Ex 7.2, 17 - Integrate x / ex2 - Chapter 7 Class 12 - Integration by substitution - e^x

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  1. Chapter 7 Class 12 Integrals
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Ex 7.2, 17 Integrate the function: ๐‘ฅ/๐‘’^(๐‘ฅ^2 ) Step 1: Let ๐‘ฅ2 = ๐‘ก Differentiating both sides ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ 2๐‘ฅ^(2 โˆ’ 1)= ๐‘‘๐‘ก/๐‘‘๐‘ฅ 2๐‘ฅ=๐‘‘๐‘ก/๐‘‘๐‘ฅ " " ๐‘‘๐‘ฅ = ๐‘‘๐‘ก/2๐‘ฅ Step 2: Integrating the function โˆซ1โ–’ใ€–" " ๐‘ฅ/๐‘’^(๐‘ฅ^2 ) " " ใ€—. ๐‘‘๐‘ฅ putting ๐‘ฅ^2=๐‘ก & ๐‘‘๐‘ฅ=๐‘‘๐‘ก/2๐‘ฅ = โˆซ1โ–’๐‘ฅ/๐‘’^๐‘ก . ๐‘‘๐‘ก/2๐‘ฅ = 1/2 โˆซ1โ–’๐‘‘๐‘ก/๐‘’^๐‘ก = 1/2 โˆซ1โ–’๐‘’^(โˆ’๐‘ก) . ๐‘‘๐‘ก = 1/2 ๐‘’^(โˆ’๐‘ก)/((โˆ’1) ) +๐ถ = โˆ’1/(2๐‘’^๐‘ก ) +๐ถ = โˆ’๐Ÿ/(๐Ÿ๐’†^(๐’™^๐Ÿ ) ) +๐‘ช

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