Ex 7.4, 3 - Chapter 7 Class 12 Integrals
Last updated at April 16, 2024 by Teachoo
Integration by specific formulaes - Formula 6
Integration by specific formulaes - Formula 6
Last updated at April 16, 2024 by Teachoo
Ex 7.4, 3 1/โ((2 โ ๐ฅ)^2 + 1) Let 2โ๐ฅ=๐ก Diff both sides w.r.t. x 0โ1=๐๐ก/๐๐ฅ ๐๐ฅ=โ๐๐ก Integrating the function ๐ค.๐.๐ก.๐ฅ โซ1โ1/โ((2 โ ๐ฅ)^2 + 1) ๐๐ฅ Put the Values of 2โ๐ฅ=๐ก and ๐๐ฅ=โ๐๐ก =โซ1โ(โ๐๐ก)/โ(๐ก^2 + 1) =โโซ1โ๐๐ก/โ(๐ก^2 +(1)^2 ) =โlogโก|๐ก+โ(๐ก^2+1) |+๐ถ =logโกใ|๐ก+โ(๐ก^2+1) |^(โ1) ใ+๐ถ =logโกใ1/|๐ก + โ(๐ก^2 + 1) | ใ +๐ถ =logโกใ1/|2 โ ๐ฅ + โ((2 โ ๐ฅ)^2 + 1) | ใ +๐ถ =logโกใ1/|2 โ ๐ฅ + โ(ใ4 + ๐ฅใ^2 โ 4๐ฅ + 1) | ใ +๐ถ =๐๐๐โกใ๐/|๐ โ ๐ + โ(๐^๐ โ ๐๐ + ๐) | ใ +๐ช