Ex 7.4, 3 - Integrate 1 / root (2 - x)2 + 1 - Class 12 - Integration by specific formulaes - Formula 6

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.4, 3 1/โˆš((2 โˆ’ ๐‘ฅ)^2 + 1) Let 2โˆ’๐‘ฅ=๐‘ก Diff both sides w.r.t. x 0โˆ’1=๐‘‘๐‘ก/๐‘‘๐‘ฅ ๐‘‘๐‘ฅ=โˆ’๐‘‘๐‘ก Integrating the function ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ โˆซ1โ–’1/โˆš((2 โˆ’ ๐‘ฅ)^2 + 1) ๐‘‘๐‘ฅ Put the Values of 2โˆ’๐‘ฅ=๐‘ก and ๐‘‘๐‘ฅ=โˆ’๐‘‘๐‘ก =โˆซ1โ–’(โˆ’๐‘‘๐‘ก)/โˆš(๐‘ก^2 + 1) =โˆ’โˆซ1โ–’๐‘‘๐‘ก/โˆš(๐‘ก^2 +(1)^2 ) =โˆ’logโก|๐‘ก+โˆš(๐‘ก^2+1) |+๐ถ =logโกใ€–|๐‘ก+โˆš(๐‘ก^2+1) |^(โˆ’1) ใ€—+๐ถ =logโกใ€–1/|๐‘ก + โˆš(๐‘ก^2 + 1) | ใ€— +๐ถ =logโกใ€–1/|2 โˆ’ ๐‘ฅ + โˆš((2 โˆ’ ๐‘ฅ)^2 + 1) | ใ€— +๐ถ =logโกใ€–1/|2 โˆ’ ๐‘ฅ + โˆš(ใ€–4 + ๐‘ฅใ€—^2 โˆ’ 4๐‘ฅ + 1) | ใ€— +๐ถ =๐’๐’๐’ˆโกใ€–๐Ÿ/|๐Ÿ โˆ’ ๐’™ + โˆš(๐’™^๐Ÿ โˆ’ ๐Ÿ’๐’™ + ๐Ÿ“) | ใ€— +๐‘ช

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