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Ex 7.4, 5 - Integrate 3x / 1 + 2x4 - Chapter 7 Class 12 - Integration by specific formulaes - Formula 3

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.4, 5 3๐‘ฅ/(1 + 2๐‘ฅ4) Let ๐‘ฅ^2=๐‘ก Differentiating both sides 2๐‘ฅ=๐‘‘๐‘ก/๐‘‘๐‘ฅ ๐‘‘๐‘ฅ=๐‘‘๐‘ก/2๐‘ฅ Integrating the function ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ โˆซ1โ–’(3๐‘ฅ )/(1 + 2๐‘ฅ^4 ) ๐‘‘๐‘ฅ =โˆซ1โ–’3๐‘ฅ/(1 + 2(๐‘ฅ^2 )^2 ) ๐‘‘๐‘ฅ Putting value of ๐‘ฅ^2=๐‘ก and ๐‘‘๐‘ฅ=๐‘‘๐‘ก/2๐‘ฅ =โˆซ1โ–’3๐‘ฅ/(1 + 2๐‘ก^2 ) ๐‘‘๐‘ฅ =โˆซ1โ–’3๐‘ฅ/(1 + 2๐‘ก^2 )ร—๐‘‘๐‘ก/2๐‘ฅ =3/2 โˆซ1โ–’๐‘‘๐‘ก/(1 + 2๐‘ก^2 ) =3/2 โˆซ1โ–’๐‘‘๐‘ก/2(1/2 + ๐‘ก^2 ) =3/(2 . 2) โˆซ1โ–’๐‘‘๐‘ก/(1/2 + ๐‘ก^2 ) =3/4 โˆซ1โ–’๐‘‘๐‘ก/(๐‘ก^2 + 1/2). ๐‘‘๐‘ก =3/4 โˆซ1โ–’๐‘‘๐‘ก/(๐‘ก^2 +(1/โˆš2)^2 ). ๐‘‘๐‘ก

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