Ex 7.4, 13 - Integrate 1 / root (x - 1) (x - 2) - Integration by specific formulaes - Formula 4

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.4, 13 1/โˆš((๐‘ฅ โˆ’ 1)(๐‘ฅ โˆ’ 2)) Integrating the function ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ โˆซ1โ–’1/โˆš((๐‘ฅ โˆ’ 1)(๐‘ฅ โˆ’ 2)) ๐‘‘๐‘ฅ =โˆซ1โ–’1/โˆš(๐‘ฅ(๐‘ฅ โˆ’ 2) โˆ’ 1 (๐‘ฅ โˆ’ 2) ) ๐‘‘๐‘ฅ =โˆซ1โ–’1/โˆš(๐‘ฅ^2 โˆ’ 2๐‘ฅ โˆ’ ๐‘ฅ + 2) ๐‘‘๐‘ฅ =โˆซ1โ–’1/โˆš(๐‘ฅ^2 โˆ’ 3๐‘ฅ + 2) ๐‘‘๐‘ฅ =โˆซ1โ–’1/โˆš(๐‘ฅ^2 โˆ’ 2(3/2)(๐‘ฅ) + 2) ๐‘‘๐‘ฅ =โˆซ1โ–’1/โˆš(๐‘ฅ^2 โˆ’ 2(3/2)(๐‘ฅ) + (3/2)^2โˆ’ (3/2)^2+ 2) ๐‘‘๐‘ฅ =โˆซ1โ–’1/โˆš((๐‘ฅ โˆ’ 3/2)^2 โˆ’ (3/2)^2 + 2) ๐‘‘๐‘ฅ =โˆซ1โ–’1/โˆš((๐‘ฅ โˆ’ 3/2)^2 โˆ’ 9/4 + 2) ๐‘‘๐‘ฅ =โˆซ1โ–’1/โˆš((๐‘ฅ โˆ’ 3/2)^2 โˆ’ 1/4 ) ๐‘‘๐‘ฅ =โˆซ1โ–’1/โˆš((๐‘ฅ โˆ’ 3/2)^2 โˆ’ (1/2)^2 ) ๐‘‘๐‘ฅ =๐‘™๐‘œ๐‘”โก|๐‘ฅโˆ’ 3/2+โˆš((๐‘ฅโˆ’ 3/2)^2 โˆ’ (1/2)^2 )|+๐ถ =๐‘™๐‘œ๐‘”โก|๐‘ฅโˆ’ 3/2+โˆš(๐‘ฅ^2+(3/2)^2โˆ’2(๐‘ฅ)(3/2)โˆ’ 1/4)|+๐ถ =๐‘™๐‘œ๐‘”โก|๐‘ฅโˆ’ 3/2+โˆš(๐‘ฅ^2+9/4โˆ’3๐‘ฅโˆ’ 1/4)|+๐ถ =๐‘™๐‘œ๐‘”โก|๐‘ฅโˆ’ 3/2+โˆš(๐‘ฅ^2โˆ’3๐‘ฅ+9/4โˆ’ 1/4)|+๐ถ =๐‘™๐‘œ๐‘”โก|๐‘ฅโˆ’ 3/2+โˆš(๐‘ฅ^2โˆ’3๐‘ฅ+8/4)|+๐ถ =๐’๐’๐’ˆโก|๐’™โˆ’ ๐Ÿ‘/๐Ÿ+โˆš(๐’™^๐Ÿโˆ’๐Ÿ‘๐’™+๐Ÿ)|+๐‘ช

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