# Ex 7.9, 7 - Chapter 7 Class 12 Integrals

Last updated at April 16, 2024 by Teachoo

Last updated at April 16, 2024 by Teachoo

Ex 7.9, 7 Evaluate the integrals using substitution โซ_(โ1)^(1 )โใ ๐๐ฅ/(๐ฅ^2 + 2๐ฅ + 5)ใ we can write โซ_(โ1)^1โใ๐๐ฅ/(๐ฅ^2 + 2๐ฅ + 5)=โซ_(โ1)^1โ๐๐ฅ/((๐ฅ + 2๐ฅ + 1) + 4)ใ =โซ_(โ1)^1โ๐๐ฅ/((๐ฅ + 1)^2 +ใ 2ใ^2 ) Putting ๐ฅ+1=๐ก Differentiating w.r.t.๐ฅ ๐/๐๐ฅ (๐ฅ+1)=๐๐ก/๐๐ฅ 1=๐๐ก/๐๐ฅ ๐๐ฅ=๐๐ก Hence when ๐ฅ varies from โ 1 to 1 then ๐ก varies from 0 to 2 Therefore, โซ_(โ1)^1โใ๐๐ฅ/((๐ฅ+1)^2 + 2^2 )=โซ_0^2โ๐๐ก/(๐ก^2 + 2^2 )ใ =[1/2 tan^(โ1)โกใ๐ก/2ใ ]_0^2 =1/2 tan^(โ1)โกใ2/2โ1/2 tan^(โ1)โกใ0/2ใ ใ =1/2 tan^(โ1)โกใ1โ1/2 tan^(โ1)โก0 ใ =1/2 ร ๐/4โ0 =๐ /๐