅ๐จ๐  ใโกใ(๐ + ๐)^๐/|๐ + ๐| ใ +๐ช As ๐๐๐ ๐จโ๐๐๐ ๐ฉ=๐๐๐ ๐ด/๐ต As (๐ฅ+2)^2is always positive

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#### Davneet Singh

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.