Ex 7.4, 16 - Integrate 4x + 1 / root 2x2 + x - 3 - Ex 7.4

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.4, 16 (4๐‘ฅ + 1)/โˆš(2๐‘ฅ^2 + ๐‘ฅ โˆ’ 3) Let 2๐‘ฅ^2+๐‘ฅโˆ’3=๐‘ก Diff both sides w.r.t. x 4๐‘ฅ+1+0=๐‘‘๐‘ก/๐‘‘๐‘ฅ ๐‘‘๐‘ฅ=๐‘‘๐‘ก/(4๐‘ฅ + 1) Now, โˆซ1โ–’(4๐‘ฅ + 1)/โˆš(2๐‘ฅ^2 + ๐‘ฅ โˆ’ 3) ๐‘‘๐‘ฅ Put the values of (2๐‘ฅ^2+๐‘ฅโˆ’3)=๐‘ก and ๐‘‘๐‘ฅ=๐‘‘๐‘ก/(4๐‘ฅ + 1) =โˆซ1โ–’(4๐‘ฅ + 1)/โˆš๐‘ก ร— ๐‘‘๐‘ก/(4๐‘ฅ + 1) =โˆซ1โ–’1/โˆš๐‘ก ๐‘‘๐‘ก =โˆซ1โ–’๐‘ก^((โˆ’1)/2) ๐‘‘๐‘ก =๐‘ก^((โˆ’1)/2 + 1)/((โˆ’1)/2 + 1) +๐ถ =๐‘ก^(1/2)/(1/2) +๐ถ =2๐‘ก^(1/2) + ๐ถ =2โˆš๐‘ก+ ๐ถ =๐Ÿโˆš(๐Ÿ๐’™^๐Ÿ+๐’™โˆ’๐Ÿ‘)+ ๐‘ช

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