Ex 7.2, 9 - Integrate (4x + 2) root(x2 + x + 1) - Ex 7.2

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.2, 9 Integrate the function: (4𝑥 + 2) ﷮𝑥2+𝑥+1﷯ Step 1: Let 𝑥﷮2﷯+𝑥+1 = 𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 2𝑥+1+0= 𝑑𝑡﷮𝑑𝑥﷯ 2𝑥+1= 𝑑𝑡﷮𝑑𝑥﷯ 𝑑𝑥= 𝑑𝑡﷮2𝑥+1﷯ Step 2: Integrating the function ﷮﷮ (4𝑥 + 2) ﷮𝑥2+𝑥+1﷯﷯ . 𝑑𝑥 = ﷮﷮2(2𝑥 +1) ﷮𝑥2+𝑥+1﷯﷯ . 𝑑𝑥 Putting 𝑥2+𝑥+1=𝑡 & 𝑑𝑥= 𝑑𝑡﷮2𝑥+1﷯ = ﷮﷮2(2𝑥 +1) ﷮𝑡﷯﷯ . 𝑑𝑡﷮2𝑥+1﷯ = ﷮﷮2 ﷮𝑡﷯﷯ . 𝑑𝑡 = 2 ﷮﷮ ﷮𝑡﷯﷯ . 𝑑𝑡 = 2 ﷮﷮ 𝑡﷮ 1﷮2﷯﷯﷯ . 𝑑𝑡 = 2 . 𝑡﷮ 1﷮2﷯ + 1﷯﷮ 1﷮2﷯ + 1﷯ + 𝐶 = 2 . 𝑡﷮ 3﷮2﷯﷯﷮ 3﷮2﷯﷯ + 𝐶 = 2 . 2﷮3﷯. 𝑡﷮ 3﷮2﷯﷯ + 𝐶 = 4﷮3﷯. 𝑡﷮ 3﷮2﷯﷯ + 𝐶 = 𝟒﷮𝟑﷯. 𝒙﷮𝟐﷯+𝒙+𝟏﷯﷮ 𝟑﷮𝟐﷯﷯ + 𝑪

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.